Geschriebene Artikel über Big Data Analytics

5 Data Privacy Predictions for 2021

September 22, 2020/in Data Security/by Shannon Flynn

2020 has been a significant year for data management. As businesses face new technological challenges amid the COVID-19 pandemic, issues of privacy have spent some time in the spotlight. In response, data privacy could see some substantial changes in 2021.

Few people will emerge from 2020 with an unchanged perception of data security. As these ideas and feelings shift, some trends will accelerate while others get replaced. Businesses will have to adapt to these changes to survive.

Here are five such changes you can expect in 2021.

International Data Privacy Standards Will Increase

Privacy concerns over Chinese-owned app TikTok caused quite a stir in 2020. With the TikTok situation bringing new attention to privacy in international services, you’ll likely see a rise in international regulations. China has already announced new security standards and asked other countries to follow.

2020 has cast doubt over a lot of international relations. More countries will likely issue new standards to ease tension and move past these doubts. This trend started before 2020, as you can see in Europe’s GDPR, but 2021 will further it.

Customers Will Demand Transparency

Governments aren’t the only ones that will expect more of tech companies’ privacy standards. Since things like TikTok have made people more aware of what apps could access, more people will demand privacy. In 2021, companies that are transparent about how they use data will likely be more successful.

According to a PwC poll, 84% of consumers said they would switch services if they don’t trust how a company uses their data. Data privacy isn’t just important to authorities or businesses anymore. The public is growing more concerned about their data, and their choices will reflect it.

Security Will Become More Automated

In response to these growing expectations, businesses will have to do more to secure people’s data. Cybersecurity companies are facing a considerable talent shortage thanks to pandemic-related complications, though. The data security world will turn to automation to fix both of these problems.

With so many businesses changing the way they operate, cybersecurity will have to become more flexible too. Automating some processes through AI will allow companies to achieve that flexibility. Security AI is still relatively new, but as it develops, it could take off in 2021.

Security Data Analytics Will Become the Norm

Big data analytics have already become standard practice in many business applications. In 2021, more companies will start using them to improve their data privacy measures, too. With major companies like Nintendo and Marriott experiencing significant data breaches this year, more will turn to analytics to find any potential shortcomings.

No one wants to be the next data breach news story, especially with more people paying attention to these issues now. Data analytics can highlight operational improvements, showing companies how to better their data security measures. With data privacy in the spotlight in 2021, taking these steps is crucial.

Third-Party Risk Assessments Will Be More Crucial

As people demand better privacy protection, businesses will have to consider their third-party partners. Consumers will be more critical of companies giving third parties access to their data. As a result, companies will have to perform more risk assessments on any third party.

Third-party data breaches affected companies like General Electric and T-Mobile in 2020, exposing thousands of records. Customers will expect businesses to hold their partners to higher standards to avoid these risks.

2021 Could Be a Landmark Year for Data Privacy

Data privacy is more prominent than ever before, mostly due to a few notable scandals. Now that the general public is more aware of these issues, businesses will have to meet higher standards for data privacy. Implementing data security processes may cause some disruption and confusion at first, but it will ultimately lead to a safer digital landscape.

All of these changes could make 2021 a turning point for data security. With higher expectations from consumers and authorities, data management will become more secure.

Data Science in Engineering Process - Product Lifecycle Management

How to develop digital products and solutions for industrial environments?

September 18, 2020/in Data Science, Insights, Main Category, Use Case, Use Cases/by Siemens Advanta Consulting

The Data Science and Engineering Process in PLM.

Huge opportunities for digital products are accompanied by huge risks

Digitalization is about to profoundly change the way we live and work. The increasing availability of data combined with growing storage capacities and computing power make it possible to create data-based products, services, and customer specific solutions to create insight with value for the business. Successful implementation requires systematic procedures for managing and analyzing data, but today such procedures are not covered in the PLM processes.

From our experience in industrial settings, organizations start processing the data that happens to be available. This data often does not fully cover the situation of interest, typically has poor quality, and in turn the results of data analysis are misleading. In industrial environments, the reliability and accuracy of results are crucial. Therefore, an enormous responsibility comes with the development of digital products and solutions. Unless there are systematic procedures in place to guide data management and data analysis in the development lifecycle, many promising digital products will not meet expectations.

Various methodologies exist but no comprehensive framework

Over the last decades, various methodologies focusing on specific aspects of how to deal with data were promoted across industries and academia. Examples are Six Sigma, CRISP-DM, JDM standard, DMM model, and KDD process. These methodologies aim at introducing principles for systematic data management and data analysis. Each methodology makes an important contribution to the overall picture of how to deal with data, but none provides a comprehensive framework covering all the necessary tasks and activities for the development of digital products. We should take these approaches as valuable input and integrate their strengths into a comprehensive Data Science and Engineering framework.

In fact, we believe it is time to establish an independent discipline to address the specific challenges of developing digital products, services and customer specific solutions. We need the same kind of professionalism in dealing with data that has been achieved in the established branches of engineering.

Data Science and Engineering as new discipline

Whereas the implementation of software algorithms is adequately guided by software engineering practices, there is currently no established engineering discipline covering the important tasks that focus on the data and how to develop causal models that capture the real world. We believe the development of industrial grade digital products and services requires an additional process area comprising best practices for data management and data analysis. This process area addresses the specific roles, skills, tasks, methods, tools, and management that are needed to succeed.

*Figure: Data Science and Engineering as new engineering discipline*

More than in other engineering disciplines, the outputs of Data Science and Engineering are created in repetitions of tasks in iterative cycles. The tasks are therefore organized into workflows with distinct objectives that clearly overlap along the phases of the PLM process.

	Feasibility of Objectives
	Understand the business situation, confirm the feasibility of the product idea, clarify the data infrastructure needs, and create transparency on opportunities and risks related to the product idea from the data perspective.
	Domain Understanding
	Establish an understanding of the causal context of the application domain, identify the influencing factors with impact on the outcomes in the operational scenarios where the digital product or service is going to be used.
	Data Management
	Develop the data management strategy, define policies on data lifecycle management, design the specific solution architecture, and validate the technical solution after implementation.
	Data Collection
	Define, implement and execute operational procedures for selecting, pre-processing, and transforming data as basis for further analysis. Ensure data quality by performing measurement system analysis and data integrity checks.
	Modeling
	Select suitable modeling techniques and create a calibrated prediction model, which includes fitting the parameters or training the model and verifying the accuracy and precision of the prediction model.
	Insight Provision
	Incorporate the prediction model into a digital product or solution, provide suitable visualizations to address the information needs, evaluate the accuracy of the prediction results, and establish feedback loops.

Real business value will be generated only if the prediction model at the core of the digital product reliably and accurately reflects the real world, and the results allow to derive not only correct but also helpful conclusions. Now is the time to embrace the unique chances by establishing professionalism in data science and engineering.

Authors

Peter Louis

Peter Louis is working at Siemens Advanta Consulting as Senior Key Expert. He has 25 years’ experience in Project Management, Quality Management, Software Engineering, Statistical Process Control, and various process frameworks (Lean, Agile, CMMI). He is an expert on SPC, KPI systems, data analytics, prediction modelling, and Six Sigma Black Belt.

Ralf Russ

Ralf Russ works as a Principal Key Expert at Siemens Advanta Consulting. He has more than two decades experience rolling out frameworks for development of industrial-grade high quality products, services, and solutions. He is Six Sigma Master Black Belt and passionate about process transparency, optimization, anomaly detection, and prediction modelling using statistics and data analytics.4

LSTM back propagation: following the flows of variables

September 7, 2020/in Artificial Intelligence, Data Science, Deep Learning, Main Category/by Yasuto Tamura

First of all, the summary of this article is: please just download my Power Point slides which I made and be patient, following the equations.

I am not supposed to use so many mathematics when I write articles on Data Science Blog. However using little mathematics when I talk about LSTM backprop is like writing German, never caring about “der,” “die,” “das,” or speaking little English in English classes (which most high school English teachers in Japan do) or writing Japanese without using any Chinese characters (which looks like a terrible handwriting by a drug addict). In short, that is ridiculous. And all the precise equations of LSTM backprop, written on a Blog is not a comfortable thing to see. So basically the whole of this article is an advertisement on my PowerPoint slides, sponsored by DATANOMIQ, and I can just give you some tips to get ready for the most tiresome part of understanding LSTM here.

*This article is the fifth article of “A gentle introduction to the tiresome part of understanding RNN.”

*In this article “Densely Connected Layers” is written as “DCL,” and “Convolutional Neural Network” as “CNN.”

1. Chain rules

This article is virtually an article on chain rules of differentiation. Even if you have clear understandings on chain rules, I recommend you to take a look at this section. If you have written down all the equations of back propagation of DCL, you would have seen what chain rules are. Even simple chain rules for backprop of normal DCL can be difficult to some people, but when it comes to backprop of LSTM, it is a pure torture. I think using graphical models would help you understand what chain rules are like. Graphical models are basically used to describe the relations of variables and functions in probabilistic models, so to be exact I am going to use “something like graphical models” in this article. Not that this is a common way to explain chain rules.

First, let’s think about the simplest type of chain rule. Assume that you have a function $f=f(x)=f(x(y))$ , and relations of the functions are displayed as the graphical model at the left side of the figure below. Variables are a type of function, so you should think that every node in graphical models denotes a function. Arrows in purple in the right side of the chart show how information propagate in differentiation.

Next, if you a function $f$ , which has two variances $x_1$ and $x_2$ . And both of the variances also share two variances $y_1$ and $y_2$ . When you take partial differentiation of $f$ with respect to $y_1$ or $y_2$ , the formula is a little tricky. Let’s think about how to calculate $\frac{\partial f}{\partial y_1}$ . The variance $y_1$ propagates to $f$ via $x_1$ and $x_2$ . In this case the partial differentiation has two terms as below.

In chain rules, you have to think about all the routes where a variance can propagate through. If you generalize chain rules, that is like below, and you need to understand chain rules in this way to understanding any types of back propagation.

The figure above shows that if you calculate partial differentiation of $f$ with respect to $y_i$ , the partial differentiation has $n$ terms in total because $y_i$ propagates to $f$ via $n$ variances. In order to understand backprop of LSTM, you constantly have to care about the flow of variances, which I showed as arrows in purple above.

2. Chain rules in LSTM

I would like you to remember the figure below, which I used in the second article to show how errors propagate backward during backprop of simple RNNs. After forward propagation, first of all, you need to calculate $\frac{\partial J}{\partial \boldsymbol{\theta}^{(t)}}$ , gradients of the error function with respect to parameters, at every time step. But you have to be careful that even though these gradients depend on time steps, the parameters $\boldsymbol{\theta}$ do not depend on time steps.

*As I mentioned in the second article I personally think $\frac{\partial J}{\partial \boldsymbol{\theta}^{(t)}}$ should be rather denoted as $(\frac{\partial J}{\partial \boldsymbol{\theta}})^{(t)}$ because parameters themselves do not depend on time. The textbook by MIT press also partly use the former notation. And you are likely to encounter this type of notation, so I think it is not bad to get ready for both.

The errors at time step $(t)$ propagate backward to all the $\boldsymbol{h} ^{(s)}, (s \leq t)$ . Conversely, in order to calculate $\frac{\partial J}{\partial \boldsymbol{\theta}^{(t)}}$ errors flowing from $J^{(s)}, (s \geq t)$ . In the chart you need arrows of errors in purple for the gradient in a purple frame, orange arrows for gradients in orange frame, red arrows for gradients in red frame. And you need to sum up $\frac{\partial J}{\partial \boldsymbol{\theta}^{(t)}}$ to calculate $\frac{\partial J}{\partial \boldsymbol{\theta}} = \sum_{t}{\frac{\partial J}{\partial \boldsymbol{\theta}^{(t)}}}$ , and you need this gradient $\frac{\partial J}{\partial \boldsymbol{\theta}}$ to renew parameters, one time.

At an RNN block level, the flows of errors and how to renew parameters are the same in LSTM backprop, but the flow of errors inside each block is much more complicated in LSTM backprop. And in this article and my PowerPoint slides, I use a special notation to denote errors: $\delta \star ^{(t)}= \frac{\partial J^{(t)}}{\partial \star}$

* Again, please be careful of what $\delta \star ^{(t)}$ means. Neurons depend on time steps, but parameters do not depend on time steps. So if $\star$ are neurons, $\delta \star ^{(t)}= \frac{\partial J}{ \partial \star ^{(t)}}$ , but when $\star$ are parameters, $\delta \star ^{(t)}= \frac{\partial J^{(t)}}{ \partial \star}$ should be rather denoted like $\delta \star ^{(t)}= (\frac{\partial J}{ \partial \star ^{(t)}})$ . In the Space Odyssey paper, $\boldsymbol{\star}$ are not used as parameters, but in my PowerPoint slides and some other materials, $\boldsymbol{\star}$ are used also as parameteres.

As I wrote in the last article, you calculate $\boldsymbol{f}^{(t)}, \boldsymbol{i}^{(t)}, \boldsymbol{z}^{(t)}, \boldsymbol{o}^{(t)}$ as below. Unlike the last article, I also added the terms of peephole connections in the equations below, and I also added the variances $\bar{\boldsymbol{f}^{(t)}}, \bar{\boldsymbol{i}^{(t)}}, \bar{\boldsymbol{z}^{(t)}}, \bar{\boldsymbol{o}^{(t)}}$ for convenience.

$\boldsymbol{\bar{f}}^{(t)}=\boldsymbol{W}_{for} \cdot \boldsymbol{x}^{(t)} + \boldsymbol{R}_{for} \cdot \boldsymbol{y}^{(t-1)} + \boldsymbol{p}_{for}\odot \boldsymbol{c}^{(t-1)} + \boldsymbol{b}_{for}$
$\boldsymbol{\bar{i}}^{(t)}=\boldsymbol{W}_{in} \cdot \boldsymbol{x}^{(t)} + \boldsymbol{R}_{in} \cdot \boldsymbol{y}^{(t-1)} + \boldsymbol{p}_{in}\odot \boldsymbol{c}^{(t-1)} + \boldsymbol{b}_{in}$
$\boldsymbol{\bar{z}}^{(t)}=\boldsymbol{W}_z \cdot \boldsymbol{x}^{(t)} + \boldsymbol{R}_z \cdot \boldsymbol{y}^{(t-1)} + \boldsymbol{b}_z$
$\boldsymbol{\bar{o}}^{(t)}=\boldsymbol{W}_{out} \cdot \boldsymbol{x}^{(t)} + \boldsymbol{R}_{out} \cdot \boldsymbol{y}^{(t-1)} + \boldsymbol{p}_{out}\odot \boldsymbol{c}^{(t)} + \boldsymbol{b}_{out}$
$\boldsymbol{f}^{(t)}=\sigma( \boldsymbol{\bar{f}}^{(t)})$
$\boldsymbol{i}^{(t)}=\sigma(\boldsymbol{\bar{i}}^{(t)})$
$\boldsymbol{z}^{(t)}=tanh(\boldsymbol{\bar{z}}^{(t)})$
$\boldsymbol{o}^{(t)}=\sigma(\boldsymbol{\bar{o}}^{(t)})$

With Hadamar product operator, the renewed cell and the output are calculated as below.

$\boldsymbol{c}^{(t)} = \boldsymbol{z}^{(t)}\odot \boldsymbol{i}^{(t)} + \boldsymbol{c}^{(t-1)} \odot \boldsymbol{f}^{(t)}$
$\boldsymbol{y}^{(t)} = \boldsymbol{o}^{(t)} \odot tanh(\boldsymbol{c}^{(t)})$

In this article I would rather give instructions on how to read my PowerPoint slide. Just as general backprop, you need to calculate gradients of error functions with respect to parameters, such as $\delta \boldsymbol{W}_{\star}, \delta \boldsymbol{R}_{\star}, \delta \boldsymbol{p}_{\star}, \delta \boldsymbol{b}_{\star}$ , where $\star$ is either of $\{z, in, for, out \}$ . And just as backprop of simple RNNs, in order to calculate gradients with respect to parameters, you need to calculate errors of neurons, that is gradients of error functions with respect to neurons, such as $\delta \boldsymbol{f}^{(t)}, \delta \boldsymbol{i}^{(t)}, \delta \boldsymbol{z}^{(t)}, \delta \boldsymbol{o}^{(t)}$ .

*Again and again, keep it in mind that neurons depend on time steps, but parameters do not depend on time steps.

When you calculate gradients with respect to neurons, you can first calculate $\delta \boldsymbol{y}^{(t)}$ , but the equation for this error is the most difficult, so I recommend you to put it aside for now. After calculating $\delta \boldsymbol{y}^{(t)}$ , you can next calculate $\delta \bar{\boldsymbol{o}}^{(t)}= \frac{\partial J^{(t)}}{ \partial \bar{\boldsymbol{o}}^{(t)}}$ . If you see the LSTM block below as a graphical model which I introduced, the information of $\bar{\boldsymbol{o}}^{(t)}$ flow like the purple arrows. That means, $\bar{\boldsymbol{o}}^{(t)}$ affects $J$ only via $\boldsymbol{y}^{(t)}$ , and this structure is equal to the first graphical model which I have introduced above. And if you calculate $\bar{\boldsymbol{o}}^{(t)}$ element-wise, you get the equation $\delta \bar{o}_{k}^{(t)}=\frac{\partial J}{\partial \bar{o}_{k}^{(t)}}= \frac{\partial J}{\partial y_{k}^{(t)}} \frac{\partial y_{k}^{(t)}}{\partial \bar{o}_{k}^{(t)}}$ .

*The $k$ is an index of an element of vectors. If you can calculate element-wise gradients, it is easy to understand that as differentiation of vectors and matrices.

Next you can calculate $\delta \boldsymbol{c}^{(t)}$ , and chain rules are very important in this process. The flow of $\delta \boldsymbol{c}^{(t)}$ to $J$ can be roughly divided into two streams: the one flows to $J$ as $\bodlsymbol{y}^{(t)}$ , and the one flows to $J$ as $\bodlsymbol{c}^{(t+1)}$ . And the stream from $\bodlsymbol{c}^{(t)}$ to $\bodlsymbol{y}^{(t)}$ also have two branches: the one via $\bar{\boldsymbol{o}}^{(t)}$ and the one which directly converges as $\bodlsymbol{y}^{(t)}$ . Just as well, the stream from $\bodlsymbol{c}^{(t)}$ to $\bodlsymbol{c}^{(t+1)}$ also have three branches: the ones via $\bar{\boldsymbol{f}}^{(t)}$ , $\bar{\boldsymbol{i}}^{(t)}$ , and the one which directly converges as $\bodlsymbol{c}^{(t+1)}$ .

If you see see these flows as graphical a graphical model, that would be like the figure below.

According to this graphical model, you can calculate $\delta \boldsymbol{c} ^{(t)}$ element-wise as below.

* TO BE VERY HONEST I still do not fully understand why we can apply chain rules like above to calculate $\delta \boldsymbol{c}^{(t)}$ . When you apply the formula of chain rules, which I showed in the first section, to this case, you have to be careful of where to apply partial differential operators $\frac{\partial}{ \partial c_{k}^{(t)}}$ . In the case above, in the part $\frac{\partial y_{k}^{(t)}}{\partial c_{k}^{(t)}}$ the partial differential operator only affects $tanh(c_{k}^{(t)})$ of $o_{k}^{(t)} \cdot tanh(c_{k}^{(t)})$ , and in the part $\frac{\partial c_{k}^{(t+1)}}{\partial c_{k}^{(t)}}$ , the partial differential operator $\frac{\partial}{\partial c_{k}^{(t)}}$ only affects the part $c_{k}^{(t)}$ of the term $c^{t}_{k} \cdot f_{k}^{(t+1)}$ . In the $\frac{\partial \bar{o}_{k}^{(t)}}{\partial c_{k}^{(t)}}$ part, only $(p_{out})_{k} \cdot c_{k}^{(t)}$ , in the $\frac{\partial \bar{i}_{k}^{(t+1)}}{\partial c_{k}^{(t)}}$ part, only $(p_{in})_{k} \cdot c_{k}^{(t)}$ , and in the $\frac{\partial \bar{f}_{k}^{(t+1)}}{\partial c_{k}^{(t)}}$ part, only $(p_{in})_{k} \cdot c_{k}^{(t)}$ . But some other parts, which are not affected by $\frac{\partial}{ \partial c_{k}^{(t)}}$ are also functions of $c_{k}^{(t)}$ . For example $o_{k}^{(t)}$ of $o_{k}^{(t)} \cdot tanh(c_{k}^{(t)})$ is also a function of $c_{k}^{(t)}$ . And I am still not sure about the logic behind where to affect those partial differential operators.

*But at least, these are the only decent equations for LSTM backprop which I could find, and a frequently cited paper on LSTM uses implementation based on these equations. Computer science is more of practical skills, rather than rigid mathematical logic. It If you have any comments or advice on this point, please let me know.

Calculating $\delta \bar{\boldsymbol{f}}^{(t)}$ , $\delta \bar{\boldsymbol{i}}^{(t)}$ , $\delta \bar{\boldsymbol{z}}^{(t)}$ are also relatively straigtforward as calculating $\delta \bar{\boldsymbol{o}}^{(t)}$ . They all use the first type of chain rule in the first section. Thereby you can get these gradients: $\delta \bar{f}_{k}^{(t)}=\frac{\partial J}{ \partial \bar{f}_{k}^{(t)}} =\frac{\partial J}{\partial c_{k}^{(t)}} \frac{\partial c_{k}^{(t)}}{ \partial \bar{f}_{k}^{(t)}}$ , $\delta \bar{i}_{k}^{(t)}=\frac{\partial J}{\partial \bar{i}_{k}^{(t)}} =\frac{\partial J}{\partial c_{k}^{(t)}} \frac{\partial c_{k}^{(t)}}{ \partial \bar{i}_{k}^{(t)}}$ , and $\delta \bar{z}_{k}^{(t)}=\frac{\partial J}{\partial \bar{z}_{k}^{(t)}} =\frac{\partial J}{\partial c_{k}^{(t)}} \frac{\partial c_{k}^{(t)}}{ \partial \bar{i}_{k}^{(t)}}$ .

All the gradients which we have calculated use the error $\delta \boldsymbol{y}^{(t)}$ , but when it comes to calculating $\delta \boldsymbol{y}^{(t)}$ ….. I can only say “Please be patient. I did my best in my PowerPoint slides to explain that.” It is not a kind of process which I want to explain on Word Press. In conclusion you get an error like this: $\delta \boldsymbol{y}^{(t)}=\frac{\partial J^{(t)}}{\partial \boldsymbol{y}^{(t)}} + \boldsymbol{R}_{for}^{T} \delta \bar{\boldsymbol{f}}^{(t+1)} + \boldsymbol{R}_{in}^{T}\delta \bar{\boldsymbol{i}}^{(t+1)} + \boldsymbol{R}_{out}^{T}\delta \bar{\boldsymbol{o}}^{(t+1)} + \boldsymbol{R}_{z}^{T}\delta \bar{\boldsymbol{z}}^{(t+1)}$ , and the flows of $\boldsymbol{y}^{(t)}$ are as blow.

Combining the gradients we have got so far, we can calculate gradients with respect to parameters. For concrete results, please check the Space Odyssey paper or my PowerPoint slide.

3. How LSTMs tackle exploding/vanishing gradients problems

*If you are allergic to mathematics, you should not read this section or download my PowerPoint slide.

*Part of this section is more or less subjective, so if you really want to know how LSTM mitigate the problems, I highly recommend you to also refer to other materials. But at least I did my best for this article.

LSTMs do not completely solve, vanishing gradient problems. They mitigate vanishing/exploding gradient problems. I am going to roughly explain why they can tackle those problems. I think you find many explanations on that topic, but many of them seems to have some mathematical mistakes (even the slide used in a lecture in Stanford University) and I could not partly agree with some statements. I also could not find any papers or materials which show the whole picture of how LSTMs can tackle those problems. So in this article I am only going to give instructions on the most mainstream way to explain this topic.

First let’s see how gradients actually “vanish” or “explode” in simple RNNs. As I in the second article of this series, simple RNNs propagate forward as the equations below.

$\boldsymbol{a}^{(t)} = \boldsymbol{b} + \boldsymbol{W} \cdot \boldsymbol{h}^{(t-1)} + \boldsymbol{U} \cdot \boldsymbol{x}^{(t)}$
$\boldsymbol{h}^{(t)}= g(\boldsymbol{a}^{(t)})$
$\boldsymbol{o}^{(t)} = \boldsymbol{c} + \boldsymbol{V} \cdot \boldsymbol{h}^{(t)}$
$\hat{\boldsymbol{y}} ^{(t)} = f(\boldsymbol{o}^{(t)})$

And every time step, you get an error function $J^{(t)}$ . Let’s consider the gradient of $J^{(t)}$ with respect to $\boldsymbol{h}^{(k)}$ , that is the error flowing from $J^{(t)}$ to $\boldsymbol{h}^{(k)}$ . This error is the most used to calculate gradients of the parameters.

If you calculate this error more concretely, $\frac{\partial J^{(t)}}{\partial \boldsymbol{h}^{(k)}} = \frac{\partial J^{(t)}}{\partial \boldsymbol{h}^{(t)}} \frac{\partial \boldsymbol{h}^{(t)}}{\partial \boldsymbol{h}^{(t-1)}} \cdots \frac{\partial \boldsymbol{h}^{(k+2)}}{\partial \boldsymbol{h}^{(k+1)}} \frac{\partial \boldsymbol{h}^{(k+1)}}{\partial \boldsymbol{h}^{(k)}} = \frac{\partial J^{(t)}}{\partial \boldsymbol{h}^{(t)}} \prod_{k< s \leq t} \frac{\partial \boldsymbol{h}^{(s)}}{\partial \boldsymbol{h}^{(s-1)}}$ , where $\frac{\partial \boldsymbol{h}^{(s)}}{\partial \boldsymbol{h}^{(s-1)}} = \boldsymbol{W} ^T \cdot diag(g'(\boldsymbol{b} + \boldsymbol{W}\cdot \boldsymbol{h}^{(s-1)} + \boldsymbol{U}\cdot \boldsymbol{x}^{(s)})) = \boldsymbol{W} ^T \cdot diag(g'(\boldsymbol{a}^{(s)}))$ .

* If you see the figure as a type of graphical model, you should be able to understand the why chain rules can be applied as the equation above.

*According to this paper $\frac{\partial \boldsymbol{h}^{(s)}}{\partial \boldsymbol{h}^{(s-1)}} = \boldsymbol{W} ^T \cdot diag(g'(\boldsymbol{a}^{(s)}))$ , but it seems that many study materials and web sites are mistaken in this point.

Hence $\frac{\partial J^{(t)}}{\partial \boldsymbol{h}^{(k)}} = \frac{\partial J^{(t)}}{\partial \boldsymbol{h}^{(t)}} \prod_{k< s \leq t} \boldsymbol{W} ^T \cdot diag(g'(\boldsymbol{a}^{(s)})) = \frac{\partial J^{(t)}}{\partial \boldsymbol{h}^{(t)}} (\boldsymbol{W} ^T )^{(t - k)} \prod_{k< s \leq t} diag(g'(\boldsymbol{a}^{(s)}))$ . If you take norms of the members you get an equality $\left\lVert \frac{\partial J^{(t)}}{\partial \boldsymbol{h}^{(k)}} \right\rVert \leq \left\lVert \frac{\partial J^{(t)}}{\partial \boldsymbol{h}^{(t)}} \right\rVert \left\lVert \boldsymbol{W} ^T \right\rVert ^{(t - k)} \prod_{k< s \leq t} \left\lVert diag(g'(\boldsymbol{a}^{(s)}))\right\rVert$ . I will not go into detail anymore, but it is known that according to this inequality, multiplication of weight vectors exponentially converge to 0 or to infinite number.

We have seen that the error $\frac{\partial J^{(t)}}{\partial \boldsymbol{h}^{(k)}}$ is the main factor causing vanishing/exploding gradient problems. In case of LSTM, $\frac{\partial J^{(t)}}{\partial \boldsymbol{c}^{(k)}}$ is an equivalent. For simplicity, let’s calculate only $\frac{\partial \boldsymbol{c}^{(t)}}{\partial \boldsymbol{c}^{(t-1)}}$ , which is equivalent to $\frac{\partial \boldsymbol{h}^{(t)}}{\partial \boldsymbol{h}^{(t-1)}}$ of simple RNN backprop.

* Just as I noted above, you have to be careful of which part the partial differential operator $\frac{\partial}{\partial \boldsymbol{c}^{(t-1)}}$ affects in the chain rule above. That is, you need to calculate $\frac{\partial}{\partial \boldsymbol{c}^{(t-1)}} (\boldsymbol{c}^{(t-1)} \odot \boldsymbol{f}^{(t)})$ , and the partial differential operator only affects $\boldsymbol{c}^{(t-1)}$ . I think this is not a correct mathematical notation, but please forgive me for doing this for convenience.

If you continue calculating the equation above more concretely, you get the equation below.

I cannot mathematically explain why, but it is known that this characteristic of gradients of LSTM backprop mitigate the vanishing/exploding gradient problem. We have seen that if you take a norm of $\frac{\partial J^{(t)}}{\partial \boldsymbol{h}^{(k)}}$ , that is equal or smaller than repeated multiplication of the norm of the same weight matrix, and that soon leads to vanishing/exploding gradient problem. But according to the equation above, even if you take a norm of repeatedly multiplied $\frac{\partial \boldsymbol{c}^{(t)}}{\partial \boldsymbol{c}^{(t-1)}}$ , its norm cannot be evaluated with a simple value like repeated multiplication of the norm of the same weight matrix. The outputs of each gate are different from time steps to time steps, and that adjust the value of $\frac{\partial \boldsymbol{c}^{(t)}}{\partial \boldsymbol{c}^{(t-1)}}$ .

*I personally guess the item $diag(\boldsymbol{f}^{(t)})$ is every effective. The unaffected value of can directly $diag(\boldsymbol{f}^{(t)})$ adjust the value of $\frac{\partial \boldsymbol{c}^{(t)}}{\partial \boldsymbol{c}^{(t-1)}}$ . And as a matter of fact, it is known that performances of LSTM drop the most when you gite rid of forget gates.

When it comes to tackling exploding gradient problems, there is a much easier technique called gradient clipping. This algorithm is very simple: you just have to adjust the size of gradient so that the absolute value of gradient is under a threshold at every time step. Imagine that you decide in which direction to move by calculating gradients, but when the footstep is going to be too big, you just adjust the size of footstep to the threshold size you have set. In a pseudo code, write a gradient clipping part only with two line code as below.

* $\boldsymbol{g}$ is a gradient at the time step $threshold$ is the maximum size of the “step.”

The figure below, cited from a deep learning text from MIT press textbook, is a good and straightforward explanation on gradient clipping.It is known that a strongly nonlinear function, such as error functions of RNN, can have very steep or plain areas. If you artificially visualize the idea in 3-dimensional space, as the surface of a loss function $J$ with two variants $w, b$ , that means the loss function $J$ has plain areas and very steep cliffs like in the figure.Without gradient clipping, at the left side, you can see that the black dot all of a sudden climb the cliff and could jump to an unexpected area. But with gradient clipping, you avoid such “big jumps” on error functions.

Source: Source: Goodfellow and Yoshua Bengio and Aaron Courville, Deep Learning, (2016), MIT Press, 409p

I am glad that I have finally finished this article series. I am not sure how many of the readers would have read through all of the articles in this series, including my PowerPoint slides. I bet that is not so many. I spent a great deal of my time for making these contents, but sadly even when I was studying LSTM, it was becoming old-fashioned, at least in natural language processing (NLP) field: a very promising algorithm named Transformer has been replacing the position of LSTM. Deep learning is a very fast changing field. I also would like to make illustrative introductions on attention mechanism in NLP, from seq2seq model to Transformer. And I think LSTM would still remain as one of the algorithms in sequence data processing, such as hidden Hidden Markov model, or particle filter.

Hypothesis Test for real problems

August 26, 2020/in Data Science, Main Category, Statistics/by Saurav Singla

Hypothesis tests are significant for evaluating answers to questions concerning samples of data.

A statistical hypothesis is a belief made about a population parameter. This belief may or might not be right. In other words, hypothesis testing is a proper technique utilized by scientist to support or reject statistical hypotheses. The foremost ideal approach to decide if a statistical hypothesis is correct is examine the whole population.

Since that’s frequently impractical, we normally take a random sample from the population and inspect the equivalent. Within the event sample data set isn’t steady with the statistical hypothesis, the hypothesis is refused.

Types of hypothesis:

There are two sort of hypothesis and both the Null Hypothesis (Ho) and Alternative Hypothesis (Ha) must be totally mutually exclusive events.

• Null hypothesis is usually the hypothesis that the event wont’t happen.

• Alternative hypothesis is a hypothesis that the event will happen.

Why we need Hypothesis Testing?

Suppose a specific cosmetic producing company needs to launch a new Shampoo in the market. For this situation they will follow Hypothesis Testing all together decide the success of new product in the market.

Where likelihood of product being ineffective in market is undertaken as Null Hypothesis and likelihood of product being profitable is undertaken as Alternative Hypothesis. By following the process of Hypothesis testing they will foresee the accomplishment.

How to Calculate Hypothesis Testing?

State the two theories with the goal that just one can be correct, to such an extent that the two occasions are totally unrelated.
Now figure a study plan, that will lay out how the data will be assessed.
Now complete the plan and genuinely investigate the sample dataset.
Finally examine the outcome and either accept or reject the null hypothesis.

Another example

Assume, Person have gone after a typing job and he has expressed in the resume that his composing speed is 70 words per minute. The recruiter might need to test his case. On the off chance that he sees his case as adequate, he will enlist him in any case reject him. Thus, he types an example letter and found that his speed is 63 words a minute. Presently, he can settle on whether to employ him or not. In the event that he meets all other qualification measures. This procedure delineates Hypothesis Testing in layman’s terms.

In statistical terms Hypothesis his typing speed is 70 words per minute is a hypothesis to be tested so-called null hypothesis. Clearly, the alternating hypothesis his composing speed isn’t 70 words per minute.

So, normal composing speed is population parameter and sample composing speed is sample statistics.

The conditions of accepting or rejecting his case is to be chosen by the selection representative. For instance, he may conclude that an error of 6 words is alright to him so he would acknowledge his claim between 64 to 76 words per minute. All things considered, sample speed 63 words per minute will close to reject his case. Furthermore, the choice will be he was producing a fake claim.

In any case, if the selection representative stretches out his acceptance region to positive/negative 7 words that is 63 to 77 words, he would be tolerating his case.

In this way, to finish up, Hypothesis Testing is a procedure to test claims about the population dependent on sample. It is a fascinating reasonable subject with a quite statistical jargon. You have to dive more to get familiar with the details.

Significance Level and Rejection Region for Hypothesis

Type I error probability is normally indicated by α and generally set to 0.05. The value of α is recognized as the significance level.

The rejection region is the set of sample data that prompts the rejection of the null hypothesis. The significance level, α, decides the size of the rejection region. Sample results in the rejection region are labelled statistically significant at level of α .

The impact of differing α is that If α is small, for example, 0.01, the likelihood of a type I error is little, and a ton of sample evidence for the alternative hypothesis is needed before the null hypothesis can be dismissed. Though, when α is bigger, for example, 0.10, the rejection region is bigger, and it is simpler to dismiss the null hypothesis.

Significance from p-values

A subsequent methodology is to evade the utilization of a significance level and rather just report how significant the sample evidence is. This methodology is as of now more widespread. It is accomplished by method of a p value. P value is gauge of power of the evidence against null hypothesis. It is the likelihood of getting the observed value of test statistic, or value with significantly more prominent proof against null hypothesis (Ho), if the null hypothesis of an investigation question is true. The less significant the p value, the more proof there is supportive of the alternative hypothesis. Sample evidence is measurably noteworthy at the α level just if the p value is less than α. They have an association for two tail tests. When utilizing a confidence interval to playout a two-tailed hypothesis test, reject the null hypothesis if and just if the hypothesized value doesn’t lie inside a confidence interval for the parameter.

Hypothesis Tests and Confidence Intervals

Hypothesis tests and confidence intervals are cut out of the same cloth. An event whose 95% confidence interval reject the hypothesis is an event for which p<0.05 under the relating hypothesis test, and the other way around. A p value is letting you know the greatest confidence interval that despite everything prohibits the hypothesis. As such, if p<0.03 against the null hypothesis, that implies that a 97% confidence interval does exclude the null hypothesis.

Hypothesis Tests for a Population Mean

We do a t test on the ground that the population mean is unknown. The general purpose is to contrast sample mean with some hypothetical population mean, to assess whether the watched the truth is such a great amount of unique in relation to the hypothesis that we can say with assurance that the hypothetical population mean isn’t, indeed, the real population mean.

Hypothesis Tests for a Population Proportion

At the point when you have two unique populations Z test facilitates you to choose if the proportion of certain features is the equivalent or not in the two populations. For instance, if the male proportion is equivalent between two nations.

Hypothesis Test for Equal Population Variances

F Test depends on F distribution and is utilized to think about the variance of the two impartial samples. This is additionally utilized with regards to investigation of variance for making a decision about the significance of more than two sample.

T test and F test are totally two unique things. T test is utilized to evaluate the population parameter, for example, population mean, and is likewise utilized for hypothesis testing for population mean. However, it must be utilized when we don’t know about population standard deviation. On the off chance that we know the population standard deviation, we will utilize Z test. We can likewise utilize T statistic to approximate population mean. T statistic is likewise utilised for discovering the distinction in two population mean with the assistance of sample means.

Z statistic or T statistic is utilized to assess population parameters such as population mean and population proportion. It is likewise used for testing hypothesis for population mean and population proportion. In contrast to Z statistic or T statistic, where we manage mean and proportion, Chi Square or F test is utilized for seeing if there is any variance inside the samples. F test is the proportion of fluctuation of two samples.

Conclusion

Hypothesis encourages us to make coherent determinations, the connection among variables, and gives the course to additionally investigate. Hypothesis for the most part results from speculation concerning studied behaviour, natural phenomenon, or proven theory. An honest hypothesis ought to be clear, detailed, and reliable with the data. In the wake of building up the hypothesis, the following stage is validating or testing the hypothesis. Testing of hypothesis includes the process that empowers to concur or differ with the expressed hypothesis.

Understanding LSTM forward propagation in two ways

August 21, 2020/in Artificial Intelligence, Data Mining, Data Science, Data Science Hack, Deep Learning, Machine Learning, Main Category, Predictive Analytics/by Yasuto Tamura

*This article is only for the sake of understanding the equations in the second page of the paper named “LSTM: A Search Space Odyssey”. If you have no trouble understanding the equations of LSTM forward propagation, I recommend you to skip this article and go the the next article.

1. Preface

I heard that in Western culture, smart people write textbooks so that other normal people can understand difficult stuff, and that is why textbooks in Western countries tend to be bulky, but also they are not so difficult as they look. On the other hand in Asian culture, smart people write puzzling texts on esoteric topics, and normal people have to struggle to understand what noble people wanted to say. Publishers also require the authors to keep the texts as short as possible, so even though the textbooks are thin, usually students have to repeat reading the textbooks several times because usually they are too abstract.

Both styles have cons and pros, and usually I prefer Japanese textbooks because they are concise, and sometimes it is annoying to read Western style long texts with concrete straightforward examples to reach one conclusion. But a problem is that when it comes to explaining LSTM, almost all the text books are like Asian style ones. Every study material seems to skip the proper steps necessary for “normal people” to understand its algorithms. But after actually making concrete slides on mathematics on LSTM, I understood why: if you write down all the equations on LSTM forward/back propagation, that is going to be massive, and actually I had to make 100-page PowerPoint animated slides to make it understandable to people like me.

I already had a feeling that “Does it help to understand only LSTM with this precision? I should do more practical codings.” For example François Chollet, the developer of Keras, in his book, said as below.

For me that sounds like “We have already implemented RNNs for you, so just shut up and use Tensorflow/Keras.” Indeed, I have never cared about the architecture of my Mac Book Air, but I just use it every day, so I think he is to the point. To make matters worse, for me, a promising algorithm called Transformer seems to be replacing the position of LSTM in natural language processing. But in this article series and in my PowerPoint slides, I tried to explain as much as possible, contrary to his advice.

But I think, or rather hope, it is still meaningful to understand this 23-year-old algorithm, which is as old as me. I think LSTM did build a generation of algorithms for sequence data, and actually Sepp Hochreiter, the inventor of LSTM, has received Neural Network Pioneer Award 2021 for his work.

I hope those who study sequence data processing in the future would come to this article series, and study basics of RNN just as I also study classical machine learning algorithms.

*In this article “Densely Connected Layers” is written as “DCL,” and “Convolutional Neural Network” as “CNN.”

2. Why LSTM?

First of all, let’s take a brief look at what I said about the structures of RNNs, in the first and the second article. A simple RNN is basically densely connected network with a few layers. But the RNN gets an input every time step, and it gives out an output at the time step. Part of information in the middle layer are succeeded to the next time step, and in the next time step, the RNN also gets an input and gives out an output. Therefore, virtually a simple RNN behaves almost the same way as densely connected layers with many layers during forward/back propagation if you focus on its recurrent connections.

That is why simple RNNs suffer from vanishing/exploding gradient problems, where the information exponentially vanishes or explodes when its gradients are multiplied many times through many layers during back propagation. To be exact, I think you need to consider this problem precisely like you can see in this paper. But for now, please at least keep it in mind that when you calculate a gradient of an error function with respect to parameters of simple neural networks, you have to multiply parameters many times like below, and this type of calculation usually leads to vanishing/exploding gradient problem.

LSTM was invented as a way to tackle such problems as I mentioned in the last article.

3. How to display LSTM

I would like you to just go to image search on Google, Bing, or Yahoo!, and type in “LSTM.” I think you will find many figures, but basically LSTM charts are roughly classified into two types: in this article I call them “Space Odyssey type” and “electronic circuit type”, and in conclusion, I highly recommend you to understand LSTM as the “electronic circuit type.”

*I just randomly came up with the terms “Space Odyssey type” and “electronic circuit type” because the former one is used in the paper I mentioned, and the latter one looks like an electronic circuit to me. You do not have to take how I call them seriously.

However, not that all the well-made explanations on LSTM use the “electronic circuit type,” and I am sure you sometimes have to understand LSTM as the “space odyssey type.” And the paper “LSTM: A Search Space Odyssey,” which I learned a lot about LSTM from, also adopts the “Space Odyssey type.”

The main reason why I recommend the “electronic circuit type” is that its behaviors look closer to that of simple RNNs, which you would have seen if you read my former articles.

*Behaviors of both of them look different, but of course they are doing the same things.

If you have some understanding on DCL, I think it was not so hard to understand how simple RNNs work because simple RNNs are mainly composed of linear connections of neurons and weights, whose structures are the same almost everywhere. And basically they had only straightforward linear connections as you can see below.

But from now on, I would like you to give up the ideas that LSTM is composed of connections of neurons like the head image of this article series. If you do that, I think that would be chaotic and I do not want to make a figure of it on Power Point. In short, sooner or later you have to understand equations of LSTM.

4. Forward propagation of LSTM in “electronic circuit type”

*For further understanding of mathematics of LSTM forward/back propagation, I recommend you to download my slides.

The behaviors of an LSTM block is quite similar to that of a simple RNN block: an RNN block gets an input every time step and gets information from the RNN block of the last time step, via recurrent connections. And the block succeeds information to the next block.

Let’s look at the simplified architecture of an LSTM block. First of all, you should keep it in mind that LSTM have two streams of information: the one going through all the gates, and the one going through cell connections, the “highway” of LSTM block. For simplicity, we will see the architecture of an LSTM block without peephole connections, the lines in blue. The flow of information through cell connections is relatively uninterrupted. This helps LSTMs to retain information for a long time.

In a LSTM block, the input and the output of the former time step separately go through sections named “gates”: input gate, forget gate, output gate, and block input. The outputs of the forget gate, the input gate, and the block input join the highway of cell connections to renew the value of the cell.

*The small two dots on the cell connections are the “on-ramp” of cell conection highway.

*You would see the terms “input gate,” “forget gate,” “output gate” almost everywhere, but how to call the “block gate” depends on textbooks.

Let’s look at the structure of an LSTM block a bit more concretely. An LSTM block at the time step $(t)$ gets $\boldsymbol{y}^{(t-1)}$ , the output at the last time step, and $\boldsymbol{c}^{(t-1)}$ , the information of the cell at the time step $(t-1)$ , via recurrent connections. The block at time step $(t)$ gets the input $\boldsymbol{x}^{(t)}$ , and it separately goes through each gate, together with $\boldsymbol{y}^{(t-1)}$ . After some calculations and activation, each gate gives out an output. The outputs of the forget gate, the input gate, the block input, and the output gate are respectively $\boldsymbol{f}^{(t)}, \boldsymbol{i}^{(t)}, \boldsymbol{z}^{(t)}, \boldsymbol{o}^{(t)}$ . The outputs of the gates are mixed with $\boldsymbol{c}^{(t-1)}$ and the LSTM block gives out an output $\boldsymbol{y}^{(t)}$ , and gives $\boldsymbol{y}^{(t)}$ and $\boldsymbol{c}^{(t)}$ to the next LSTM block via recurrent connections.

You calculate $\boldsymbol{f}^{(t)}, \boldsymbol{i}^{(t)}, \boldsymbol{z}^{(t)}, \boldsymbol{o}^{(t)}$ as below.

$\boldsymbol{f}^{(t)}= \sigma(\boldsymbol{W}_{for} \boldsymbol{x}^{(t)} + \boldsymbol{R}_{for} \boldsymbol{y}^{(t-1)} + \boldsymbol{b}_{for})$
$\boldsymbol{i}^{(t)}=\sigma(\boldsymbol{W}_{in} \boldsymbol{x}^{(t)} + \boldsymbol{R}_{in} \boldsymbol{y}^{(t-1)} + \boldsymbol{b}_{in})$
$\boldsymbol{z}^{(t)}=tanh(\boldsymbol{W}_z \boldsymbol{x}^{(t)} + \boldsymbol{R}_z \boldsymbol{y}^{(t-1)} + \boldsymbol{b}_z)$
$\boldsymbol{o}^{(t)}=\sigma(\boldsymbol{W}_{out} \boldsymbol{x}^{(t)} + \boldsymbol{R}_{out} \boldsymbol{y}^{(t-1)} + \boldsymbol{b}_{out})$

*You have to keep it in mind that the equations above do not include peephole connections, which I am going to show with blue lines in the end.

The equations above are quite straightforward if you understand forward propagation of simple neural networks. You add linear products of $\boldsymbol{y}^{(t)}$ and $\boldsymbol{c}^{(t)}$ with different weights in each gate. What makes LSTMs different from simple RNNs is how to mix the outputs of the gates with the cell connections. In order to explain that, I need to introduce a mathematical operator called Hadamard product, which you denote as $\odot$ . This is a very simple operator. This operator produces an elementwise product of two vectors or matrices with identical shape.

With this Hadamar product operator, the renewed cell and the output are calculated as below.

$\boldsymbol{c}^{(t)} = \boldsymbol{z}^{(t)}\odot \boldsymbol{i}^{(t)} + \boldsymbol{c}^{(t-1)} \odot \boldsymbol{f}^{(t)}$
$\boldsymbol{y}^{(t)} = \boldsymbol{o}^{(t)} \odot tanh(\boldsymbol{c}^{(t)})$

The values of $\boldsymbol{f}^{(t)}, \boldsymbol{i}^{(t)}, \boldsymbol{z}^{(t)}, \boldsymbol{o}^{(t)}$ are compressed into the range of $[0, 1]$ or $[-1, 1]$ with activation functions. You can see that the input gate and the block input give new information to the cell. The part $\boldsymbol{c}^{(t-1)} \odot \boldsymbol{f}^{(t)}$ means that the output of the forget gate “forgets” the cell of the last time step by multiplying the values from 0 to 1 elementwise. And the cell $\boldsymbol{c}^{(t)}$ is activated with $tanh()$ and the output of the output gate “suppress” the activated value of $\boldsymbol{c}^{(t)}$ . In other words, the output gatedecides how much information to give out as an output of the LSTM block. The output of every gate depends on the input $\boldsymbol{x}^{(t)}$ , and the recurrent connection $\boldsymbol{y}^{(t-1)}$ . That means an LSTM block learns to forget the cell of the last time step, to renew the cell, and to suppress the output. To describe in an extreme manner, if all the outputs of every gate are always $(1, 1, …1)^T$ , LSTMs forget nothing, retain information of inputs at every time step, and gives out everything. And if all the outputs of every gate are always $(0, 0, …0)^T$ , LSTMs forget everything, receive no inputs, and give out nothing.

This model has one problem: the outputs of each gate do not directly depend on the information in the cell. To solve this problem, some LSTM models introduce some flows of information from the cell to each gate, which are shown as lines in blue in the figure below.

LSTM models, for example the one with or without peephole connection, depend on the library you use, and the model I have showed is one of standard LSTM structure. However no matter how complicated structure of an LSTM block looks, you usually cover it with a black box as below and show its behavior in a very simplified way.

5. Space Odyssey type

I personally think there is no advantages of understanding how LSTMs work with this Space Odyssey type chart, but in several cases you would have to use this type of chart. So I will briefly explain how to look at that type of chart, based on understandings of LSTMs you have gained through this article.

In Space Odyssey type of LSTM chart, at the center is a cell. Electronic circuit type of chart, which shows the flow of information of the cell as an uninterrupted “highway” in an LSTM block. On the other hand, in a Spacey Odyssey type of chart, the information of the cell rotate at the center. And each gate gets the information of the cell through peephole connections, $\boldsymbol{x}^{(t)}$ , the input at the time step $(t)$ , sand $\boldsymbol{y}^{(t-1)}$ , the output at the last time step $(t-1)$ , which came through recurrent connections. In Space Odyssey type of chart, you can more clearly see that the information of the cell go to each gate through the peephole connections in blue. Each gate calculates its output.

Just as the charts you have seen, the dotted line denote the information from the past. First, the information of the cell at the time step $(t-1)$ goes to the forget gate and get mixed with the output of the forget cell In this process the cell is partly “forgotten.” Next, the input gate and the block input are mixed to generate part of new value of the the cell at time step $(t)$ . And the partly “forgotten” $\boldsymbol{c}^{(t-1)}$ goes back to the center of the block and it is mixed with the output of the input gate and the block input. That is how $\boldsymbol{c}^{(t)}$ is renewed. And the value of new cell flow to the top of the chart, being mixed with the output of the output gate. Or you can also say the information of new cell is “suppressed” with the output gate.

I have finished the first four articles of this article series, and finally I am gong to write about back propagation of LSTM in the next article. I have to say what I have written so far is all for the next article, and my long long Power Point slides.

[References]

[1] Klaus Greff, Rupesh Kumar Srivastava, Jan Koutník, Bas R. Steunebrink, Jürgen Schmidhuber, “LSTM: A Search Space Odyssey,” (2017)

[2] Francois Chollet, Deep Learning with Python,(2018), Manning , pp. 202-204

[3] “Sepp Hochreiter receives IEEE CIS Neural Networks Pioneer Award 2021”, Institute of advanced research in artificial intelligence, (2020)
URL: https://www.iarai.ac.at/news/sepp-hochreiter-receives-ieee-cis-neural-networks-pioneer-award-2021/?fbclid=IwAR27cwT5MfCw4Tqzs3MX_W9eahYDcIFuoGymATDR1A-gbtVmDpb8ExfQ87A

[4] Oketani Takayuki, “Machine Learning Professional Series: Deep Learning,” (2015), pp. 120-125
岡谷貴之著, 「機械学習プロフェッショナルシリーズ深層学習」, (2015), pp. 120-125

[5] Harada Tatsuya, “Machine Learning Professional Series: Image Recognition,” (2017), pp. 252-257
原田達也著, 「機械学習プロフェッショナルシリーズ画像認識」, (2017), pp. 252-257

[6] “Understandable LSTM ~ With the Current Trends,” Qiita, (2015)
「わかるLSTM ～最近の動向と共に」, Qiita, (2015)
URL: https://qiita.com/t_Signull/items/21b82be280b46f467d1b

How Data Science Can Benefit Nonprofits

August 4, 2020/in Data Science, Use Case/by Luke Smith

Image Source: https://pixabay.com/vectors/pixel-cells-pixel-creative-commons-3704068/

Data science is the poster child of the 21st century and for good reason. Data-based decisions have streamlined, automated, and made businesses more efficient than ever before, and there are practically no industries that haven’t recognized its immense potential. But when you think of data science application, sectors like marketing, finance, technology, SMEs, and even education are the first that come to mind. There’s one more sector that’s proving to be an untapped market for data—the social sector. At first, one might question why non-profit organizations even need complex data applications, but that’s just it—they don’t. What they really need is data tools that are simple and reliable, because if anything, accountability is the most important component of the way non-profits run.

Challenges for Non-profits and Data Science

If you’re wondering why many non-profits haven’t already hopped onto the data bandwagon, its because in most cases they lack one big thing—quality data.

One reason is that effective data application requires clean data, and heaps of it, something non-profits struggle with. Most don’t sell products or services, and their success is reliant on broad, long-term (sometimes decades) results and changes, which means their outcomes are highly unmeasurable. Metrics and data seem out of place when appealing to donors, who are persuaded more by emotional campaigns. Data collection is also rare, perhaps only being recorded when someone signs up to the program or leaves, and hardly any tracking in between. The result is data that’s too little and unreliable to make effective change.

Perhaps the most important phase, data collection relies heavily on accurate and organized processes. For non-profits that don’t have the resources for accurate and manual record-keeping, clean, and quality data collection is a huge pain point. However, that is an issue now easily avoidable. For instance, avoiding duplicate files, adopting record-keeping methods like off-site and cloud storage, digital retention, and of course back-up plans—are all processes that could save non-profits time, effort, and risk. On the other hand, poor record management has its consequences, namely on things like fund allocation, payroll, budgeting, and taxes. It could lead to financial risk, legal trouble, and data loss — all added worries for already under-resourced non-profit organizations.

But now, as non-governmental organizations (NGOs) and non-profits catch up and invest more in data collection processes, there’s room for data science to make its impact. A growing global movement, ‘Data For Good’ represents individuals, companies, and organizations volunteering to create or use data to help further social causes ad support non-profit organizations. This ‘Data For Good’ movement includes tools for data work that are donated or subsidized, as well as educational programs that serve marginalized communities. As the movement gains momentum, non-profits are seeing data seep into their structures and turn processes around.

How Can Data Do Social Good?

With data science set to take the non-profit sector by storm, let’s look at some of the ways data can do social good:

Improving communication with donors: Knowing when to reach out to your donors is key. In between a meeting? You’re unlikely to see much enthusiasm. Once they’re at home with their families? You may see wonderful results, as pointed out in this Forbes article. The article opines that data can help non-profits understand and communicate with their donors better.
Donor targetting: Cold calls are a hit and miss, and with data on their side, non-profits can discover and define their ideal donor and adapt their messaging to reach out to them for better results.
Improving cost efficiency: Costs are a major priority for non-profits and every penny counts. Data can help decrease costs and streamline financial planning
Increasing new member sign-ups and renewals: Through data, non-profits can reach out to the right people they want on-board, strengthen recruitment processes and keep track of volunteers reaching out to them for future events or recruitment drives.
Modeling and forecasting performance: With predictive modeling tools, non-profits can make data-based decisions on where they should allocate time and money for the future, rather than go on gut instinct.
Measuring return on investment: For a long time, the outcomes of social campaigns have been perceived as intangible and immeasurable—it’s hard to measure empowerment or change. With data, non-profits can measure everything from the amount a fundraiser raised against a goal, the cost of every lead in a lead generation campaign, etc
Streamlining operations: Finally, non-profits can use data tools to streamline their business processes internally and invest their efforts into resources that need it.

It’s true, measuring good and having social change down to a science is a long way off — but data application is a leap forward into a more efficient future for the social sector. With mission-aligned processes, data-driven non-profits can realize their potential, redirect their focus from trivial tasks, and onto the bigger picture to drive true change.

A brief history of neural nets: everything you should know before learning LSTM

July 16, 2020/in Artificial Intelligence, Data Mining, Data Science, Data Science Hack, Deep Learning, Machine Learning, Main Category, Predictive Analytics, TensorFlow/by Yasuto Tamura

This is not a college course or something on deep learning with strict deadlines for assignments, so let’s take a detour from practical stuff and take a brief look at the history of neural networks.

The history of neural networks is also a big topic, which could be so long that I had to prepare another article series. And usually I am supposed to begin such articles with something like “The term ‘AI’ was first used by John McCarthy in Dartmouth conference 1956…” but you can find many of such texts written by people with much more experiences in this field. Therefore I am going to write this article from my point of view, as an intern writing articles on RNN, as a movie buff, and as one of many Japanese men who spent a great deal of childhood with video games.

We are now in the third AI boom, and some researchers say this boom began in 2006. A professor in my university said there we are now in a kind of bubble economy in machine learning/data science industry, but people used to say “Stop daydreaming” to AI researchers. The second AI winter is partly due to vanishing/exploding gradient problem of deep learning. And LSTM was invented as one way to tackle such problems, in 1997.

1, First AI boom

In the first AI boom, I think people were literally “daydreaming.” Even though the applications of machine learning algorithms were limited to simple tasks like playing chess, checker, or searching route of 2d mazes, and sometimes this time is called GOFAI (Good Old Fashioned AI).

Even today when someone use the term “AI” merely for tasks with neural networks, that amuses me because for me deep learning is just statistically and automatically training neural networks, which are capable of universal approximation, into some classifiers/regressors. Actually the algorithms behind that is quite impressive, but the structure of human brains is much more complicated. The hype of “AI” already started in this first AI boom. Let me take an example of machine translation in this video. In fact the research of machine translation already started in the early 1950s, and of specific interest in the time was translation between English and Russian due to Cold War. In the first article of this series, I said one of the most famous applications of RNN is machine translation, such as Google Translation, DeepL. They are a type of machine translation called neural machine translation because they use neural networks, especially RNNs. Neural machine translation was an astonishing breakthrough around 2014 in machine translation field. The former major type of machine translation was statistical machine translation, based on statistical language models. And the machine translator in the first AI boom was rule base machine translators, which are more primitive than statistical ones.

The most remarkable invention in this time was of course perceptron by Frank Rosenblatt. Some people say that this is the first neural network. Even though you can implement perceptron with a-few-line codes in Python, obviously they did not have Jupyter Notebook in those days. The perceptron was implemented as a huge instrument named Mark 1 Perceptron, and it was composed of randomly connected wires. I do not precisely know how it works, but it was a huge effort to implement even the most primitive type of neural networks. They needed to use a big lighting fixture to get a 20*20 pixel image using 20*20 array of cadmium sulphide photocells. The research by Rosenblatt, however, was criticized by Marvin Minsky in his book because perceptrons could only be used for linearly separable data. To make matters worse the criticism prevailed as that more general, multi-layer perceptrons were also not useful for linearly inseparable data (as I mentioned in the first article, multi-layer perceptrons, namely normal neural networks, can be universal approximators, which have potentials to classify/regress various types of complex data). In case you do not know what “linearly separable” means, imagine that there are data plotted on a piece of paper. If an elementary school kid can draw a border line between two clusters of the data with a ruler and a pencil on the paper, the 2d data is “linearly separable”….

With big disappointments to the research on “electronic brains,” the budget of AI research was reduced and AI research entered its first winter.

I think the frame problem(1969), by John McCarthy and Patrick J. Hayes, is also an iconic theory in the end of the first AI boom. This theory is known as a story of creating a robot trying to pull out its battery on a wheeled wagon in a room. The first prototype of the robot, named R1, naively tried to pull out the wagon form the room, and the bomb exploded. The problems was obvious: R1 was not programmed to consider the risks by taking each action, so the researchers made the next prototype named R1D1, which was programmed to consider the potential risks of taking each action. When R1D1 tried to pull out the wagon, it realized the risk of pulling the bomb together with the battery. But soon it started considering all the potential risks, such as the risk of the ceiling falling down, the distance between the wagon and all the walls, and so on, when the bomb exploded. The next problem was also obvious: R1D1 was not programmed to distinguish if the factors are relevant of irrelevant to the main purpose, and the next prototype R2D1 was programmed to do distinguish them. This time, R2D1 started thinking about “whether the factor is irrelevant to the main purpose,” on every factor measured, and again the bomb exploded. How can we get a perfect AI, R2D2?

The situation of mentioned above is a bit extreme, but it is said AI could also get stuck when it try to take some super simple actions like finding a number in a phone book and make a phone call. It is difficult for an artificial intelligence to decide what is relevant and what is irrelevant, but humans will not get stuck with such simple stuff, and sometimes the frame problem is counted as the most difficult and essential problem of developing AI. But personally I think the original frame problem was unreasonable in that McCarthy, in his attempts to model the real world, was inflexible in his handling of the various equations involved, treating them all with equal weight regardless of the particular circumstances of a situation. Some people say that McCarthy, who was an advocate for AI, also wanted to see the field come to an end, due to its failure to meet the high expectations it once aroused.

Not only the frame problem, but also many other AI-related technological/philosophical problems have been proposed, such as Chinese room (1980), the symbol grounding problem (1990), and they are thought to be as hardships in inventing artificial intelligence, but I omit those topics in this article.

*The name R2D2 did not come from the famous story of frame problem. The story was Daniel Dennett first proposed the story of R2D2 in his paper published in 1984. Star Wars was first released in 1977. It is said that the name R2D2 came from “Reel 2, Dialogue 2,” which George Lucas said while film shooting. And the design of C3PO came from Maria in Metropolis(1927). It is said that the most famous AI duo in movie history was inspired by Tahei and Matashichi in The Hidden Fortress(1958), directed by Kurosawa Akira.

Interestingly, in the end of the first AI boom, 2001: A Space Odyssey, directed by Stanley Kubrick, was released in 1968. Unlike conventional fantasylike AI characters, for example Maria in Metropolis(1927), HAL 9000 was portrayed as a very realistic AI, and the movie already pointed out the risk of AI being insane when it gets some commands from several users. HAL 9000 still has been a very iconic character in AI field. For example when you say some quotes from 2001: A Space Odyssey to Siri you get some parody responses. I also thin you should keep it in mind that in order to make an AI like HAL 9000 come true, for now RNNs would be indispensable in many ways: you would need RNNs for better voice recognition, better conversational system, and for reading lips.

*Just as you cannot understand Monty Python references in Python official tutorials without watching Monty Python and the Holy Grail, you cannot understand many parodies in AI contexts without watching 2001: A Space Odyssey. Even thought the movie had some interview videos with some researchers and some narrations, Stanley Kubrick cut off all the footage and made the movie very difficult to understand. Most people did not or do not understand that it is a movie about aliens who gave homework of coming to Jupiter to human beings.

2, Second AI boom/winter

I am not going to write about the second AI boom in detail, but at least you should keep it in mind that convolutional neural network(CNN) is a keyword in this time. Neocognitron, an artificial model of how sight nerves perceive thing, was invented by Kunihiko Fukushima in 1980, and the model is said to be the origin on CNN. And Neocognitron got inspired by the Hubel and Wiesel’s research on sight nerves. In 1989, a group in AT & T Bell Laboratory led by Yann LeCun invented the first practical CNN to read handwritten digit.

Another turning point in this second AI boom was that back propagation algorithm was discovered, and the CNN by LeCun was also trained with back propagation. LeCun made a deep neural networks with some layers in 1998 for more practical uses.

But his research did not gain so much attention like today, because AI research entered its second winter at the beginning of the 1990s, and that was partly due to vanishing/exploding gradient problem of deep learning. People knew that neural networks had potentials of universal approximation, but when they tried to train naively stacked neural nets the gradients, which you need to train neural networks, exponentially increased/decreased. Even though the CNN made by LeCun was the first successful case of “deep” neural nets which did not suffer from the vanishing/exploding gradient problem, deep learning research also stagnated in this time.

The ultimate goal of this article series is to understand LSTM at a more abstract/mathematical level because it is one of the practical RNNs, but the idea of LSTM (Long Short Term Memory) itself was already proposed in 1997 as an RNN algorithm to tackle vanishing gradient problem. (Exploding gradient problem is solved with a technique named gradient clipping, and this is easier than techniques for preventing vanishing gradient problems. I am also going to explain it in the next article.) After that some other techniques like introducing forget gate, peephole connections, were discovered, but basically it took some 20 years till LSTM got attentions like today. The reasons for that is lack of hardware and data sets, and that was also major reasons for the second AI winter.

In the 1990s, the mid of second AI winter, the Internet started prevailing for commercial uses. I think one of the iconic events in this time was the source codes WWW(World Wide Web) were announced in 1993. Some of you might still remember that you little by little became able to transmit more data online in this time. That means people came to get more and more access to various datasets in those days, which is indispensable for machine learning tasks.

After all, we could not get HAL 9000 by the end of 2001, but instead we got Xbox console.

3, Video game industry and GPU

Even though research on neural networks stagnated in the 1990s the same period witnessed an advance in the computation of massive parallel linear transformations, due to their need in fields such as image processing.

Computer graphics move or rotate in 3d spaces, and that is also linear transformations. When you think about a car moving in a city, it is convenient to place the car, buildings, and other objects on a fixed 3d space. But when you need to make computer graphics of scenes of the city from a view point inside the car, you put a moving origin point in the car and see the city. The spatial information of the city is calculated as vectors from the moving origin point. Of course this is also linear transformations. Of course I am not talking about a dot or simple figures moving in the 3d spaces. Computer graphics are composed of numerous plane panels, and each of them have at least three vertexes, and they move on 3d spaces. Depending on viewpoints, you need project the 3d graphics in 3d spaces on 2d spaces to display the graphics on devices. You need to calculate which part of the panel is projected to which pixel on the display, and that is called rasterization. Plus, in order to get photophotorealistic image, you need to think about how lights from light sources reflect on the panel and projected on the display. And you also have to put some textures on groups of panels. You might also need to change color spaces, which is also linear transformations.

My point is, in short, you really need to do numerous linear transformations in parallel in image processing.

When it comes to the use of CGI in movies, two pioneer movies were released during this time: Jurassic Park in 1993, and Toy Story in 1995. It is famous that Pixar used to be one of the departments in ILM(Industrial Light and Magic), founded by George Lucas, and Steve Jobs bought the department. Even though the members in Pixar had not even made a long feature film in their lives, after trial and errors, they made the first CGI animated feature movie. On the other hand, in order to acquire funds for the production of Schindler’s List(1993), Steven Spielberg took on Jurassic Park(1993), consequently changing the history of CGI through this “side job.”

*I think you have realized that George Lucas is mentioned almost everywhere in this article. His influences on technologies are not only limited to image processing, but also sound measuring system, nonlinear editing system. Photoshop was also originally developed under his company. I need another article series for this topic, but maybe not in Data Science Blog.

Considering that the first wire-frame computer graphics made and displayed by computers appeared in the scene of displaying the wire frame structure of Death Star in a war room, in Star Wars: A New Hope, the development of CGI was already astonishing at this time. But I think deep learning owe its development more to video game industry.

*I said that the Death Star scene is the first use of graphics made and DISPLAYED by computers, because I have to say one of the first graphics in movie MADE by computer dates back to the legendary title sequence of Vertigo(1958).

When it comes to 3D video games the processing unit has to constantly deal with real time commands from controllers. It is famous that GPU was originally specifically designed for plotting computer graphics. Video game market is the biggest in entertainment industry in general, and it is said that the quality of computer graphics have the strongest correlation with video games sales, therefore enhancing this quality is a priority for the video game console manufacturers.

One good example to see how much video games developed is comparing original Final Fantasy 7 and the remake one. The original one was released in 1997, the same year as when LSTM was invented. And recently the remake version of Final Fantasy 7 was finally released this year. The original one was also made with very big budget, and it was divided into three CD-ROMs. The original one was also very revolutionary given that the former ones of Final Fantasy franchise were all 2d video retro style video games. But still the computer graphics looks like polygons, and in almost all scenes the camera angle was fixed in the original one. On the other hand the remake one is very photorealistic and you can move the angle of the camera as you want while you play the video game.

There were also fierce battles by graphic processor manufacturers in computer video game market in the 1990s, but personally I think the release of Xbox console was a turning point in the development of GPU. To be concrete, Microsoft adopted a type of NV20 GPU for Xbox consoles, and that left some room of programmability for developers. The chief architect of NV20, which was released under the brand of GeForce3, said making major changes in the company’s graphic chips was very risky. But that decision opened up possibilities of uses of GPU beyond computer graphics.

I think that the idea of a programmable GPU provided other scientific fields with more visible benefits after CUDA was launched. And GPU gained its position not only in deep learning, but also many other fields including making super computers.

*When it comes to deep learning, even GPUs have strong rivals. TPU(Tensor Processing Unit) made by Google, is specialized for deep learning tasks, and have astonishing processing speed. And FPGA(Field Programmable Gate Array), which was originally invented customizable electronic circuit, proved to be efficient for reducing electricity consumption of deep learning tasks.

*I am not so sure about this GPU part. Processing unit, including GPU is another big topic, that is beyond my capacity to be honest. I would appreciate it if you could share your view and some references to confirm your opinion, on the comment section or via email.

*If you are interested you should see this video of game fans’ reactions to the announcement of Final Fantasy 7. This is the industry which grew behind the development of deep learning, and many fields where you need parallel computations owe themselves to the nerds who spent a lot of money for video games, including me.

*But ironically the engineers who invented the GPU said they did not play video games simply because they were busy. If you try to study the technologies behind video games, you would not have much time playing them. That is the reality.

We have seen that the in this second AI winter, Internet and GPU laid foundation of the next AI boom. But still the last piece of the puzzle is missing: let’s look at the breakthrough which solved the vanishing /exploding gradient problem of deep learning in the next section.

4, Pretraining of deep belief networks: “The Dawn of Deep Learning”

Some researchers say the invention of pretraining of deep belief network by Geoffrey Hinton was a breakthrough which put an end to the last AI winter. Deep belief networks are different type of networks from the neural networks we have discussed, but their architectures are similar to those of the neural networks. And it was also unknown how to train deep belief nets when they have several layers. Hinton discovered that training the networks layer by layer in advance can tackle vanishing gradient problems. And later it was discovered that you can do pretraining neural networks layer by layer with autoencoders.

*Deep belief network is beyond the scope of this article series. I have to talk about generative models, Boltzmann machine, and some other topics.

The pretraining techniques of neural networks is not mainstream anymore. But I think it is very meaningful to know that major deep learning techniques such as using ReLU activation functions, optimization with Adam, dropout, batch normalization, came up as more effective algorithms for deep learning after the advent of the pretraining techniques, and now we are in the third AI boom.

In the next next article we are finally going to work on LSTM. Specifically, I am going to offer a clearer guide to a well-made paper on LSTM, named “LSTM: A Search Space Odyssey.”

* I make study materials on machine learning, sponsored by DATANOMIQ. I do my best to make my content as straightforward but as precise as possible. I include all of my reference sources. If you notice any mistakes in my materials, including grammatical errors, please let me know (email: yasuto.tamura@datanomiq.de). And if you have any advice for making my materials more understandable to learners, I would appreciate hearing it.

Data Analytics and Mining for Dummies

July 2, 2020/in Data Mining, Data Science, Deep Learning, Predictive Analytics, Tool Introduction/by Sharma Srishti

Data Analytics and Mining is often perceived as an extremely tricky task cut out for Data Analysts and Data Scientists having a thorough knowledge encompassing several different domains such as mathematics, statistics, computer algorithms and programming. However, there are several tools available today that make it possible for novice programmers or people with no absolutely no algorithmic or programming expertise to carry out Data Analytics and Mining. One such tool which is very powerful and provides a graphical user interface and an assembly of nodes for ETL: Extraction, Transformation, Loading, for modeling, data analysis and visualization without, or with only slight programming is the KNIME Analytics Platform.

KNIME, or the Konstanz Information Miner, was developed by the University of Konstanz and is now popular with a large international community of developers. Initially KNIME was originally made for commercial use but now it is available as an open source software and has been used extensively in pharmaceutical research since 2006 and also a powerful data mining tool for the financial data sector. It is also frequently used in the Business Intelligence (BI) sector.

KNIME as a Data Mining Tool

KNIME is also one of the most well-organized tools which enables various methods of machine learning and data mining to be integrated. It is very effective when we are pre-processing data i.e. extracting, transforming, and loading data.

KNIME has a number of good features like quick deployment and scaling efficiency. It employs an assembly of nodes to pre-process data for analytics and visualization. It is also used for discovering patterns among large volumes of data and transforming data into more polished/actionable information.

Some Features of KNIME:

Free and open source
Graphical and logically designed
Very rich in analytics capabilities
No limitations on data size, memory usage, or functionalities
Compatible with Windows ,OS and Linux
Written in Java and edited with Eclipse.

A node is the smallest design unit in KNIME and each node serves a dedicated task. KNIME contains graphical, drag-drop nodes that require no coding. Nodes are connected with one’s output being another’s input, as a workflow. Therefore end-to-end pipelines can be built requiring no coding effort. This makes KNIME stand out, makes it user-friendly and make it accessible for dummies not from a computer science background.

KNIME workflow designed for graduate admission prediction

KNIME has nodes to carry out Univariate Statistics, Multivariate Statistics, Data Mining, Time Series Analysis, Image Processing, Web Analytics, Text Mining, Network Analysis and Social Media Analysis. The KNIME node repository has a node for every functionality you can possibly think of and need while building a data mining model. One can execute different algorithms such as clustering and classification on a dataset and visualize the results inside the framework itself. It is a framework capable of giving insights on data and the phenomenon that the data represent.

Some commonly used KNIME node groups include:

Input-Output or I/O: Nodes in this group retrieve data from or to write data to external files or data bases.
Data Manipulation: Used for data pre-processing tasks. Contains nodes to filter, group, pivot, bin, normalize, aggregate, join, sample, partition, etc.
Views: This set of nodes permit users to inspect data and analysis results using multiple views. This gives a means for truly interactive exploration of a data set.
Data Mining: In this group, there are nodes that implement certain algorithms (like K-means clustering, Decision Trees, etc.)

Comparison with other tools

The first version of the KNIME Analytics Platform was released in 2006 whereas Weka and R studio were released in 1997 and 1993 respectively. KNIME is a proper data mining tool whereas Weka and R studio are Machine Learning tools which can also do data mining. KNIME integrates with Weka to add machine learning algorithms to the system. The R project adds statistical functionalities as well. Furthermore, KNIME’s range of functions is impressive, with more than 1,000 modules and ready-made application packages. The modules can be further expanded by additional commercial features.

Simple RNN: the first foothold for understanding LSTM

June 17, 2020/in Artificial Intelligence, Data Science, Deep Learning, Machine Learning, Main Category, Mathematics/by Yasuto Tamura

*In this article “Densely Connected Layers” is written as “DCL,” and “Convolutional Neural Network” as “CNN.”

In the last article, I mentioned “When it comes to the structure of RNN, many study materials try to avoid showing that RNNs are also connections of neurons, as well as DCL or CNN.” Even if you manage to understand DCL and CNN, you can be suddenly left behind once you try to understand RNN because it looks like a different field. In the second section of this article, I am going to provide a some helps for more abstract understandings of DCL/CNN , which you need when you read most other study materials.

My explanation on this simple RNN is based on a chapter in a textbook published by Massachusetts Institute of Technology, which is also recommended in some deep learning courses of Stanford University.

First of all, you should keep it in mind that simple RNN are not useful in many cases, mainly because of vanishing/exploding gradient problem, which I am going to explain in the next article. LSTM is one major type of RNN used for tackling those problems. But without clear understanding forward/back propagation of RNN, I think many people would get stuck when they try to understand how LSTM works, especially during its back propagation stage. If you have tried climbing the mountain of understanding LSTM, but found yourself having to retreat back to the foot, I suggest that you read through this article on simple RNNs. It should help you to gain a solid foothold, and you would be ready for trying to climb the mountain again.

*This article is the second article of “A gentle introduction to the tiresome part of understanding RNN.”

1, A brief review on back propagation of DCL.

Simple RNNs are straightforward applications of DCL, but if you do not even have any ideas on DCL forward/back propagation, you will not be able to understand this article. If you more or less understand how back propagation of DCL works, you can skip this first section.

Deep learning is a part of machine learning. And most importantly, whether it is classical machine learning or deep learning, adjusting parameters is what machine learning is all about. Parameters mean elements of functions except for variants. For example when you get a very simple function $f(x)=a + bx + cx^2 + dx^3$ , then $x$ is a variant, and $a, b, c, d$ are parameters. In case of classical machine learning algorithms, the number of those parameters are very limited because they were originally designed manually. Such functions for classical machine learning is useful for features found by humans, after trial and errors(feature engineering is a field of finding such effective features, manually). You adjust those parameters based on how different the outputs(estimated outcome of classification/regression) are from supervising vectors(the data prepared to show ideal answers).

In the last article I said neural networks are just mappings, whose inputs are vectors, matrices, or sequence data. In case of DCLs, inputs are vectors. Then what’s the number of parameters ? The answer depends on the the number of neurons and layers. In the example of DCL at the right side, the number of the connections of the neurons is the number of parameters(Would you like to try to count them? At least I would say “No.”). Unlike classical machine learning you no longer need to do feature engineering, but instead you need to design networks effective for each task and adjust a lot of parameters.

*I think the hype of AI comes from the fact that neural networks find features automatically. But the reality is difficulty of feature engineering was just replaced by difficulty of designing proper neural networks.

It is easy to imagine that you need an efficient way to adjust those parameters, and the method is called back propagation (or just backprop). As long as it is about DCL backprop, you can find a lot of well-made study materials on that, so I am not going to cover that topic precisely in this article series. Simply putting, during back propagation, in order to adjust parameters of a layer you need errors in the next layer. And in order calculate the errors of the next layer, you need errors in the next next layer.

*You should not think too much about what the “errors” exactly mean. Such “errors” are defined in this context, and you will see why you need them if you actually write down all the mathematical equations behind backprops of DCL.

The red arrows in the figure shows how errors of all the neurons in a layer propagate backward to a neuron in last layer. The figure shows only some sets of such errors propagating backward, but in practice you have to think about all the combinations of such red arrows in the whole back propagation(this link would give you some ideas on how DCLs work).

These points are minimum prerequisites for continuing reading this RNN this article. But if you are planning to understand RNN forward/back propagation at an abstract/mathematical level that you can read academic papers, I highly recommend you to actually write down all the equations of DCL backprop. And if possible you should try to implement backprop of three-layer DCL.

2, Forward propagation of simple RNN

In fact the simple RNN which we are going to look at in this article has only three layers. From now on imagine that inputs of RNN come from the bottom and outputs go up. But RNNs have to keep information of earlier times steps during upcoming several time steps because as I mentioned in the last article RNNs are used for sequence data, the order of whose elements is important. In order to do that, information of the neurons in the middle layer of RNN propagate forward to the middle layer itself. Therefore in one time step of forward propagation of RNN, the input at the time step propagates forward as normal DCL, and the RNN gives out an output at the time step. And information of one neuron in the middle layer propagate forward to the other neurons like yellow arrows in the figure. And the information in the next neuron propagate forward to the other neurons, and this process is repeated. This is called recurrent connections of RNN.

*To be exact we are just looking at a type of recurrent connections. For example Elman RNNs have simpler recurrent connections. And recurrent connections of LSTM are more complicated.

Whether it is a simple one or not, basically RNN repeats this process of getting an input at every time step, giving out an output, and making recurrent connections to the RNN itself. But you need to keep the values of activated neurons at every time step, so virtually you need to consider the same RNNs duplicated for several time steps like the figure below. This is the idea of unfolding RNN. Depending on contexts, the whole unfolded DCLs with recurrent connections is also called an RNN.

In many situations, RNNs are simplified as below. If you have read through this article until this point, I bet you gained some better understanding of RNNs, so you should little by little get used to this more abstract, blackboxed way of showing RNN.

You have seen that you can unfold an RNN, per time step. From now on I am going to show the simple RNN in a simpler way, based on the MIT textbook which I recomment. The figure below shows how RNN propagate forward during two time steps $(t-1), (t)$ .

The input $\boldsymbol{x}^{(t-1)}$ at time step $(t-1)$ propagate forward as a normal DCL, and gives out the output $\hat{\boldsymbol{y}} ^{(t)}$ (The notation on the $\boldsymbol{y} ^{(t)}$ is called “hat,” and it means that the value is an estimated value. Whatever machine learning tasks you work on, the outputs of the functions are just estimations of ideal outcomes. You need to adjust parameters for better estimations. You should always be careful whether it is an actual value or an estimated value in the context of machine learning or statistics). But the most important parts are the middle layers.

*To be exact I should have drawn the middle layers as connections of two layers of neurons like the figure at the right side. But I made my figure closer to the chart in the MIT textbook, and also most other study materials show the combinations of the two neurons before/after activation as one neuron.

$\boldsymbol{a}^{(t)}$ is just linear summations of $\boldsymbol{x}^{(t)}$ (If you do not know what “linear summations” mean, please scroll this page a bit), and $\boldsymbol{h}^{(t)}$ is a combination of activated values of $\boldsymbol{a}^{(t)}$ and linear summations of $\boldsymbol{h}^{(t-1)}$ from the last time step, with recurrent connections. The values of $\boldsymbol{h}^{(t)}$ propagate forward in two ways. One is normal DCL forward propagation to $\hat{\boldsymbol{y}} ^{(t)}$ and $\boldsymbol{o}^{(t)}$ , and the other is recurrent connections to $\boldsymbol{h}^{(t+1)}$ .

These are equations for each step of forward propagation.

$\boldsymbol{a}^{(t)} = \boldsymbol{b} + \boldsymbol{W} \cdot \boldsymbol{h}^{(t-1)} + \boldsymbol{U} \cdot \boldsymbol{x}^{(t)}$
$\boldsymbol{h}^{(t)}= g(\boldsymbol{a}^{(t)})$
$\boldsymbol{o}^{(t)} = \boldsymbol{c} + \boldsymbol{V} \cdot \boldsymbol{h}^{(t)}$
$\hat{\boldsymbol{y}} ^{(t)} = f(\boldsymbol{o}^{(t)})$

*Please forgive me for adding some mathematical equations on this article even though I pledged not to in the first article. You can skip the them, but for some people it is on the contrary more confusing if there are no equations. In case you are allergic to mathematics, I prescribed some treatments below.

*Linear summation is a type of weighted summation of some elements. Concretely, when you have a vector $\boldsymbol{x}=(x_0, x_1, x_2)$ , and weights $\boldsymbol{w}=(w_0,w_1, w_2)$ , then $\boldsymbol{w}^T \cdot \boldsymbol{x} = w_0 \cdot x_0 + w_1 \cdot x_1 +w_2 \cdot x_2$ is a linear summation of $\boldsymbol{x}$ , and its weights are $\boldsymbol{w}$ .

*When you see a product of a matrix and a vector, for example a product of $\boldsymbol{W}$ and $\boldsymbol{v}$ , you should clearly make an image of connections between two layers of a neural network. You can also say each element of $\boldsymbol{u}}$ is a linear summations all the elements of $\boldsymbol{v}}$ , and $\boldsymbol{W}$ gives the weights for the summations.

A very important point is that you share the same parameters, in this case $\boldsymbol{\theta \in \{\boldsymbol{U}, \boldsymbol{W}, \boldsymbol{b}, \boldsymbol{V}, \boldsymbol{c} \}}$ , at every time step.

And you are likely to see this RNN in this blackboxed form.

3, The steps of back propagation of simple RNN

In the last article, I said “I have to say backprop of RNN, especially LSTM (a useful and mainstream type or RNN), is a monster of chain rules.” I did my best to make my PowerPoint on LSTM backprop straightforward. But looking at it again, the LSTM backprop part still looks like an electronic circuit, and it requires some patience from you to understand it. If you want to understand LSTM at a more mathematical level, understanding the flow of simple RNN backprop is indispensable, so I would like you to be patient while understanding this step (and you have to be even more patient while understanding LSTM backprop).

This might be a matter of my literacy, but explanations on RNN backprop are very frustrating for me in the points below.

Most explanations just show how to calculate gradients at each time step.
Most study materials are visually very poor.
Most explanations just emphasize that “errors are back propagating through time,” using tons of arrows, but they lack concrete instructions on how actually you renew parameters with those errors.

If you can relate to the feelings I mentioned above, the instructions from now on could somewhat help you. And I am going to share some study materials on simple RNNs in an external link so that you can gain a clear and mathematical understanding on how simple RNNs work.

Backprop of RNN , as long as you are thinking about simple RNNs, is not so different from that of DCLs. But you have to be careful about the meaning of errors in the context of RNN backprop. Back propagation through time (BPTT) is one of the major methods for RNN backprop, and I am sure most textbooks explain BPTT. But most study materials just emphasize that you need errors from all the time steps, and I think that is very misleading and confusing.

You need all the gradients to adjust parameters, but you do not necessarily need all the errors to calculate those gradients. Gradients in the context of machine learning mean partial derivatives of error functions (in this case $J$ ) with respect to certain parameters, and mathematically a gradient of $J$ with respect to $\boldsymbol{\theta \in \{\boldsymbol{U}, \boldsymbol{W}, \boldsymbol{b}^{(t)}, \boldsymbol{V}, \boldsymbol{c} \}}$ is denoted as $( \frac{\partial J}{\partial \boldsymbol{\theta}} )$ . And another confusing point in many textbooks, including the MIT one, is that they give an impression that parameters depend on time steps. For example some study materials use notations like $\frac{\partial J}{\partial \boldsymbol{\theta}^{(t)}}$ , and I think this gives an impression that this is a gradient with respect to the parameters at time step $(t)$ . In my opinion this gradient rather should be written as $( \frac{\partial J}{\partial \boldsymbol{\theta}} )^{(t)}$ . But many study materials denote gradients of those errors in the former way, so from now on let me use the notations which you can see in the figures in this article.

In order to calculate the gradient $\frac{\partial J}{\partial \boldsymbol{x}^{(t)}}$ you need errors from time steps $s (s \geq t) \quad$ (as you can see in the figure, in order to calculate a gradient in a colored frame, you need all the errors in the same color).

*Another confusing point is that the $\frac{\partial J}{\partial \boldsymbol{\ast ^{(t)}}}, \boldsymbol{\ast} \in \{\boldsymbol{a}^{(t)}, \boldsymbol{h}^{(t)}, \boldsymbol{o}^{(t)}, \dots \}$ are correct notations, because $\boldsymbol{\ast}$ are values of neurons after forward propagation. They depend on time steps, and these are very values which I have been calling “errors.” That is why parameters do not depend on time steps, whereas errors depend on time steps.

As I mentioned before, you share the same parameters at every time step. Again, please do not assume that parameters are different from time step to time step. It is gradients/errors (you need errors to calculate gradients) which depend on time step. And after calculating errors at every time step, you can finally adjust parameters one time, and that’s why this is called “back propagation through time.” (It is easy to imagine that this method can be very inefficient. If the input is the whole text on a Wikipedia link, you need to input all the sentences in the Wikipedia text to renew parameters one time. To solve this problem there is a backprop method named “truncated BPTT,” with which you renew parameters based on a part of a text. )

And after calculating those gradients $\frac{\partial J}{\partial \boldsymbol{\theta}^{(t)}}$ you can take a summation of them: $\frac{\partial J}{\partial \boldsymbol{\theta}}=\sum_{t=0}^{t=\tau}{\frac{\partial J}{\partial \boldsymbol{\theta}^{(t)}}}$ . With this gradient $\frac{\partial J}{\partial \boldsymbol{\theta}}$ , you can finally renew the value of $\boldsymbol{\theta}$ one time.

At the beginning of this article I mentioned that simple RNNs are no longer for practical uses, and that comes from exploding/vanishing problem of RNN. This problem was one of the reasons for the AI winter which lasted for some 20 years. In the next article I am going to write about LSTM, a fancier type of RNN, in the context of a history of neural network history.

Severity of lockdowns and how they are reflected in mobility data

June 16, 2020/in Data Science, Data Science News, Insights/by Emilia Cheladze

The global spread of the SARS-CoV-2 at the beginning of March 2020 forced majority of countries to introduce measures to contain the virus. The governments found themselves facing a very difficult tradeoff between limiting the spread of the virus and bearing potentially catastrophic economical costs of a lockdown. Notably, considering the level of globalization today, the response of countries varied a lot in severity and response latency. In the overwhelming amount of media and social media information feed a lot of misinformation and anecdotal evidence surfaced and remained in people’s mind. In this article, I try to have a more systematic view on the topics of severity of response from governments and change in people’s mobility due to the pandemic.

I want to look at several countries with different approach to restraining the spread of the virus. I will look at governmental regulations, when, and how they were introduced. For that I am referring to an index called Oxford COVID-19 Government Response Tracker (OxCGRT)[1]. The OxCGRT follows, records, and rates the actions taken by governments, that are available publicly. However, looking just at the regulations and taking them for granted does not provide that we have the whole picture. Therefore, equally interesting is the investigation of how the recommended levels of self-isolation and social distancing is reflected in the mobility data and we will look at it first.

The mobility dataset

The mobility data used in this article was collected by Google and made freely accessible[2]. The data reflects how the number of visits and their length changed as compared to a baseline from before the pandemic. The baseline is the median value for the corresponding day of the week in the period from 3.01.2020 – 6.02.2020. The dataset contains data in six categories. Here we look at only 4 of them: public transport stations, places of residence, workplaces, and retail/recreation (including shopping centers, libraries, gastronomy, culture). The analysis intentionally omits parks (public beaches, gardens etc.) and grocery/pharmacy category. Mobility in parks is excluded due to huge weather change confound. The baseline was created in winter and increased/decreased (depending on the hemisphere) activity in parks is expected as the weather changes. It would be difficult to detangle tis change from the change caused by the pandemic without referring to a different baseline. The grocery shops and pharmacies are excluded because the measures regarding the shopping were very similar across the countries.

Amid the Covid-19 pandemic a lot of anecdotal information surfaced, that some countries, like Sweden, acted completely against the current by not introducing a lockdown. It was reported that there were absolutely no restrictions and Sweden can be basically treated as a control group for comparing the different approaches to lockdown on the spread of the coronavirus. Looking at the mobility data (below), we can see however, that there was a change in the mobility of Swedish citizens in comparison to the baseline.

Fig. 1 Moving average (+/- 6 days) of the mobility data in Sweden in four categories.

Looking at the change in mobility in Sweden, we can see that the change in the residential areas is small, but it is indicating some change in behavior. A change in the retail and recreational sector is more noticeable. Most interestingly it is approaching the baseline levels at the beginning of June. The most substantial changes, however, are in the workplaces and transit categories. They are also much slower to come back to the baseline, although a trend in that direction starts to be visible.

Next, let us have a look at the change in mobility in selected countries, separately for each category. Here, I compare Germany, Sweden, Italy, and New Zealand. (To see the mobility data for other countries visit https://covid19.datanomiq.de/#section-mobility).

Fig. 2 Moving average (+/- 6 days) of the mobility data.

Looking at the data, we can see that the change in mobility in Germany and Sweden was somewhat similar in orders of magnitude, in comparison to changes in mobility in countries like Italy and New Zealand. Without a doubt, the behavior in Sweden changed the least from the baseline in all the categories. Nevertheless, claiming that people’s reaction to the pandemic in Sweden in Germany were polar opposites is not necessarily correct. The biggest discrepancy between Sweden and Germany is in the retail and recreation sector out of all categories presented. The changes in Italy and New Zealand reached very comparable levels, but in New Zealand they seem to be much more dynamic, especially in approaching the baseline levels again.

The government response dataset

Oxford COVID-19 Government Response Tracker records regulations from number of countries, rates them and categorizes into a few indices. The number between 1 and 100 reflects the level of the action taken by a government. Here, I focus on the Containment and Health sub-index that includes 11 indicators from categories: containment and closure policies and health system policies[3]. The actions included in the index are for example: school and workplace closing, restrictions on public events, travel restrictions, public information campaigns, testing policy and contact tracing.

Below, we look at a plot with the Containment and Health sub-index value for the four aforementioned countries. Data and documentation is available here[4]

Fig. 3 Oxford COVID-19 Government Response Tracker, the Containment and Health sub-index.

Here the difference between Sweden and the other countries that we are looking at becomes more apparent. Nevertheless, the Swedish government did take some measures in order to condemn the spread of the SARS-CoV-2. At the highest, the index reached value 45 points in Sweden, 73 in Germany, 92 in Italy and 94 in New Zealand. In all these countries except for Sweden the index started dropping again, while the drop is the most dynamic in New Zealand and the index has basically reached the level of Sweden.

Conclusions

As we have hopefully seen, the response to the COVID-19 pandemic from governments differed substantially, as well as the resulting change in mobility behavior of the inhabitants did. However, the discrepancies were probably not as big as reported in the media.

The overwhelming presence of the social media could have blown some of the mentioned differences out of proportion. For example, the discrepancy in the mobility behavior between Sweden and Germany was biggest in recreation sector, that involves cafes, restaurants, cultural resorts, and shopping centers. It is possible, that those activities were the ones that people in lockdown missed the most. Looking at Swedes, who were participating in them it was easy to extrapolate on the overall landscape of the response to the virus in the country.

It is very hard to say which of the world country’s approach will bring the best effects for the people’s well-being and the economies. The ongoing pandemic will remain a topic of extensive research for many years to come. We will (most probably) eventually find out which approach to the lockdown was the most optimal (or at least come close to finding out). For the time being, it is however important to remember that there are many factors in play and looking into one type of data might be misleading. Comparing countries with different history, weather, political and economic climate, or population density might be misleading as well. But it is still more insightful than not looking into the data at all.

[1] Hale, Thomas, Sam Webster, Anna Petherick, Toby Phillips, and Beatriz Kira (2020). Oxford COVID-19 Government Response Tracker, Blavatnik School of Government. Data use policy: Creative Commons Attribution CC BY standard.

[2] Google LLC “Google COVID-19 Community Mobility Reports”. https://www.google.com/covid19/mobility/ retrived: 04.06.2020

[3] See documentation https://github.com/OxCGRT/covid-policy-tracker/tree/master/documentation

[4] https://github.com/OxCGRT/covid-policy-tracker retrieved on 04.06.2020

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The Data Science and Engineering Process in PLM.

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1. Chain rules

2. Chain rules in LSTM

3. How LSTMs tackle exploding/vanishing gradients problems

1. Preface

2. Why LSTM?

3. How to display LSTM

4. Forward propagation of LSTM in “electronic circuit type”

5. Space Odyssey type

Challenges for Non-profits and Data Science

How Can Data Do Social Good?

1, First AI boom

2, Second AI boom/winter

3, Video game industry and GPU

4, Pretraining of deep belief networks: “The Dawn of Deep Learning”

1, A brief review on back propagation of DCL.

2, Forward propagation of simple RNN

3, The steps of back propagation of simple RNN

The mobility dataset

The government response dataset

Conclusions

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