Attribution Models in Marketing

Attribution Models

A Business and Statistical Case

INTRODUCTION

A desire to understand the causal effect of campaigns on KPIs

Advertising and marketing costs represent a huge and ever more growing part of the budget of companies. Studies have found out this share is as high as 10% and increases with the size of companies (CMO study by American Marketing Association and Duke University, 2017). Measuring precisely the impact of a specific marketing campaign on the sales of a company is a critical step towards an efficient allocation of this budget. Would the return be higher for an euro spent on a Facebook ad, or should we better spend it on a TV spot? How much should I spend on Twitter ads given the volume of sales this channel is responsible for?

Attribution Models have lately received great attention in Marketing departments to answer these issues. The transition from offline to online marketing methods has indeed permitted the collection of multiple individual data throughout the whole customer journey, and  allowed for the development of user-centric attribution models. In short, Attribution Models use the information provided by Tracking technologies such as Google Analytics or Webtrekk to understand customer journeys from the first click on a Facebook ad to the final purchase and adequately ponderate the different marketing campaigns encountered depending on their responsibility in the final conversion.

Issues on Causal Effects

A key question then becomes: how to declare a channel is responsible for a purchase? In other words, how can we isolate the causal effect or incremental value of a campaign ?

          1. A/B-Tests

One method to estimate the pure impact of a campaign is the design of randomized experiments, wherein a control and treated groups are compared.  A/B tests belong to this broad category of randomized methods. Provided the groups are a priori similar in every aspect except for the treatment received, all subsequent differences may be attributed solely to the treatment. This method is typically used in medical studies to assess the effect of a drug to cure a disease.

Main practical issues regarding Randomized Methods are:

  • Assuring that control and treated groups are really similar before treatment. Uually a random assignment (i.e assuring that on a relevant set of observable variables groups are similar) is realized;
  • Potential spillover-effects, i.e the possibility that the treatment has an impact on the non-treated group as well (Stable unit treatment Value Assumption, or SUTVA in Rubin’s framework);
  • The costs of conducting such an experiment, and especially the costs linked to the deliberate assignment of individuals to a group with potentially lower results;
  • The number of such experiments to design if multiple treatments have to be measured;
  • Difficulties taking into account the interaction effects between campaigns or the effect of spending levels. Indeed, usually A/B tests are led by cutting off temporarily one campaign entirely and measuring the subsequent impact on KPI’s compared to the situation where this campaign is maintained;
  • The dynamical reproduction of experiments if we assume that treatment effects may change over time.

In the marketing context, multiple campaigns must be tested in a dynamical way, and treatment effect is likely to be heterogeneous among customers, leading to practical issues in the lauching of A/B tests to approximate the incremental value of all campaigns. However, sites with a lot of traffic and conversions can highly benefit from A/B testing as it provides a scientific and straightforward way to approximate a causal impact. Leading companies such as Uber, Netflix or Airbnb rely on internal tools for A/B testing automation, which allow them to basically test any decision they are about to make.

References:

Books:

Experiment!: Website conversion rate optimization with A/B and multivariate testing, Colin McFarland, ©2013 | New Riders  

A/B testing: the most powerful way to turn clicks into customers. Dan Siroker, Pete Koomen; Wiley, 2013.

Blogs:

https://eng.uber.com/xp

https://medium.com/airbnb-engineering/growing-our-host-community-with-online-marketing-9b2302299324

Study:

https://cmosurvey.org/wp-content/uploads/sites/15/2018/08/The_CMO_Survey-Results_by_Firm_and_Industry_Characteristics-Aug-2018.pdf

        2. Attribution models

Attribution Models do not demand to create an experimental setting. They take into account existing data and derive insights from the variability of customer journeys. One key difficulty is then to differentiate correlation and causality in the links observed between the exposition to campaigns and purchases. Indeed, selection effects may bias results as exposure to campaigns is usually dependant on user-characteristics and thus may not be necessarily independant from the customer’s baseline conversion probabilities. For example, customers purchasing from a discount price comparison website may be intrinsically different from customers buying from FB ad and this a priori difference may alone explain post-exposure differences in purchasing bahaviours. This intrinsic weakness must be remembered when interpreting Attribution Models results.

                          2.1 General Issues

The main issues regarding the implementation of Attribution Models are linked to

  • Causality and fallacious reasonning, as most models do not take into account the aforementionned selection biases.
  • Their difficult evaluation. Indeed, in almost all attribution models (except for those based on classification, where the accuracy of the model can be computed), the additionnal value brought by the use of a given attribution models cannot be evaluated using existing historical data. This additionnal value can only be approximated by analysing how the implementation of the conclusions of the attribution model have impacted a given KPI.
  • Tracking issues, leading to an uncorrect reconstruction of customer journeys
    • Cross-device journeys: cross-device issue arises from the use of different devices throughout the customer journeys, making it difficult to link datapoints. For example, if a customer searches for a product on his computer but later orders it on his mobile, the AM would then mistakenly consider it an order without prior campaign exposure. Though difficult to measure perfectly, the proportion of cross-device orders can approximate 20-30%.
    • Cookies destruction makes it difficult to track the customer his the whole journey. Both regulations and consumers’ rising concerns about data privacy issues mitigate the reliability and use of cookies.1 – From 2002 on, the EU has enacted directives concerning privacy regulation and the extended use of cookies for commercial targeting purposes, which have highly impacted marketing strategies, such as the ‘Privacy and Electronic Communications Directive’ (2002/58/EC). A research was conducted and found out that the adoption of this ‘Privacy Directive’ had led to 64% decrease in advertising methods compared to the rest of the world (Goldfarb et Tucker (2011)). The effect was stronger for generalized sites (Yahoo) than for specialized sites.2 – Users have grown more and more conscious of data privacy issues and have adopted protective measures concerning data privacy, such as automatic destruction of cookies after a session is ended, or simply giving away less personnal information (Goldfarb et Tucker (2012) ) .Valuable user information may be lost, though tracking technologies evolution have permitted to maintain tracking by other means. This issue may be particularly important in countries highly concerned with data privacy issues such as Germany.
    • Offline/Online bridge: an Attribution Model should take into account all campaigns to draw valuable insights. However, the exposure to offline campaigns (TV, newspapers) are difficult to track at the user level. One idea to tackle this issue would be to estimate the proportion of conversions led by offline campaigns through AB testing and deduce this proportion from the credit assigned to the online campaigns accounted for in the Attribution Model.
    • Touch point information available: clicks are easy to follow but irrelevant to take into account the influence of purely visual campaigns such as display ads or video.

                          2.2 Today’s main practices

Two main families of Attribution Models exist:

  • Rule-Based Attribution Models, which have been used for in the last decade but from which companies are gradualy switching.

Attribution depends on the individual journeys that have led to a purchase and is solely based on the rank of the campaign in the journey. Some models focus on a single touch points (First Click, Last Click) while others account for multi-touch journeys (Bathtube, Linear). It can be calculated at the customer level and thus doesn’t require large amounts of data points. We can distinguish two sub-groups of rule-based Attribution Models:

  • One Touch Attribution Models attribute all credit to a single touch point. The First-Click model attributes all credit for a converion to the first touch point of the customer journey; last touch attributes all credit to the last campaign.
  • Multi-touch Rule-Based Attribution Models incorporate information on the whole customer journey are thus an improvement compared to one touch models. To this family belong Linear model where credit is split equally between all channels, Bathtube model where 40% of credit is given to first and last clicks and the remaining 20% is distributed equally between the middle channels, or time-decay models where credit assigned to a click diminishes as the time between the click and the order increases..

The main advantages of rule-based models is their simplicity and cost effectiveness. The main problems are:

– They are a priori known and can thus lead to optimization strategies from competitors
– They do not take into account aggregate intelligence on customer journeys and actual incremental values.
– They tend to bias (depending on the model chosen) channels that are over-represented at the beggining or end of the funnel, according to theoretical assumptions that have no observationnal back-ups.

  • Data-Driven Attribution Models

These models take into account the weaknesses of rule-based models and make a relevant use of available data. Being data-driven, following attribution models cannot be computed using single user level data. On the contrary values are calculated through data aggregation and thus require a certain volume of customer journey information.

References:

https://dspace.mit.edu/handle/1721.1/64920

 

        3. Data-Driven Attribution Models in practice

                          3.1 Issues

Several issues arise in the computation of campaigns individual impact on a given KPI within a data-driven model.

  • Selection biases: Exposure to certain types of advertisement is usually highly correlated to non-observable variables which are in turn correlated to consumption practices. Differences in the behaviour of users exposed to different campaigns may thus only be driven by core differences in conversion probabilities between groups whether than by the campaign effect.
  • Complementarity: it may be that campaigns A and B only have an effect when combined, so that measuring their individual impact would lead to misleading conclusions. The model could then try to assess the effect of combinations of campaigns on top of the effect of individual campaigns. As the number of possible non-ordered combinations of k campaigns is 2k, it becomes clear that inclusing all possible combinations would however be time-consuming.
  • Order-sensitivity: The effect of a campaign A may depend on the place where it appears in the customer journey, meaning the rank of a campaign and not merely its presence could be accounted for in the model.
  • Relative Order-sensitivity: it may be that campaigns A and B only have an effect when one is exposed to campaign A before campaign B. If so, it could be useful to assess the effect of given combinations of campaigns as well. And this for all campaigns, leading to tremendous numbers of possible combinations.
  • All previous phenomenon may be present, increasing even more the potential complexity of a comprehensive Attribution Model. The number of all possible ordered combination of k campaigns is indeed :

 

                          3.2 Main models

                                  A) Logistic Regression and Classification models

If non converting journeys are available, Attribition Model can be shaped as a simple classification issue. Campaign types or campaigns combination and volume of campaign types can be included in the model along with customer or time variables. As we are interested in inference (on campaigns effect) whether than prediction, a parametric model should be used, such as Logistic Regression. Non paramatric models such as Random Forests or Neural Networks can also be used though the interpretation of campaigns value would be more difficult to derive from the model results.

A common pitfall is the usual issue of spurious correlations on one hand and the correct interpretation of coefficients in business terms.

An advantage if the possibility to evaluate the relevance of the model using common model validation methods to evaluate its predictive power (validation set \ AUC \pseudo R squared).

                                  B) Shapley Value

Theory

The Shapley Value is based on a Game Theory framework and is named after its creator, the Nobel Price Laureate Lloyd Shapley. Initially meant to calculate the marginal contribution of players in cooperative games, the model has received much attention in research and industry and has lately been applied to marketing issues. This model is typically used by Google Adords and other ad bidding vendors. Campaigns or marketing channels are in this model seen as compementary players looking forward to increasing a given KPI.
Contrarily to Logistic Regressions, it is a non-parametric model. Contrarily to Markov Chains, all results are built using existing journeys, and not simulated ones.

Channels are considered to enter the game sequentially under a certain joining order. Shapley value try to The Shapley value of channel i is the weighted sum of the marginal values that channel i adds to all possible coalitions that don’t contain channel i.
In other words, the main logic is to analyse the difference of gains when a channel i is added after a coalition Ck of k channels, k<=n. We then sum all the marginal contributions over all possible ordered combination Ck of all campaigns excluding i, with k<=n-1.

Subsets framework

A first an most usual way to compute the Shapley Vaue is to consider that when a channel enters coalition, its additionnal value is the same irrelevant of the order in which previous channels have appeared. In other words, journeys (A>B>C) and (B>A>C) trigger the same gains.
Shapley value is computed as the gains associated to adding a channel i to a subset of channels, weighted by the number of (ordered) sequences that the (unordered) subset represents, summed up on all possible subsets of the total set of campaigns where the channel i is not present.
The Shapley value of the channel 𝑥𝑗 is then:

where |S| is the number of campaigns of a coalition S and the sum extends over all subsets S that do not not contain channel j. 𝜈(𝑆)  is the value of the coalition S and 𝜈(𝑆 ∪ {𝑥𝑗})  the value of the coalition formed by adding 𝑥𝑗 to coalition S. 𝜈(𝑆 ∪ {𝑥𝑗}) − 𝜈(𝑆) is thus the marginal contribution of channel 𝑥𝑗 to the coalition S.

The formula can be rewritten and understood as:

This method is convenient when data on the gains of on all possible permutations of all unordered k subsets of the n campaigns are available. It is also more convenient if the order of campaigns prior to the introduction of a campaign is thought to have no impact.

Ordered sequences

Let us define 𝜈((A>B)) as the value of the sequence A then B. What is we let 𝜈((A>B)) be different from 𝜈((B>A)) ?
This time we would need to sum over all possible permutation of the S campaigns present before  𝑥𝑗 and the N-(S+1) campaigns after 𝑥𝑗. Doing so we will sum over all possible orderings (i.e all permutations of the n campaigns of the grand coalition containing all campaigns) and we can remove the permutation coefficient s!(p-s+1)!.

This method is convenient when the order of channels prior to and after the introduction of another channel is assumed to have an impact. It is also necessary to possess data for all possible permutations of all k subsets of the n campaigns, and not only on all (unordered) k-subsets of the n campaigns, k<=n. In other words, one must know the gains of A, B, C, A>B, B>A, etc. to compute the Shapley Value.

Differences between the two approaches

We simulate an ordered case where the value for each ordered sequence k for k<=3 is known. We compare it to the usual Shapley value calculated based on known gains of unordered subsets of campaigns. So as to compare relevant values, we have built the gains matrix so that the gains of a subset A, B i.e  𝜈({B,A}) is the average of the gains of ordered sequences made up with A and B (assuming the number of journeys where A>B equals the number of journeys where B>A, we have 𝜈({B,A})=0.5( 𝜈((A>B)) + 𝜈((B>A)) ). We let the value of the grand coalition be different depending on the order of campaigns-keeping the constraints that it averages to the value used for the unordered case.

Note: mvA refers to the marginal value of A in a given sequence.
With traditionnal unordered coalitions:

With ordered sequences used to compute the marginal values:

 

We can see that the two approaches yield very different results. In the unordered case, the Shapley Value campaign C is the highest, culminating at 20, while A and B have the same Shapley Value mvA=mvB=15. In the ordered case, campaign A has the highest Shapley Value and all campaigns have different Shapley Values.

This example illustrates the inherent differences between the set and sequences approach to Shapley values. Real life data is more likely to resemble the ordered case as conversion probabilities may for any given set of campaigns be influenced by the order through which the campaigns appear.

Advantages

Shapley value has become popular in allocation problems in cooperative games because it is the unique allocation which satisfies different axioms:

  • Efficiency: Shaple Values of all channels add up to the total gains (here, orders) observed.
  • Symmetry: if channels A and B bring the same contribution to any coalition of campaigns, then their Shapley Value i sthe same
  • Null player: if a channel brings no additionnal gains to all coalitions, then its Shapley Value is zero
  • Strong monotony: the Shapley Value of a player increases weakly if all its marginal contributions increase weakly

These properties make the Shapley Value close to what we intuitively define as a fair attribution.

Issues

  • The Shapley Value is based on combinatory mathematics, and the number of possible coalitions and ordered sequences becomes huge when the number of campaigns increases.
  • If unordered, the Shapley Value assumes the contribution of campaign A is the same if followed by campaign B or by C.
  • If ordered, the number of combinations for which data must be available and sufficient is huge.
  • Channels rarely present or present in long journeys will be played down.
  • Generally, gains are supposed to grow with the number of players in the game. However, it is plausible that in the marketing context a journey with a high number of channels will not necessarily bring more orders than a journey with less channels involved.

References:

R package: GameTheoryAllocation

Article:
Zhao & al, 2018 “Shapley Value Methods for Attribution Modeling in Online Advertising “
https://link.springer.com/content/pdf/10.1007/s13278-017-0480-z.pdf
Courses: https://www.lamsade.dauphine.fr/~airiau/Teaching/CoopGames/2011/coopgames-7%5b8up%5d.pdf
Blogs: https://towardsdatascience.com/one-feature-attribution-method-to-supposedly-rule-them-all-shapley-values-f3e04534983d

                                  B) Markov Chains

Markov Chains are used to model random processes, i.e events that occur in a sequential manner and in such a way that the probability to move to a certain state only depends on the past steps. The number of previous steps that are taken into account to model the transition probability is called the memory parameter of the sequence, and for the model to have a solution must be comprised between 0 and 4. A Markov Chain process is thus defined entirely by its Transition Matrix and its initial vector (i.e the starting point of the process).

Markov Chains are applied in many scientific fields. Typically, they are used in weather forecasting, with the sequence of Sunny and Rainy days following a Markov Process of memory parameter 0, so that for each given day the probability that the next day will be rainy or sunny only depends on the weather of the current day. Other applications can be found in sociology to understand the dynamics of social classes intergenerational reproduction. To get more both mathematical and applied illustration, I recommend the reading of this course.

In the marketing context, Markov Chains are an interesting way to model the conversion funnel. To go from the from the Markov Model to the Attribution logic, we calculate the Removal Effect of each channel, i.e the difference in conversions that happen if the channel is removed. Please read below for an introduction to the methodology.

The first step in a Markov Chains Attribution Model is to build the transition matrix that captures the transition probabilities between the campaigns accross existing customer journeys. This Matrix is to be read as a “From state A to state B” table, from the left to the right. A first difficulty is finding the right memory parameter to use. A large memory parameter would allow to take more into account interraction effects within the conversion funnel but would lead to increased computationnal time, a non-readable transition matrix, and be more sensitive to noisy data. Please note that this transition matrix provides useful information on the conversion funnel and on the relationships between campaigns and can be used as such as an analytical tool. I suggest the clear and easily R code which can be found here or here.

Here is an illustration of a Markov Chain with memory Parameter of 0: the probability to go to a certain campaign B in the next step only depend on the campaign we are currently at:

The associated Transition Matrix is then (with null probabilities left as Blank):

The second step is  to compute the actual responsibility of a channel in total conversions. As mentionned above, the main philosophy to do so is to calculate the Removal Effect of each channel, i.e the changes in the number of conversions when a channel is entirely removed. All customer journeys which went through this channel are settled out to be unsuccessful. This calculation is done by applying the transition matrix with and without the removed channels to an initial vector that contains the number of desired simulations.

Building on our current example, we can then settle an initial vector with the desired number of simulations, e.g 10 000:

 

It is possible at this stage to add a constraint on the maximum number of times the matrix is applied to the data, i.e on the maximal number of campaigns a simulated journey is allowed to have.

Advantages

  • The dynamic journey is taken into account, as well as the transition between two states. The funnel is not assumed to be linear.
  • It is possile to build a conversion graph that maps the customer journey provides valuable insights.
  • It is possible to evaluate partly the accuracy of the Attribution Model based on Markov Chains. It is for example possible to see how well the transition matrix help predict the future by analysing the number of correct predictions at any given step over all sequences.

Disadvantages

  • It can be somewhat difficult to set the memory parameter. Complementarity effects between channels are not well taken into account if the memory is low, but a parameter too high will lead to over-sensitivity to noise in the data and be difficult to implement if customer journeys tend to have a number of campaigns below this memory parameter.
  • Long journeys with different channels involved will be overweighted, as they will count many times in the Removal Effect.  For example, if there are n-1 channels in the customer journey, this journey will be considered as failure for the n-1 channel-RE. If the volume effects (i.e the impact of the overall number of channels in a journey, irrelevant from their type° are important then results may be biased.

References:

R package: ChannelAttribution

Git:

https://github.com/MatCyt/Markov-Chain/blob/master/README.md

Course:

https://www.ssc.wisc.edu/~jmontgom/markovchains.pdf

Article:

“Mapping the Customer Journey: A Graph-Based Framework for Online Attribution Modeling”; Anderl, Eva and Becker, Ingo and Wangenheim, Florian V. and Schumann, Jan Hendrik, 2014. Available at SSRN: https://ssrn.com/abstract=2343077 or http://dx.doi.org/10.2139/ssrn.2343077

“Media Exposure through the Funnel: A Model of Multi-Stage Attribution”, Abhishek & al, 2012

“Multichannel Marketing Attribution Using Markov Chains”, Kakalejčík, L., Bucko, J., Resende, P.A.A. and Ferencova, M. Journal of Applied Management and Investments, Vol. 7 No. 1, pp. 49-60.  2018

Blogs:

https://analyzecore.com/2016/08/03/attribution-model-r-part-1

https://analyzecore.com/2016/08/03/attribution-model-r-part-2

                          3.3 To go further: Tackling selection biases with Quasi-Experiments

Exposure to certain types of advertisement is usually highly correlated to non-observable variables. Differences in the behaviour of users exposed to different campaigns may thus only be driven by core differences in converison probabilities between groups whether than by the campaign effect. These potential selection effects may bias the results obtained using historical data.

Quasi-Experiments can help correct this selection effect while still using available observationnal data.  These methods recreate the settings on a randomized setting. The goal is to come as close as possible to the ideal of comparing two populations that are identical in all respects except for the advertising exposure. However, populations might still differ with respect to some unobserved characteristics.

Common quasi-experimental methods used for instance in Public Policy Evaluation are:

  • Discontinuity Regressions
  • Matching Methods, such as Exact Matching,  Propensity-score matching or k-nearest neighbourghs.

References:

Article:

“Towards a digital Attribution Model: Measuring the impact of display advertising on online consumer behaviour”, Anindya Ghose & al, MIS Quarterly Vol. 40 No. 4, pp. 1-XX, 2016

https://pdfs.semanticscholar.org/4fa6/1c53f281fa63a9f0617fbd794d54911a2f84.pdf

        4. First Steps towards a Practical Implementation

Identify key points of interests

  • Identify the nature of touchpoints available: is the data based on clicks? If so, is there a way to complement the data with A/B tests to measure the influence of ads without clicks (display, video) ? For example, what happens to sales when display campaign is removed? Analysing this multiplier effect would give the overall responsibility of display on sales, to be deduced from current attribution values given to click-based channels. More interestingly, what is the impact of the removal of display campaign on the occurences of click-based campaigns ? This would give us an idea of the impact of display ads on the exposure to each other campaigns, which would help correct the attribution values more precisely at the campaign level.
  • Define the KPI to track. From a pure Marketing perspective, looking at purchases may be sufficient, but from a financial perspective looking at profits, though a bit more difficult to compute, may drive more interesting results.
  • Define a customer journey. It may seem obvious, but the notion needs to be clarified at first. Would it be defined by a time limit? If so, which one? Does it end when a conversion is observed? For example, if a customer makes 2 purchases, would the campaigns he’s been exposed to before the first order still be accounted for in the second order? If so, with a time decay?
  • Define the research framework: are we interested only in customer journeys which have led to conversions or in all journeys? Keep in mind that successful customer journeys are a non-representative sample of customer journeys. Models built on the analysis of biased samples may be conservative. Take an extreme example: 80% of customers who see campaign A buy the product, VS 1% for campaign B. However, campaign B exposure is great and 100 Million people see it VS only 1M for campaign A. An Attribution Model based on successful journeys will give higher credit to campaign B which is an auguable conclusion. Taking into account costs per campaign (in the case where costs are calculated by clicks) may of course tackle this issue partly, as campaign A could then exhibit higher returns, but a serious fallacious reasonning is at stake here.

Analyse the typical customer journey    

  • Performing a duration analysis on the data may help you improve the definition of the customer journey to be used by your organization. After which days are converison probabilities null? Should we consider the effect of campaigns disappears after x days without orders? For example, if 99% of orders are placed in the 30 days following a first click, it might be interesting to define the customer journey as a 30 days time frame following the first oder.
  • Look at the distribution of the number of campaigns in a typical journey. If you choose to calculate the effect of campaigns interraction in your Attribution Model, it may indeed help you determine the maximum number of campaigns to be included in a combination. Indeed, you may not need to assess the impact of channel combinations with above than 4 different channels if 95% of orders are placed after less then 4 campaigns.
  • Transition matrixes: what if a campaign A systematically leads to a campaign B? What happens if we remove A or B? These insights would give clues to ask precise questions for a latter AB test, for example to find out if there is complementarity between channels A and B – (implying none should be removed) or mere substitution (implying one can be given up).
  • If conversion rates are available: it can be interesting to perform a survival analysis i.e to analyse the likelihood of conversion based on duration since first click. This could help us excluse potential outliers or individuals who have very low conversion probabilities.

Summary

Attribution is a complex topic which will probably never be definitively solved. Indeed, a main issue is the difficulty, or even impossibility, to evaluate precisely the accuracy of the attribution model that we’ve built. Attribution Models should be seen as a good yet always improvable approximation of the incremental values of campaigns, and be presented with their intrinsinc limits and biases.

Was der BREXIT für die Cloud-Strategie bedeutet

Datensouveränität wird nach dem Brexit eine der größten Herausforderungen für Unternehmen sein. Geschäftsführer sind sich der Bedeutung dessen bewusst und fürchten die Gefahr eines „Data cliff edge“, wenn die Trennung Großbritanniens von der EU endgültig beschlossene Sache sein wird.

Ohne ein klares Gespür dafür zu haben, welche Vorschriften und Compliance-Anforderungen bald gelten werden, versuchen britische Unternehmen herauszufinden, wie sie ihre Daten bestmöglich schützen, Geschäftsverzögerungen verhindern und kostspielige Fehler vermeiden können. Die Vieldeutigkeit rund um den Brexit wirft mehr Fragen als Antworten auf, darunter: Wo sollten britische Unternehmen ihre Daten speichern? Sollten sie alle ihre Rechenzentren nach Großbritannien verlegen? Wie wirkt sich der Besitz von Rechenzentren auf den Datenschutz aus? Welche Bedrohungen bestehen, wenn nach Abschluss des Brexit Daten innerhalb oder außerhalb des Vereinigten Königreichs gespeichert werden?

Für Führungskräfte sind der Mangel an Antworten und die Angst vor dem Unbekannten frustrierend. In dieser ungewissen Zeit können smarte Geschäftsführer aber den Brexit für ihre Zwecke lenken, indem sie ihn als Chance und nicht als Hindernis für sich nutzen.

Die unsicher regulierte Zukunft

Für Unternehmen mit Sitz in Großbritannien, die Datenspeicherung und private Cloud-Dienste anbieten, ist vor allem der Ort, an dem sich die Daten befinden, von Belang. Die Gewährleistung der Sicherheit und Kontrolle über eigene Daten ist von zentraler Bedeutung. Gleichzeitig ist jedoch auch die Einhaltung unbekannter zukünftiger Vorschriften und Gesetze zum Datenschutz und zum Datentransfer ein Muss.

Grundlage ist die Einhaltung der Datenschutzverordnung (DSGVO) vom 25. Mai 2018, da das Vereinigte Königreich zu diesem Zeitpunkt noch immer Teil der EU war. Nach Angaben des Information Commissioner’s Office (ICO) des Vereinigten Königreichs – einer unabhängigen Behörde, die sich für die Wahrung von Informations- und Datenschutzrechten von Einzelpersonen einsetzt – bestätigte die britische Regierung, dass ein Austritt aus der EU keine Auswirkungen auf die DSGVO haben wird. Was in diesem Jahr, wenn sich Großbritannien und die EU endgültig voneinander trennen, passieren wird, kann man nur vermuten. Die Ratschläge von ICO sind richtungsweisend: „Bereiten Sie sich darauf vor, die Bestimmungen der DSGVO zu erfüllen und voranzukommen.“

Bemerkenswerterweise schreibt die DSGVO nicht vor, wo Unternehmen ihre Daten aufbewahren müssen. Es ist lediglich erforderlich, dass die EU-Organisationen ihre Daten innerhalb der EU speichern und außerhalb der EU unzugänglich machen müssen. Ausnahme: die Daten betreffen eine DSGVO-konforme Organisation. Wie sich dieses Mandat auf das Vereinigte Königreich auswirkt, muss noch gesehen werden. Denn das Vereinigte Königreich war ja zum Zeitpunkt der Ausarbeitung der Verordnung Teil der EU. Es ist unklar, ob das Vereinigte Königreich am Ende mit der DSGVO konform sein wird.

Aus globaler Sicht muss Großbritannien herausfinden, wie der Datenaustausch und der grenzüberschreitende Datenfluss reguliert werden können. Der freie Datenfluss ist wichtig für Unternehmen und Innovation, was bedeutet, dass das Vereinigte Königreich Vereinbarungen, wie die EU sie mit den USA getroffen haben, benötigt. Ein Privacy Shield, das den Austausch personenbezogener Daten zu gewerblichen Zwecken ermöglicht. Ob das Vereinigte Königreich Vereinbarungen wie den Privacy Shield umsetzen kann, oder neue Vereinbarungen mit Ländern wie den USA treffen muss, ist etwas, was nur die Zeit zeigen wird.

Wo sind die Daten?

Rechenzentren können heute durch freien Datenfluss, sowohl im Vereinigten Königreich als auch in der EU betrieben werden. Das Vereinigte Königreich unterliegt gleichem Schutz und gleichen Vorschriften wie die EU. Viele Spekulationen beinhalten allerdings, dass in naher Zukunft britische Kunden von einem in Großbritannien ansässigen Rechenzentrum bedient werden müssen, ebenso wie europäische Kunden ein EU-Rechenzentrum benötigen. Es gibt keine Garantien. Unklar ist auch, ob diese Situation die Anbieter von Rechenzentren dazu veranlassen wird, den Umzug aus Großbritannien in Betracht zu ziehen, um sich stärker auf den Kontinent zu konzentrieren, oder ob sie sich an beiden Standorten gleichzeitig niederlassen werden. Das Wahrscheinlichste: Die Anbieter tendieren zu letzterem, wie auch Amazon Web Services (AWS). Selbst nach dem Brexit-Votum hielt Amazon an seinem Wort fest und eröffnete Ende letzten Jahres sein erstes AWS-Rechenzentrum in London. Dies unterstreicht sowohl sein Engagement für Großbritannien als auch das unternehmerische Engagement.

Aus dem Brexit eine Geschäftsmöglichkeit machen

Die Automatisierung des IT-Betriebs und die Einführung einer Cloud-Strategie könnten die ersten Schritte sein, um die unbeantworteten Fragen des Brexit zu lösen und daraus einen Vorteil zu machen. Es ist an der Zeit, die Vorteile dessen zu erkennen, teure Hardware und Software von Unternehmen vor Ort durch den Umstieg auf die öffentliche Cloud zu ersetzen. Dies ist nicht nur die kostengünstigere Option. Cloud-Anbieter wie AWS, Microsoft Azure und Google Cloud Platform (GCP) ersparen in diesem politischen Umfeld sogar Unternehmen die Verwaltung und Wartung von Rechenzentren. Einige Unternehmen sind möglicherweise besorgt über die steigenden Raten von Public-Cloud-Anbietern, ihre Preisanpassungen scheinen jedoch an den relativen Wertverlust des Sterlings gebunden zu sein. Selbst bei geringen Erhöhungen sind die Preise einiger Anbieter, wie AWS, noch immer deutlich niedriger als die Kosten, die mit dem Betrieb von Rechenzentren und privaten Clouds vor Ort verbunden sind, insbesondere wenn Wartungskosten einbezogen werden. Wenn man diesen Gedanken noch einen Schritt weiterführt, wie kann der Brexit als eine Chance für Unternehmen betrachtet werden?Organisationen sammeln alle Arten von Daten. Aber nur eine Handvoll von ihnen verwendet effektive Datenanalysen, die Geschäftsentscheidungen unterstützen. Nur wenige Unternehmen tun mehr, als ihre Daten zu speichern, da ihnen die Tools und Ressourcen fehlen, um nahtlos auf ihre Daten zuzugreifen, oder weil Abfragen teuer sind. Ohne ein für die Cloud konstruiertes Data Warehouse ist dieser Prozess bestenfalls eine Herausforderung, und der wahre Wert der Daten geht dabei verloren. Ironischerweise bietet der Brexit die Möglichkeit, dies zu ändern, da Unternehmen ihre IT-Abläufe neu bewerten und alternative, kostengünstigere Methoden zum Speichern von Daten suchen müssen. Durch den Wechsel zu einer öffentlichen Cloud und die Nutzung eines Data Warehouses für die Cloud können Unternehmen Beschränkungen und Einschränkungen ihrer Daten aufheben und diese für die Entscheidungsfindung zugänglich machen.

Der Brexit dient also als Katalysator einer datengesteuerten Organisation, die Daten verwendet, anstatt sie für schlechte Zeiten zu speichern. Am Ende scheint die Prognose der Verhandlungen in Brüssel doch eine ziemlich stürmische zu sein.

Introduction to ROC Curve

The abbreviation ROC stands for Receiver Operating Characteristic. Its main purpose is to illustrate the diagnostic ability of classifier as the discrimination threshold is varied. It was developed during World War II when Radar operators had to decide if the blip on the screen is an enemy target, a friendly ship or just a noise.  For these purposes they measured the ability of a radar receiver operator to make these important distinctions, which was called the Receiver Operating Characteristic.

Later it was found useful in interpreting medical test results and then in Machine learning classification problems. In order to get an introduction to binary classification and terms like ‘precision’ and ‘recall’ one can look into my earlier blog  here.

True positive rate and false positive rate

Let’s imagine a situation where a fire alarm is installed in a kitchen. The alarm is supposed to emit a sound in case fire smoke is detected in the room. Unfortunately, there is a lot of cooking done in the kitchen and the alarm may trigger the sound too often. Thus, instead of serving a purpose the alarm becomes a nuisance due to a large number of false alarms. In statistical terms these types of errors are called type 1 errors, or false positives.

One way to deal with this problem is to simply decrease sensitivity of the device. We do this by increasing the trigger threshold at the alarm setting. But then, not every alarm should have the same threshold setting. Consider the same type of device but kept in a bedroom. With high threshold, the device might miss smoke from a real short-circuit in the wires which poses a real danger of fire. This kind of failure is called Type 2 error or a false negative. Although the two devices are the same, different types of threshold settings are optimal for different circumstances.

To specify this more formally, let us describe the performance of a binary classifier at a particular threshold by the following parameters:

 

These parameters take different values at different thresholds. Hence, they define the performance of the classifier at particular threshold. But we want to examine in overall how good a classifier is. Fortunately, there is a way to do that. We plot the True Positive Rate (TPR) and False Positive rate (FPR) at different thresholds and this plot is called ROC curve.

Let’s try to understand this with an example.

A case with a distinct population distribution

Let’s suppose there is a disease which can be identified with deficiency of some parameter (maybe a certain vitamin). The distribution of population with this disease has a mean vitamin concentration sharply distinct from the mean of a healthy population, as shown below.

This is result of dummy data simulating population of 2000 people,the link to the code is given  in the end of this blog.  As the two populations are distinctly separated (there is no  overlap between the two distributions), we can expect that a classifier would have an easy job distinquishing healthy from sick people. We can run a logistic regression classifier with a threshold of .5 and be 100% succesful in detecting the decease.

The confusion matrix may look something like this.

In this ideal case with a threshold  of  .5 we do not make a single wrong classification. The True positive rate and False positive rate are 1 and 0, respectively. But we can shift the threshold. In that case, we will  get different confusion matrices. First we plot threshold vs. TPR.

We see for most values of threshold the TPR is close to 1 which again proves data is easy to classify and the classifier is returning high probabilities  for the most of positives .

Similarly Let’s plot threshold vs. FPR.

For most of the data points FPR is close to zero. This is also good. Now its time to plot the ROC curve using these results (TPR vs FPR).

Let’s try to interpret  the results,  all the points lie on line x=0 and y=1, it means for all the points FPR is zero or TPR is one, making  the curve a square. which means the classifier does perfectly well.

Case with overlapping  population distribution

The above example was about a perfect classifer. However, life is often not so easy. Now let us consider another more realistic situation in which the parameter distribution of the population is not as distinct as in the previous case. Rather, the mean of the parameter with healthy and not healthy datapoints are close and the distributions overlap, as shown in the next figure.

If we set the threshold to 0.5, the confusion matrix may look like this.

Now, any new choice of threshold location will affect both false positives and false negatives. In fact, there is a trade-off. If we shift the threshold with the goal to reduce false negatives, false positives will increase. If we move the threshold to the other direction and reduce false positive, false negatives will increase.

The plots (TPR vs Threshold) , (FPR vs Threshold) are shown below

If we plot the ROC curve from these results, it looks like this:

From the curve we see the classifier does not perform as well as the earlier one.

What else can be infered from this curve? We first need to understand what the diagonal in this plot represent. The diagonal represents ‘Line of no discrimination’, which we obtain if we randomly guess. This is the ROC curve for the worst possible classifier. Therefore, by comparing the obtained ROC curve with the diagonal, we see how much better our classifer is from random guessing.

The further away ROC curve from the diagonal is (the closest it is to the top left corner) , better the classifier is.

Area Under the curve

The overall performance of the classifier is given by the area under the ROC curve and is usually denoted as AUC. Since TPR and FPR lie within the range of 0 to 1, the AUC also assumes values between 0 and 1. The higher the value of AUC, the better is the overall performance of the classifier.

Let’s see this for the two different distributions which we saw earlier.

As we know the classifier had worked perfectly in the first case with points at (0,1) the area under the curve is 1 which is perfect. In the latter case the classifier was not able to perform as good, the ROC curve is between the diagonal and left hand corner. The AUC as we can see is less than 1.

Some other general characteristics

There are still few points that needs to be discussed on a General ROC curve

  • The ROC curve does not provide information about the actual values of thresholds used for the classifier.
  • Performance of different classifiers can be compared using the AUC of different Classifier. The larger the AUC, the better the classifier.
  • The vertical distance of the ROC curve from the no discrimination line gives a measure of ‘INFORMEDNESS’. This is known as Youden’s J satistic. This statistics can take values between 0 and 1.

Youden’s  J statistic is defined for every point on the ROC curve . The point at which Youden’s  J satistics reaches its maximum for a given ROC curve can be used to guide the selection of the threshold to be used for that classifier.

I hope this post does the job of providing an understanding of ROC curves  and AUC. The  Python program for simulating the example given earlier can be found here .

Please feel free to adjust the mean of the distributions and see the changes in the plot.