A common trap when it comes to sampling from a population that intrinsically includes outliers

I will discuss a common fallacy concerning the conclusions drawn from calculating a sample mean and a sample standard deviation and more importantly how to avoid it.

Suppose you draw a random sample x_1, x_2, … x_N of size N and compute the ordinary (arithmetic) sample mean  x_m and a sample standard deviation sd from it.  Now if (and only if) the (true) population mean µ (first moment) and population variance (second moment) obtained from the actual underlying PDF  are finite, the numbers x_m and sd make the usual sense otherwise they are misleading as will be shown by an example.

By the way: The common correlation coefficient will also be undefined (or in practice always point to zero) in the presence of infinite population variances. Hopefully I will create an article discussing this related fallacy in the near future where a suitable generalization to Lévy-stable variables will be proposed.

 Drawing a random sample from a heavy tailed distribution and discussing certain measures

As an example suppose you have a one dimensional random walker whose step length is distributed by a symmetric standard Cauchy distribution (Lorentz-profile) with heavy tails, i.e. an alpha-stable distribution with alpha being equal to one. The PDF of an individual independent step is given by p(x) = \frac{\pi^{-1}}{(1 + x^2)} , thus neither the first nor the second moment exist whereby the first exists and vanishes at least in the sense of a principal value due to symmetry.

Still let us generate N = 3000 (pseudo) standard Cauchy random numbers in R* to analyze the behavior of their sample mean and standard deviation sd as a function of the reduced sample size n \leq N.

*The R-code is shown at the end of the article.

Here are the piecewise sample mean (in blue) and standard deviation (in red) for the mentioned Cauchy sampling. We see that both the sample mean and sd include jumps and do not converge.

Especially the mean deviates relatively largely from zero even after 3000 observations. The sample sd has no target due to the population variance being infinite.

If the data is new and no prior distribution is known, computing the sample mean and sd will be misleading. Astonishingly enough the sample mean itself will have the (formally exact) same distribution as the single step length p(x). This means that the sample mean is also standard Cauchy distributed implying that with a different Cauchy sample one could have easily observed different sample means far of the presented values in blue.

What sense does it make to present the usual interval x_m \pm sd / \sqrt{N} in such a case? What to do?

The sample median, median absolute difference (mad) and Inter-Quantile-Range (IQR) are more appropriate to describe such a data set including outliers intrinsically. To make this plausible I present the following plot, whereby the median is shown in black, the mad in green and the IQR in orange.

This example shows that the median, mad and IQR converge quickly against their assumed values and contain no major jumps. These quantities do an obviously better job in describing the sample. Even in the presence of outliers they remain robust, whereby the mad converges more quickly than the IQR. Note that a standard Cauchy sample will contain half of its sample in the interval median \pm mad meaning that the IQR is twice the mad.

Drawing a random sample from a PDF that has finite moments

Just for comparison I also show the above quantities for a standard normal (pseudo) sample labeled with the same color as before as a counter example. In this case not only do both the sample mean and median but also the sd and mad converge towards their expected values (see plot below). Here all the quantities describe the data set properly and there is no trap since there are no intrinsic outliers. The sample mean itself follows a standard normal, so that the sd in deed makes sense and one could calculate a standard error \frac{sd}{\sqrt{N}} from it to present the usual stochastic confidence intervals for the sample mean.

A careful observation shows that in contrast to the Cauchy case here the sampled mean and sd converge more quickly than the sample median and the IQR. However still the sampled mad performs about as well as the sd. Again the mad is twice the IQR.

And here are the graphs of the prementioned quantities for a pseudo normal sample:

The take-home-message:

Just be careful when you observe outliers and calculate sample quantities right away, you might miss something. At best one carefully observes how the relevant quantities change with sample size as demonstrated in this article.

Such curves should become of broader interest in order to improve transparency in the Data Science process and reduce fallacies as well.

Thank you for reading.

P.S.: Feel free to play with the set random seed in the R-code below and observe how other quantities behave with rising sample size. Of course you can also try different PDFs at the beginning of the code. You can employ a Cauchy, Gaussian, uniform, exponential or Holtsmark (pseudo) random sample.


QUIZ: Which one of the recently mentioned random samples contains a trap** and why?

**in the context of this article


R-code used to generate the data and for producing plots:


#R-script for emphasizing convergence and divergence of sample means

####install and load relevant packages ####

#uncomment these lines if necessary

#####drawing random samples #####

#Setting a random seed for being able to reproduce results  
N= 2000     #sample size

#Choose a PDF from which a sample shall be drawn
#To do so (un)comment the respective lines of following code

data <- rcauchy(N)    # option1(default): standard Cauchy sampling

#data <- rnorm(N)     #option2: standard Gaussian sampling
#data <- rexp(N)    # option3: standard exponential sampling

#data <- rstable(N,alpha=1.5,beta=0)  # option4: standard symmetric Holtsmark sampling

#data <- runif(N)              #option5: standard uniform sample

#####descriptive statistics####

SUM = vector()
sd =vector()
mean = vector()
SQ =vector()
SQUARES = vector()
median = vector()
mad =vector()
quantiles = data.frame()
sem =vector()

#piecewise calculaion of descrptive quantities

for (k in 1:length(data)){              #mainloop
SUM[k] <- sum(data[1:k])            # sum of sample
mean[k] <- mean(data[1:k])          # arithmetic mean
sd[k] <- sd(data[1:k])              # standard deviation
sem[k] <- sd[k]/(sqrt(k))          #standard error of the sample mean (for finite variances)
mad[k] <- mad(data[1:k],const=1)   # median absolute deviation    

for (j in 1:5){
qq <- quantile(data[1:k],na.rm = T)
quantiles[k,j] <- qq[j]         #quantiles of sample
colnames(quantiles) <- c('min','Q1','median','Q3','max')

for (i in 1:length(data[1:k])){
SQUARES[i] <- data[i]*data[i]    
SQ[k] <- sum(SQUARES[1:k])    #sum of squares of random sample
}  #end of mainloop

#create table containing all relevant data
TABLE <-  as.data.frame(cbind(quantiles,mean,sd,SQ,SUM,sem))

#####plotting results###
geom_point(size=.5)+xlab('sample size n')+ylab('sample median'))
print(ggplot(TABLE,aes(1:N,mad))+geom_point(size=.5,color ='green')+
xlab('sample size n')+ylab('sample median absolute difference'))
print(ggplot(TABLE,aes(1:N,sd))+geom_point(size=.5,color ='red')+
xlab('sample size n')+ylab('sample standard deviation'))
print(ggplot(TABLE,aes(1:N,mean))+geom_point(size=.5, color ='blue')+
xlab('sample size n')+ylab('sample mean'))
print(ggplot(TABLE,aes(1:N,Q3-Q1))+geom_point(size=.5, color ='blue')+
xlab('sample size n')+ylab('IQR'))

#uncomment the following lines of code to see further plots

#xlab('sample size n')+ylab('sample sum of r.v.'))
#xlab('sample size n')+ylab('sample sum of r.v.'))
#xlab('sample size n')+ylab('sample sum of squares'))


Fuzzy Matching mit dem Jaro-Winkler-Score zur Auswertung von Markenbekanntheit und Werbeerinnerung

Für Unternehmen sind Markenbekanntheit und Werbeerinnerung wichtige Zielgrößen, denn anhand dieser lässt sich ableiten, ob Konsumenten ein Produkt einer Marke kaufen werden oder nicht. Zielgrößen wie diese werden von Marktforschungsinstituten über Befragungen ermittelt. Dafür wird in regelmäßigen Zeitabständen eine gleichbleibende Anzahl an Personen befragt, ob diese sich an Marken einer bestimmten Branche erinnern oder sich an Werbung erinnern. Die Personen füllen dafür in der Regel einen Onlinefragebogen aus.

Die Ergebnisse der Befragung liegen in einer Datenmatrix (siehe Tabelle) vor und müssen zur Auswertung zunächst bearbeitet werden.

Laufende Nummer Marke 1 Marke 2 Marke 3 Marke 4
1 ING-Diba Citigroup Sparkasse
2 Sparkasse Consorsbank
3 Commerbank Deutsche Bank Sparkasse ING-DiBa
4 Sparkasse Targobank

Ziel ist es aus diesen Daten folgende 0/1 codierte Matrix zu generieren. Wenn eine Marke bekannt ist, wird in die zur Marke gehörende Spalte eine Eins eingetragen, ansonsten eine Null.

Alle Marken ING-Diba Citigroup Sparkasse Targobank
ING-Diba, Citigroup, Sparkasse 1 1 1 0
Sparkasse, Consorsbank 0 0 1 0
Commerzbank, Deutsche Bank, Sparkasse, ING-Diba 1 0 0 0
Sparkasse, Targobank 0 0 1 1

Der Workflow um diese Datentransformation durchzuführen ist oftmals mittels eines Teilstrings einer Marke zu suchen ob diese in einem über alle Nennungen hinweg zusammengeführten String vorkommt oder nicht (z.B. „argo“ bei Targobank). Das Problem dieser Herangehensweise ist, dass viele falsch geschriebenen Wörter so nicht erfasst werden und die Erfahrung zeigt, dass falsch geschriebene Marken in vielfältigster Weise auftreten. Hier mussten in der Vergangenheit Mitarbeiter sich in stundenlangem Kampf durch die Ergebnisse wühlen und falsch zugeordnete oder nicht zugeordnete Marken händisch korrigieren und alle Variationen der Wörter notieren, um für die nächste Befragung das Suchpattern zu optimieren.

Eine Alternative diesen aufwändigen Workflow stellt die Ermittlung von falsch geschriebenen Wörtern mittels des Jaro-Winkler-Scores dar. Dafür muss zunächst die Jaro-Winkler-Distanz zwischen zwei Strings berechnet werden. Diese berechnet sich wie folgt:

d_j = \frac{1}{3}(\frac{m}{|s_1|}+\frac{m}{|s_2|}+\frac{m - t}{m})

  • m: Anzahl der übereinstimmenden Buchstaben
  • s: Länge des Strings
  • t: Hälfte der Anzahl der Umstellungen der Buchstaben die nötig sind, damit Strings identisch sind. („Ta“ und „gobank“ befinden sich bereits in der korrekten Reihenfolge, somit gilt: t = 0)

Aus dem Ergebnis lässt sich der Jaro-Winkler Score berechnen:
d_w = \d_j + (l_p (1 - d_j))
ist dabei die Jaro-Winkler-Distanz, l die Länge der übereinstimmenden Buchstaben von Beginn des Wortes bis zum maximal vierten Buchstaben und p ein konstanter Faktor von 0,1.

Für die Strings „Targobank“ und „Tangobank“ ergibt sich die Jaro-Winkler-Distanz:

d_j = \frac{1}{3}(\frac{8}{9}+\frac{8}{9}+\frac{8 - 0}{9})

Daraus wird im nächsten Schritt der Jaro-Winkler Score berechnet:

d_w = 0,9259 + (2 \cdot 0,1 (1 - 0,9259)) = 0,9407407

Bisherige Erfahrungen haben gezeigt, dass sich Scores ab 0,8 bzw. 0,9 am besten zur Suche von ähnlichen Wörtern eignen. Ein Schwellenwert darunter findet sehr viele Wörter, die sich z.B. auch anderen Wörtern zuordnen lassen. Ein Schwellenwert über 0,9 identifiziert falsch geschriebene Wörter oftmals nicht mehr.

Nach diesem theoretischen Exkurs möchte ich nun zeigen, wie sich das Ganze praktisch anwenden lässt. Da sich das Ganze um ein fiktives Beispiel handelt, werden zur Demonstration der Praxistauglichkeit Fakedaten mit folgendem Code erzeugt. Dabei wird angenommen, dass Personen unterschiedlich viele Banken kennen und diese mit einer bestimmten Wahrscheinlichkeit falsch schreiben.

# Erstellung von Fakeantworten

konsonant <- c("r", "n", "g", "h", "b")
vokal <- c("a", "e", "o", "i", "u")

# Funktion, die mit einer zu bestimmenden Wahrscheinlichkeit, einen zufälligen Buchstaben erzeugt.
generate_wrong_words <- function(x, p, k = TRUE) {
  if(runif(1, 0, 1) > p) { # Zufallswert zwischen 0 und 1
    if(k == TRUE) { # Konsonant oder Vokal erzeugen
      string <- konsonant[sample.int(5, 1)] # Zufallszahl, die Index des Konsonnanten-Vektors bestimmt.
    } else {
      string <- vokal[sample.int(5, 1)] # Zufallszahl, die Index eines Vokal-Vecktors bestimmt.
  } else {
    string <- x

randombank <- function(x) {
  random_num <- runif(1, 0, 1)
  if(random_num  > x) { ## Wahrscheinlichkeit, dass Person keine Bank kennt.
    number <- sample.int(7, 1)
    if(number == 1) {
      bank <- paste0("Ta", generate_wrong_words(x = "r", p = 0.7), "gob", generate_wrong_words(x = "a", p = 0.9), "nk")
    } else if (number == 2) {
      bank <- paste0("Ing-di", generate_wrong_words(x = "b", p = 0.6), "a")
    } else if (number == 3) {
      bank <- paste0("com", generate_wrong_words(x = "m", p = 0.7), "erzb", generate_wrong_words(x = "a", p = 0.8), "nk")
    } else if (number == 4){
      bank <- paste0("Deutsch", generate_wrong_words(x = "e", p = 0.6, k = FALSE), " Ban", generate_wrong_words(x = "k", p = 0.8))
    } else if (number == 5) {
      bank <- paste0("Spark", generate_wrong_words(x = "a", p = 0.7, k = FALSE), "sse")
    } else if (number == 6) {
      bank <- paste0("Cons", generate_wrong_words(x = "o", p = 0.7, k = FALSE), "rsbank")
    } else {
      bank <- paste0("Cit", generate_wrong_words(x = "i", p = 0.7, k = FALSE), "gro", generate_wrong_words(x = "u", p = 0.9, k = FALSE), "p")
  } else {
    bank <- "" # Leerer String, wenn keine Bank bekannt.

# DataFrame erzeugen, in dem Werte gespeichert werden.
df_raw <- data.frame(matrix(ncol = 8, nrow = 2500))

# Erzeugen von richtig und falsch geschrieben Banken mit einer durch bestimmten Variabilität an Banken, welche die Personen kennen.
for(i in 1:2500) {
  df_raw [i, 1] <- i # Laufende Nummer des Befragten
  df_raw [i, 2] <- randombank(x = 0.05)
  if(df_raw [i, 2] == "") { df_raw [i, 3] <- "" } else {df_raw [i, 3] <- randombank(x = 0.1)}
  if(df_raw [i, 3] == "") { df_raw [i, 4] <- "" } else {df_raw [i, 4] <- randombank(x = 0.1)}
  if(df_raw [i, 4] == "") { df_raw [i, 5] <- "" } else {df_raw [i, 5] <- randombank(x = 0.15)} 
  if(df_raw [i, 5] == "") { df_raw [i, 6] <- "" } else {df_raw [i, 6] <- randombank(x = 0.15)}
  if(df_raw [i, 6] == "") { df_raw [i, 7] <- "" } else {df_raw [i, 7] <- randombank(x = 0.2)} 
  if(df_raw [i, 7] == "") { df_raw [i, 8] <- "" } else {df_raw [i, 8] <- randombank(x = 0.2)} 
colnames(df_raw)[1] <- "lfdn"



Nun werden die Inhalte der Spalten in eine einzige Spalte zusammengefasst und jede Marke per Komma getrennt.

df <- unite(df_raw, united, c(2:ncol(df_raw)), sep = ",")
colnames(df)[2] <- "text"
# Gesuchte Banken (nur korrekt geschrieben)
startliste <- c("Targobank", "Ing-DiBa", "Commerzbank", "Deutsche Bank", "Sparkasse", "Consorsbank", "Citigroup")

Damit Sonderzeichen, Leerzeichen oder Groß- und Kleinschreibung keine Rolle spielen, werden alle Strings vereinheitlicht und störende Zeichen entfernt.

dftext <- tolower(dftext)
dftext <- str_trim(dftext)
dftext <- gsub(" ", "", dftext)
dftext <- gsub("[?]", "", dftext)
dftext <- gsub("[-]", "", dftext)
dftext <- gsub("[_]", "", dftext)

startliste <- tolower(startliste)
startliste <- str_trim(startliste)
startliste <- gsub(" ", "", startliste)
startliste <- gsub("[?]", "", startliste)
startliste <- gsub("[-]", "", startliste)
startliste <- gsub("[_]", "", startliste)

Im nächsten Schritt wird geprüft welche Schreibweisen überhaupt existieren. Dafür eignet sich eine Word-Frequency-Matrix, mit der alle einzigartigen Wörter und deren Häufigkeiten in einem Vektor gezählt wird.

words <- as.data.frame(wfm(dftext)) # Jedes einzigartige Wort und dazugehörige Häufigkeiten. words <- rownames(words) # wfm zählt Häufigkeiten jedes Wortes und schreibt Wörter in rownames, wir brauchen jedoch das Wort selbst. </pre> Danach wird eine leere Liste erstellt, in der iterativ für jedes Element des Suchvektors ein Charactervektor erzeugt wird, der Wörter enthält, die einen Jaro-Winker Score von 0,9 oder höher besitzen. <pre class="theme:github lang:r decode:true ">for(i in 1:length(startliste)) {   finalewortliste[[i]] <- words[which(jarowinkler(startliste[[i]], words) > 0.9)] } </pre> Jetzt wird ein leerer DataFrame erzeugt, der die Zeilenlänge des originalen DataFrames besitzt sowie die Anzahl der Marken als Spaltenlänge. <pre class="theme:github lang:r decode:true ">finaldf <- data.frame(matrix(nrow = nrow(df), ncol = length(startliste))) colnames(finaldf) <- startliste </pre> Im nächsten Schritt wird nun aus den ähnlichen Wörtern mit einer oder-Verknüpfung einen String erzeugt, der alle durch den Jaro-Winkler-Score identifizierten Wörter beinhaltet. Wenn ein Treffer gefunden wird, wird in der Suchspalte eine Eins eingetragen, ansonsten eine Null. <pre class="theme:github lang:r decode:true ">for(i in 1:ncol(finaldf)) {   finaldf[i] <- ifelse(str_detect(dftext, paste(finalewortliste[[i]], collapse = "|")) == TRUE, 1, 0) 

Zuletzt wird eine Spalte erzeugt, in die eine Eins geschrieben wird, wenn keine der Marken gefunden wurde.

finaldfkeinedergeannten <- ifelse(rowSums(finaldf) > 0, 0, 1) # Wenn nicht mindestens eine der gesuchten Banken bekannt </pre> Nach der fertigen Berechnung der Matrix können nun die finalen KPI´s berechnet und als Report in eine .xlsx Datei geschrieben werden. <pre class="theme:github lang:r decode:true "># Prozentuale Anteile berechnen. anteil <- as.data.frame(t(sapply(finaldf, sum) / nrow(finaldf) * 100)) # Ordne dem DataFrame die ursprünglichen Nenneungen zu. finaldf <- cbind(dftext, finaldf)
colnames(finaldf)[1] <- "text"

# Ergebnisse in eine .xlsx Datei schreiben.
wb <- createWorkbook()
addWorksheet(wb, "Ergebnisse")    
writeData(wb, "Ergebnisse", anteil, startCol = 2, startRow = 1, rowNames = FALSE)
writeData(wb, "Ergebnisse", finaldf, startCol = 1, startRow = 4, rowNames = FALSE)
saveWorkbook(wb, paste0("C:/Users/User/Desktop/Results_", Sys.Date(), ".xlsx"), overwrite = TRUE)  

Dieses Vorgehen kann natürlich nicht verhindern, dass sich jemand mit kritischem Auge die Daten anschauen muss. In mehreren Tests ergaben sich bei einer Fallzahl von ~10.000 Antworten Genauigkeiten zwischen 95% und 100%, was bisherige Ansätze um ein Vielfaches übertrifft.9407407

How To Remotely Send R and Python Execution to SQL Server from Jupyter Notebooks


Did you know that you can execute R and Python code remotely in SQL Server from Jupyter Notebooks or any IDE? Machine Learning Services in SQL Server eliminates the need to move data around. Instead of transferring large and sensitive data over the network or losing accuracy on ML training with sample csv files, you can have your R/Python code execute within your database. You can work in Jupyter Notebooks, RStudio, PyCharm, VSCode, Visual Studio, wherever you want, and then send function execution to SQL Server bringing intelligence to where your data lives.

This tutorial will show you an example of how you can send your python code from Juptyter notebooks to execute within SQL Server. The same principles apply to R and any other IDE as well. If you prefer to learn through videos, this tutorial is also published on YouTube here:


Environment Setup Prerequisites

  1. Install ML Services on SQL Server

In order for R or Python to execute within SQL, you first need the Machine Learning Services feature installed and configured. See this how-to guide.

  1. Install RevoscalePy via Microsoft’s Python Client

In order to send Python execution to SQL from Jupyter Notebooks, you need to use Microsoft’s RevoscalePy package. To get RevoscalePy, download and install Microsoft’s ML Services Python Client. Documentation Page or Direct Download Link (for Windows).

After downloading, open powershell as an administrator and navigate to the download folder. Start the installation with this command (feel free to customize the install folder): .\Install-PyForMLS.ps1 -InstallFolder “C:\Program Files\MicrosoftPythonClient”

Be patient while the installation can take a little while. Once installed navigate to the new path you installed in. Let’s make an empty folder and open Jupyter Notebooks: mkdir JupyterNotebooks; cd JupyterNotebooks; ..\Scripts\jupyter-notebook

Create a new notebook with the Python 3 interpreter:


To test if everything is setup, import revoscalepy in the first cell and execute. If there are no error messages you are ready to move forward.

Database Setup (Required for this tutorial only)

For the rest of the tutorial you can clone this Jupyter Notebook from Github if you don’t want to copy paste all of the code. This database setup is a one time step to ensure you have the same data as this tutorial. You don’t need to perform any of these setup steps to use your own data.

  1. Create a database

Modify the connection string for your server and use pyodbc to create a new database.

import pyodbc  
# creating a new db to load Iris sample in 
new_db_name = "MLRemoteExec" connection_string = "Driver=SQL Server;Server=localhost\MSSQLSERVER2017;Database={0};Trusted_Connection=Yes;" 

cnxn = pyodbc.connect(connection_string.format("master"), autocommit=True) 

cnxn.cursor().execute("IF EXISTS(SELECT * FROM sys.databases WHERE [name] = '{0}') DROP DATABASE {0}".format(new_db_name)) 

cnxn.cursor().execute("CREATE DATABASE " + new_db_name)


print("Database created") 
  1. Import Iris sample from SkLearn

Iris is a popular dataset for beginner data science tutorials. It is included by default in sklearn package.

from sklearn import datasetsimport pandas as pd
# SkLearn has the Iris sample dataset built in to the packageiris = datasets.load_iris()
df = pd.DataFrame(iris.data, columns=iris.feature_names)
  1. Use RecoscalePy APIs to create a table and load the Iris data

(You can also do this with pyodbc, sqlalchemy or other packages)

from revoscalepy import RxSqlServerData, rx_data_step
# Example of using RX APIs to load data into SQL table. You can also do this with pyodbc
table_ref = RxSqlServerData(connection_string=connection_string.format(new_db_name), table="Iris")rx_data_step(input_data = df, output_file = table_ref, overwrite = True)print("New Table Created: Iris")
print("Sklearn Iris sample loaded into Iris table")

Define a Function to Send to SQL Server

Write any python code you want to execute in SQL. In this example we are creating a scatter matrix on the iris dataset and only returning the bytestream of the .png back to Jupyter Notebooks to render on our client.

def send_this_func_to_sql():
    from revoscalepy import RxSqlServerData, rx_import
    from pandas.tools.plotting import scatter_matrix
    import matplotlib.pyplot as plt
    import io    
# remember the scope of the variables in this func are within our SQL Server Python Runtime
    connection_string = "Driver=SQL Server;Server=localhost\MSSQLSERVER2017; Database=MLRemoteExec;Trusted_Connection=Yes;"

# specify a query and load into pandas dataframe df
    sql_query = RxSqlServerData(connection_string=connection_string, sql_query = "select * from Iris")

    df = rx_import(sql_query)

# return bytestream of image created by scatter_matrix
    buf = io.BytesIO()
    plt.savefig(buf, format="png")
    return buf.getvalue()

Send execution to SQL

Now that we are finally set up, check out how easy sending remote execution really is! First, import revoscalepy. Create a sql_compute_context, and then send the execution of any function seamlessly to SQL Server with RxExec. No raw data had to be transferred from SQL to the Jupyter Notebook. All computation happened within the database and only the image file was returned to be displayed.

from IPython import display
import matplotlib.pyplot as plt 
from revoscalepy import RxInSqlServer, rx_exec# create a remote compute context with connection to SQL Server

sql_compute_context = RxInSqlServer(connection_string=connection_string.format(new_db_name))

# use rx_exec to send the function execution to SQL Server

image = rx_exec(send_this_func_to_sql, compute_context=sql_compute_context)[0]

# only an image was returned to my jupyter client. All data remained secure and was manipulated in my db.


While this example is trivial with the Iris dataset, imagine the additional scale, performance, and security capabilities that you now unlocked. You can use any of the latest open source R/Python packages to build Deep Learning and AI applications on large amounts of data in SQL Server. We also offer leading edge, high-performance algorithms in Microsoft’s RevoScaleR and RevoScalePy APIs. Using these with the latest innovations in the open source world allows you to bring unparalleled selection, performance, and scale to your applications.

Learn More

Check out SQL Machine Learning Services Documentation to learn how you can easily deploy your R/Python code with SQL stored procedures making them accessible in your ETL processes or to any application. Train and store machine learning models in your database bringing intelligence to where your data lives.

Other YouTube Tutorials:

Bringing intelligence to where data lives: Python & R embedded in T-SQL


Did you know that you can write R and Python code within your T-SQL statements? Machine Learning Services in SQL Server eliminates the need for data movement. Instead of transferring large and sensitive data over the network or losing accuracy with sample csv files, you can have your R/Python code execute within your database. Easily deploy your R/Python code with SQL stored procedures making them accessible in your ETL processes or to any application. Train and store machine learning models in your database bringing intelligence to where your data lives.

You can install and run any of the latest open source R/Python packages to build Deep Learning and AI applications on large amounts of data in SQL Server. We also offer leading edge, high-performance algorithms in Microsoft’s RevoScaleR and RevoScalePy APIs. Using these with the latest innovations in the open source world allows you to bring unparalleled selection, performance, and scale to your applications.

If you are excited to try out SQL Server Machine Learning Services, check out the hands on tutorial below. If you do not have Machine Learning Services installed in SQL Server,you will first want to follow the getting started tutorial I published here: 

How-To Tutorial

In this tutorial, I will cover the basics of how to Execute R and Python in T-SQL statements. If you prefer learning through videos, I also published the tutorial on YouTube.


Open up SQL Server Management Studio and make a connection to your server. Open a new query and paste this basic example: (While I use Python in these samples, you can do everything with R as well)

EXEC sp_execute_external_script @language = N'Python',
@script = N'print(3+4)'

Sp_execute_external_script is a special system stored procedure that enables R and Python execution in SQL Server. There is a “language” parameter that allows us to choose between Python and R. There is a “script” parameter where we can paste R or Python code. If you do not see an output print 7, go back and review the setup steps in this article.

Parameter Introduction

Now that we discussed a basic example, let’s start adding more pieces:

EXEC sp_execute_external_script  @language =N'Python', 
@script = N' 
OutputDataSet = InputDataSet;
@input_data_1 =N'SELECT 1 AS Col1';

Machine Learning Services provides more natural communications between SQL and R/Python with an input data parameter that accepts any SQL query. The input parameter name is called “input_data_1”.
You can see in the python code that there are default variables defined to pass data between Python and SQL. The default variable names are “OutputDataSet” and “InputDataSet” You can change these default names like this example:

EXEC sp_execute_external_script  @language =N'Python', 
@script = N' 
MyOutput = MyInput;
@input_data_1_name = N'MyInput',
@input_data_1 =N'SELECT 1 AS foo',
@output_data_1_name =N'MyOutput';

As you executed these examples, you might have noticed that they each return a result with “(No column name)”? You can specify a name for the columns that are returned by adding the WITH RESULT SETS clause to the end of the statement which is a comma separated list of columns and their datatypes.

EXEC sp_execute_external_script  @language =N'Python', 
MyOutput = MyInput;
@input_data_1_name = N'MyInput',
@input_data_1 =N'
SELECT 1 AS foo,
2 AS bar
@output_data_1_name =N'MyOutput'
WITH RESULT SETS ((MyColName int, MyColName2 int));

Input/Output Data Types

Alright, let’s discuss a little more about the input/output data types used between SQL and Python. Your input SQL SELECT statement passes a “Dataframe” to python relying on the Python Pandas package. Your output from Python back to SQL also needs to be in a Pandas Dataframe object. If you need to convert scalar values into a dataframe here is an example:

EXEC sp_execute_external_script  @language =N'Python', 
import pandas as pd
c = 1/2
d = 1*2
s = pd.Series([c,d])
df = pd.DataFrame(s)
OutputDataSet = df

Variables c and d are both scalar values, which you can add to a pandas Series if you like, and then convert them to a pandas dataframe. This one shows a little bit more complicated example, go read up on the python pandas package documentation for more details and examples:

EXEC sp_execute_external_script  @language =N'Python', 
import pandas as pd
s = {"col1": [1, 2], "col2": [3, 4]}
df = pd.DataFrame(s)
OutputDataSet = df

You now know the basics to execute Python in T-SQL!

Did you know you can also write your R and Python code in your favorite IDE like RStudio and Jupyter Notebooks and then remotely send the execution of that code to SQL Server? Check out these documentation links to learn more: https://aka.ms/R-RemoteSQLExecution https://aka.ms/PythonRemoteSQLExecution

Check out the SQL Server Machine Learning Services documentation page for more documentation, samples, and solutions. Check out these E2E tutorials on github as well.

Would love to hear from you! Leave a comment below to ask a question, or start a discussion!