These slides are from a talk I at the papis conference in Boston in 2016. The main subject is uplift modelling. Starting from a churn model approach for an e-gaming company, we introduce when to apply uplift methods, how to mathematically model them, and finally, how to evaluate them. I tried to bridge the gap between causal inference theory and uplift theory, especially concerning how to properly cross validate the results. The notation used is the one from uplift modelling.

1. Beyond Churn Prediction :
An Introduction to Uplift Modelling
Pierre Gutierrez

2. Plan
• Introduction / Client situation
• Uplift Use Cases
• Global Uplift Strategy
• Machine learning for Uplift
• Uplift Evaluation
• Conclusion
Material
• Complete project
http://gallery.dataiku.com/projects/DKU_UPLIFT/
• Notebooks & Data
https://github.com/PGuti/Uplift.git

3. Dataiku
• Founded in 2013
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• Paris, New-York, London, San Francisco
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Data Science Software Editor of Dataiku DSS

4. Motivations

5. Client situation
• Client : French Online Gaming Company (MMORPG)
• Users are leaving (more than 10 years old )
• let’s do a churn prediction model !
• Target : no come back in 14 or 28 days.
(14 missing days -> 80 % of chance not to come back
28 missing days -> 90 % of chance not to come back)
• Features :
• Connection features :
• Time played in 1,7,15,30,… days
• Time since last connection
• Connection frequency
• Days of week / hours of days played
• Equivalent for payments and subscriptions
• Age, sex, country
• Number of account, is a bot …
• No in game features (no data)

6. Client situation
• Model Results :
• AUC 0.88
• Very stable model in time
• Marketing actions :
• 7 different actions based on customer segmentation
(offers, promotion, … )
• A/B test
-> -5 % churn for persons contacted by email
• Going further :
• Feature engineering : guilds, close network, in game actions, …
• Study long term churn …

7. Uplift Definition
• But wait !
• Strong hypothesis : target the person that are the most likely to churn

8. Uplift Definition
• But wait !
• Strong hypothesis : target the person that are the most likely to churn
• What is the gain / person for an action ?
• cost of action
• fixed value of the customer
• independent variables
• “treated” population and “control” population
•
• Value with action :
• Value without action :
• Gain :
c
vi i
X
T C
Y =
⇢
1 if customer churn
0 otherwise
ET
(Vi) = vi(1 PT
(Y = 1|X)) c
EC
(Vi) = vi(1 PC
(Y = 1|X))
E(Gi) = vi(PC
(Y = 1|X) PT
(Y = 1|X)) c
vi(hypothesis
:
independent
of
ac1on)

9. Uplift Definition
• But wait !
• Strong hypothesis : target the person that are the most likely to churn
• What is the gain / person for an action ?
• Real Target :
People who are †he most likely to change positively their behavior if there is an action
Upli5
=
Model
E(Gi) = vi(PC
(Y = 1|X) PT
(Y = 1|X)) c
P

10. Uplift Definition
• Gain to maximize:
• Targeting churner:
Does not optimize the difference !
Is good if treatment good.
• Intuitive examples:
• : action is expected to make the situation worst. Spam ?
• : user does not care
E(Gi) = vi(PC
(Y = 1|X) PT
(Y = 1|X)) c
PC
(Y = 1) ⇡ PT
(Y = 1)
PC
(Y = 1) < PT
(Y = 1)

11. Uplift Definition
If not treated
Positive Response Negative Response
Unnecessary costs Negative impact
Positive Response
Negative Response
If treated
Unnecessary costs
The people we want
to target
SURE THINGS SLEEPING DOGS
PERSUADABLES LOST CAUSES

12. Uplift Use Cases

13. Uplift Use Cases
• Healthcare :
• Typical medical trial:
• Treatment group: gets the treatment
• Control group: gets placebo (or another treatment)
• Statistical test show that the treatment works or not globally
• With uplift modeling we can find out for whom the treatment works best
• Personalized medicine
• Ex : What is the gain in survival probability ?
-> classification/uplift problem

14. Uplift Use Cases
• Churn :
• E-gaming
• Other Ex : Coyote
• Retail :
• Compare effect of
coupons campaigns
• Marketing / CRM :
• Churn
• E-Mailing

15. Example
• Mailing : Hillstrom challenge
• 2 campaigns :
• one men email
• one woman email
• Question : who are the people to target / that have the best response rate

16. Uplift VS Causal Inference methods
• Causal inference closer to econometrics
• Uplift closer to ML, more practical
• Evaluation based on Cross Validation
• Usage of classical ML models
• Sometimes lack of theory
• Different people who don’t really talk together:
• Different Notations (sorry). Today is uplift’s
• Different evaluation functions
• Different models ?
Not really !

17. Global Uplift Strategy

18. Uplift as a natural evolution
Train
Data
Step 1 : train a (churn) model
Training
Churn
Model

19. Uplift as a natural evolution
Train
Data
Test
Data
A/B
test
on
scored
dataset
Step 2 : A/B test the model
Training
Churn
Model

20. Uplift as a natural evolution
Train
Data
Test
Data
A/B
test
on
scored
dataset
Step 3 : train your uplift model
Training
Churn
Model
Training

21. Uplift as a natural evolution
Train
Data
Test
Data
A/B
test
on
scored
dataset
New
scoring
Step 4 : deploy
Training
Churn
Model
New
Test
Data
Upli5
Model
Training

22. Uplift as a natural evolution
Train
Data
Test
Data
A/B
test
on
scored
dataset
New
scoring
Capitalize on your A/B test data !
Training
Churn
Model
New
Test
Data
Upli5
Model
Training
Today’s Focus

23. Machine learning Model

24. Uplift modeling
• Three main methods in Uplift Literature:
• Two models approach
• Class variable modification
• Modification of existing machine learning models
(tree based methods, out of the scope of today).
• Generalization: Causal inference approach
• Main Assumption (Uncofoundedness) :
Control and Treatment belonging should be independent of the response

25. Uplift modeling : Two model approach
• Build a model on treatment to get
• Build a model on control to get
• Set :
PT
(Y |X)
PC
(Y |X)
P = PT
(Y |X) PC
(Y |X)

26. Uplift modeling : Two model approach
• Advantages :
• Standard ML models can be used
• In theory, two good estimators -> a good uplift model
• Works well in practice
• Generalize to regression and multi-treatment easily
• Drawbacks
• Difference of estimators is probably not the best estimator of the difference
• The two classifier can ignore the weaker uplift signal (since it’s not their target)
• Algorithm focusing on estimating the difference should perform better

27. Uplift modeling : Class variable transformation
• Introduced in Jaskowski, Jaroszewicz 2012
• Allows any classifier to be updated to uplift modeling
• Let denote the group membership (Treatment or Control)
• Let’s define the new target variable :
• This corresponds to flipping the target in the control dataset.
G 2 {T, C}
Z =
8
<
:
1 if G = T and Y = 1
1 if G = C and Y = 0
0 otherwise

28. • Why does it work ?
• By design (A/B test warning !), should be independent from
• Possibly with a reweighting of the datasets we should have :
thus
P(Z = 1|X) = PT
(Y = 1|X)P(G = T|X) + PC
(Y = 0|X)P(G = C|X)
P(Z = 1|X) = PT
(Y = 1|X)P(G = T) + PC
(Y = 0|X)P(G = C)
G X
P(G = T) = P(G = C) = 1/2
2P(Z = 1|X) = PT
(Y = 1|X) + PC
(Y = 0|X)
Uplift modeling : Class variable transformation

29. • Why does it work ?
Thus
And sorting by is the same as sorting by
2P(Z = 1|X) = PT
(Y = 1|X) + PC
(Y = 0|X)
= PT
(Y = 1|X) + 1 PC
(Y = 1|X)
P = 2P(Z = 1|X) 1
P(Z = 1|X) P
Uplift modeling : Class variable transformation

30. • Summary :
• Flip class for control dataset
• Concatenate test and control dataset
• Build a classifier
• Target users with highest probability
• Advantages :
• Any classifier can be used
• Directly predict uplift (and not each class separately)
• Single model on a larger dataset (instead of two small ones)
• Drawbacks :
• Complex decision surface -> model can perform poorly
Uplift modeling : Class variable transformation

31. Generalization :
• From Athey:
Y ?
= Y G e(X)
e(X)(1 e(X))Let
• Any classical estimator can be used
• Generalize to more advanced A/B test schemed
• Specific estimator can be derived (see paper)
With
E(Y ?
= P)Then (Unconfoundedness)
e(X) = P(G = 1|X)

32. Uplift modeling : Other methods
• Based on decision trees :
• Rzepakowski Jaroszewicz 2012
new decision tree split criterion based on information theory
• Soltys Rzepakowski Jaroszewicz 2013
Ensemble methods for uplift modeling
(out of today scope )

33. Model Evaluation

34. Evaluation
• Problem :
• We don’t have a clear 0/1 target.
• We would need to know for each customer
• Response to treatment
• Response to control
-> not possible
• Cross Validation :
• Train and Validation split
• Stratified on target/control variable.

35. Evaluation: Uplift Decile / Bins
• Uplift bins:
• Sort dataset by predicted uplift descending
• Calculate uplift per bin
• Hard to compare models
YT number of positive in treated
YC number of positive in control
NT number in treated
NC number in control
U = YT
NT
YC
NC

36. Evaluation: Uplift Decile / Bins
• Cumulative Uplift bins :
• Sort dataset by predicted uplift descending
• Calculate uplift on all bins preceding
• Cumulative Uplift Gain bins :
• Sort dataset by predicted uplift descending
• Calculate uplift on all bins preceding
• Multiply by number of instances

37. Evaluation: Uplift Curve
• Generalization of the previous curve
Parametric curve defined by:
• Similar to lift / ROC Curve
• Models can be compared ! AUC

38. Evaluation: Qini
• Introduced in Radcliffe
Parametric curve defined by: f(t) = YT (t) YC(t) ⇤ NT (t)/NC(t)
t (observa1ons)

39. Evaluation: Qini
• Best model :
• Take first all positive in target and last all positive in control.
• No theoretic best model :
• depends on possibility of negative effect
• Displayed for no negative effect
• Random model :
• Corresponds to global effect of treatment
• Hillstrom Dataset :
• For women models are comparable and useful
• For men, there is no clear individuals to target

40. Evaluation: Qini
t (observa1ons)

41. Evaluation: Qini
t (observa1ons)

42. Conclusion
• Uplift Modeling :
• Surprisingly little literature / examples
• The theory is rather easy to test
• Two models
• Class modification
• The intuition and evaluation are not easy to grasp
• On the client side :
• A good lead to select the best offer for a customer
-> Can lead to more customer personalization
• Applications :
• Churn, mailing, retail couponing, personalized medicine…

43. Thank you for your attention !

44. A few references
• Data :
• Churn in gaming :
WOWAH dataset
• Uplift for healthcare :
Colon Dataset
• Uplift in mailing :
Hillstrom data challenge
• Uplift in General :
Simulated data : available on gallery.dataiku.com
• Demo :
• http://gallery.dataiku.com/projects/DKU_UPLIFT/

45. A few references
• Application
• Uplift modeling for clinical trial data (Jaskowski, Jaroszewicz)
• Uplift Modeling in Direct Marketing (Rzepakowski, Jaroszewicz)
• Modeling techniques :
• Rzepakowski Jaroszewicz 2011 (decision trees)
• Soltys Rzepakowski Jaroszewicz 2013 (ensemble for uplift)
• Jaskowski Jaroszewicz 2012 (Class modification model)
• Evaluation
• Using Control Groups to Target on Predicted Lift (Radcliffe)
• Testing a New Metric for Uplift Models (Mesalles Naranjo)

46. A few references
• Causal inference
• Machine Learning Methods for Estimating Heterogeneous Causal Effects (Athey, Imbens 2015)
• Introduction to Causal Inference (Sprites 2010)
• Causal inference in statistics: An overview (Pearl 2009)