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Causal Inference +
Estimating Heterogeneous
Treatment Effects using ML
Agenda
● The Fundamental Problem in Causal Inference
● ATE vs CATE
● Why do we care about CATE?
● Propensity Score Matching
● Meta-Learners
○ S Learner
○ T Learner
○ X Learner
● Uplift Curves
● Interpreting/Explaining the Lift
● Validating the Model
Steve Steve (copy)Steve (copy)
The Fundamental Problem in
Causal Inference
Our
Universe
Alternate
Universe
Our
Universe
Alternate
Universe
The Fundamental Problem in
Causal Inference
Our
Universe
Steve
Alternate
Universe
Steve (copy)
Our
Universe
Steve
Alternate
Universe
Steve (copy)
A
People like Steve
B
People like Steve
Impossible
Gold Standard
It’s Much Harder in Observational Data
People like Steve People like Steve
People unlike Steve
Did Not ClickClicked
A
People like Steve
B
People like Steve
Gold Standard
ATE vs CATE
Average Treatment Effect (ATE) =
Conditional Average Treatment Effect (CATE) =
E[Y | Treatment] - E[Y | Control]
E[Y | Treatment, X] - E[Y | Control, X]
Population Level
User/Segment Level
ATE can mask subgroups
with big CATEs
If you have those with a positive and a
negative CATE at the level of the total
experimental population, it might happen
that the ATE is close to zero while the
CATEs within the subpopulations are
statistically significant.
Negative CATES
On the one hand, you most of the time
want to target those with the highest
predicted uplift. On the other hand, you’ll
also want to avoid targeting those who
might have a negative CATE. For example,
some customers could be put off by CRM
comms.
Target those with the
highest uplift
If the treatment costs money, then it
makes sense to target a subset of the total
population. Most of the time, the best way
to do such targeting is to select the
subgroup with the highest predicted
treatment effect. Example: churn
prevention with incentives.
Why do we care about CATE?
Procedure
1. Build a propensity (binary classification) model
for all users.
2. For every user uT in Treatment,
3. Calculate a vector of distances/similarities
from uT to all Control users
4. Select the top k similar users (k=1 to achieve
balanced post-match set), filtered by a
specified threshold/caliper
5. Repeat Step 2 with/without replacement, until all
users in Treatment group have their
corresponding matched Control user
Propensity Score Matching
People like Steve People like Steve
People unlike Steve
ControlTreatment
Propensity Score Matching
Treatment
Period
(3 Mon)
Pre-Treatment
Period
(3 Mon)
Post-Treatment
Period
(3 Mon)
Treatment
Group
Control
Group
Feature
Collection
Treatment
Observation
GB
Observation
- Treatment Group: Riders who converted to Eaters within treatment period
- Control Group: Riders who were not converted to Eaters until the end of post-treatment period
Propensity Score Matching
Before Matching After Matching
Treatment
Control
Treatment
Control
S Learner
X Learner R Learner
Model
T
C
T
Pred
C
PredInput Train
T, CT, C
ModelT
T
PredInput Train
C ModelC
Cpred
Actual Estimate
Tpred
Ctrue
Ttrue
Propensity-weighted
average
CATE
CATE
=
=
-
-
T Learner
ModelT
T
Pred PredInput Train
C ModelC
CATE
--
CATE
Cest
Test
Modelm Modele
Family of Meta-Learners
Procedure
1. Create a binary feature is_treatment,
indicating whether a user is from the
treatment group
2. Train a single (S) model
3. For all users, set is_treatment to 1 and
calculate yhatis_treatment=1
4. For all users, set is_treatment to 0 and
calculate yhatis_treatment=0
5. CATE = yhatis_treatment=0 - yhatis_treatment=1
S Learner
Model
T
C
T
Pred
C
PredInput Train
CATE
-
S Learner
Procedure
1. Train two (T) separate models, one for
Treatment group and one for Control group
2. For all users, predict output based on the
Treatment model, i.e. yhatT_model
3. For all users, predict output based on the
Control model, i.e. yhatC_model
4. CATE = yhatT_model - yhatC_model
T, CT, C
T Learner
ModelT
T
Pred PredInput Train
C ModelC
CATE
-
T Learner
Procedure
1. Train two separate models, like in T-Learner case
2. For Control users, predict yhatT_model
3. For Treatment users, predict yhatC_model
4. For Control users, compute
○ tauC_users = yhatT_model_C_users - yC_users
○ Build a model to predict tauC_users
5. For Treatment users, compute
○ tauT_users = yT_users - yhatC_model_T_users
○ Build a model to predict tauT_users
6. CATE = (1 - p) * tauT_users + p * tauC_users
X Learner
ModelT
T
PredInput Train
C ModelC
Cpred
Actual Estimate
Tpred
Ctrue
Ttrue
Propensity-weighted
average
CATE
=
=
-
-
Cest
Test
X Learner
ATE can mask subgroups
with big CATEs
If you have those with a positive and a
negative CATE at the level of the total
experimental population, it might happen
that the ATE is close to zero while the
CATEs within the subpopulations are
statistically significant.
Negative CATES
On the one hand, you most of the time
want to target those with the highest
predicted uplift. On the other hand, you’ll
also want to avoid targeting those who
might have a negative CATE. For example,
some customers could be put off by CRM
comms.
Target those with the
highest uplift
If the treatment costs money, then it
makes sense to target a subset of the total
population. Most of the time, the best way
to do such targeting is to select the
subgroup with the highest predicted
treatment effect. Example: churn
prevention with incentives.
Why do we care about CATE?
Targeting Users with Highest Uplift
0% 100%
CumulativeUplift
Population Targeted (%)
Targeting Users with Highest Uplift
0% 100%10%
40% uplift achieved
from targeted just
10% of users
*Note: x axis not drawn to scale - annotation serves as interpretation example
CumulativeUplift
Population Targeted (%)
CumulativeUplift
Population Targeted (%)
0% 100%
Targeting Users with Highest Uplift
Offer Promos to
these customers!
Stop spamming
these customers!
What’s actually “causing” the lift?
What’s actually “causing” the lift?
What’s actually “causing” the lift?
Synthetic Data
We can use different synthetic data
generation processes to generate data
where we know the true labels (treatment
effects). This allows us to measure the
accuracy on CATE, but the downside is
that it is highly dependent on the data
generation process (and in reality the data
you observe will most likely not follow the
same process)
Consistency
Like any other machine learning problem,
we should run all meta-learners and
observe how different the results are in
each case. If we observe a high level of
inconsistency, it’s likely that the input
data is too noisy, or that there isn’t
enough data for the meta-learners to
learn.
Experimentation
Recall that the gold standard for
measuring ATE is running a randomized
controlled experiment (i.e. A/B test). Same
applies here! We can measure the ATE of
the experiment to validate whether the
ATE of our meta-learner is accurate. But
this won’t necessarily prove that CATE is
accurate on a user-level.
Validating the Estimated Treatment
Effects
Subset Validation
Remove a random subset of the data, then
re-train the meta-learner.
Replace/Add Irrelevant
Confounder
Add/replace a random variable to
introduce noise to the system, then re-
train the meta-learner.
Placebo Treatment
Replace the treatment with a random
variable, then re-train the meta-learner.
Sensitivity Analysis: measuring the
robustness of meta-learners
CausalML
https://github.com/uber/causalml
Questions?

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Why start using uplift models for more efficient marketing campaigns

  • 1. Causal Inference + Estimating Heterogeneous Treatment Effects using ML
  • 2.
  • 3.
  • 4. Agenda ● The Fundamental Problem in Causal Inference ● ATE vs CATE ● Why do we care about CATE? ● Propensity Score Matching ● Meta-Learners ○ S Learner ○ T Learner ○ X Learner ● Uplift Curves ● Interpreting/Explaining the Lift ● Validating the Model
  • 5. Steve Steve (copy)Steve (copy) The Fundamental Problem in Causal Inference Our Universe Alternate Universe Our Universe Alternate Universe
  • 6. The Fundamental Problem in Causal Inference Our Universe Steve Alternate Universe Steve (copy) Our Universe Steve Alternate Universe Steve (copy) A People like Steve B People like Steve Impossible Gold Standard
  • 7. It’s Much Harder in Observational Data People like Steve People like Steve People unlike Steve Did Not ClickClicked A People like Steve B People like Steve Gold Standard
  • 8. ATE vs CATE Average Treatment Effect (ATE) = Conditional Average Treatment Effect (CATE) = E[Y | Treatment] - E[Y | Control] E[Y | Treatment, X] - E[Y | Control, X] Population Level User/Segment Level
  • 9. ATE can mask subgroups with big CATEs If you have those with a positive and a negative CATE at the level of the total experimental population, it might happen that the ATE is close to zero while the CATEs within the subpopulations are statistically significant. Negative CATES On the one hand, you most of the time want to target those with the highest predicted uplift. On the other hand, you’ll also want to avoid targeting those who might have a negative CATE. For example, some customers could be put off by CRM comms. Target those with the highest uplift If the treatment costs money, then it makes sense to target a subset of the total population. Most of the time, the best way to do such targeting is to select the subgroup with the highest predicted treatment effect. Example: churn prevention with incentives. Why do we care about CATE?
  • 10. Procedure 1. Build a propensity (binary classification) model for all users. 2. For every user uT in Treatment, 3. Calculate a vector of distances/similarities from uT to all Control users 4. Select the top k similar users (k=1 to achieve balanced post-match set), filtered by a specified threshold/caliper 5. Repeat Step 2 with/without replacement, until all users in Treatment group have their corresponding matched Control user Propensity Score Matching People like Steve People like Steve People unlike Steve ControlTreatment
  • 11. Propensity Score Matching Treatment Period (3 Mon) Pre-Treatment Period (3 Mon) Post-Treatment Period (3 Mon) Treatment Group Control Group Feature Collection Treatment Observation GB Observation - Treatment Group: Riders who converted to Eaters within treatment period - Control Group: Riders who were not converted to Eaters until the end of post-treatment period
  • 12. Propensity Score Matching Before Matching After Matching Treatment Control Treatment Control
  • 13. S Learner X Learner R Learner Model T C T Pred C PredInput Train T, CT, C ModelT T PredInput Train C ModelC Cpred Actual Estimate Tpred Ctrue Ttrue Propensity-weighted average CATE CATE = = - - T Learner ModelT T Pred PredInput Train C ModelC CATE -- CATE Cest Test Modelm Modele Family of Meta-Learners
  • 14. Procedure 1. Create a binary feature is_treatment, indicating whether a user is from the treatment group 2. Train a single (S) model 3. For all users, set is_treatment to 1 and calculate yhatis_treatment=1 4. For all users, set is_treatment to 0 and calculate yhatis_treatment=0 5. CATE = yhatis_treatment=0 - yhatis_treatment=1 S Learner Model T C T Pred C PredInput Train CATE - S Learner
  • 15. Procedure 1. Train two (T) separate models, one for Treatment group and one for Control group 2. For all users, predict output based on the Treatment model, i.e. yhatT_model 3. For all users, predict output based on the Control model, i.e. yhatC_model 4. CATE = yhatT_model - yhatC_model T, CT, C T Learner ModelT T Pred PredInput Train C ModelC CATE - T Learner
  • 16. Procedure 1. Train two separate models, like in T-Learner case 2. For Control users, predict yhatT_model 3. For Treatment users, predict yhatC_model 4. For Control users, compute ○ tauC_users = yhatT_model_C_users - yC_users ○ Build a model to predict tauC_users 5. For Treatment users, compute ○ tauT_users = yT_users - yhatC_model_T_users ○ Build a model to predict tauT_users 6. CATE = (1 - p) * tauT_users + p * tauC_users X Learner ModelT T PredInput Train C ModelC Cpred Actual Estimate Tpred Ctrue Ttrue Propensity-weighted average CATE = = - - Cest Test X Learner
  • 17. ATE can mask subgroups with big CATEs If you have those with a positive and a negative CATE at the level of the total experimental population, it might happen that the ATE is close to zero while the CATEs within the subpopulations are statistically significant. Negative CATES On the one hand, you most of the time want to target those with the highest predicted uplift. On the other hand, you’ll also want to avoid targeting those who might have a negative CATE. For example, some customers could be put off by CRM comms. Target those with the highest uplift If the treatment costs money, then it makes sense to target a subset of the total population. Most of the time, the best way to do such targeting is to select the subgroup with the highest predicted treatment effect. Example: churn prevention with incentives. Why do we care about CATE?
  • 18. Targeting Users with Highest Uplift 0% 100% CumulativeUplift Population Targeted (%)
  • 19. Targeting Users with Highest Uplift 0% 100%10% 40% uplift achieved from targeted just 10% of users *Note: x axis not drawn to scale - annotation serves as interpretation example CumulativeUplift Population Targeted (%)
  • 20. CumulativeUplift Population Targeted (%) 0% 100% Targeting Users with Highest Uplift Offer Promos to these customers! Stop spamming these customers!
  • 24. Synthetic Data We can use different synthetic data generation processes to generate data where we know the true labels (treatment effects). This allows us to measure the accuracy on CATE, but the downside is that it is highly dependent on the data generation process (and in reality the data you observe will most likely not follow the same process) Consistency Like any other machine learning problem, we should run all meta-learners and observe how different the results are in each case. If we observe a high level of inconsistency, it’s likely that the input data is too noisy, or that there isn’t enough data for the meta-learners to learn. Experimentation Recall that the gold standard for measuring ATE is running a randomized controlled experiment (i.e. A/B test). Same applies here! We can measure the ATE of the experiment to validate whether the ATE of our meta-learner is accurate. But this won’t necessarily prove that CATE is accurate on a user-level. Validating the Estimated Treatment Effects
  • 25. Subset Validation Remove a random subset of the data, then re-train the meta-learner. Replace/Add Irrelevant Confounder Add/replace a random variable to introduce noise to the system, then re- train the meta-learner. Placebo Treatment Replace the treatment with a random variable, then re-train the meta-learner. Sensitivity Analysis: measuring the robustness of meta-learners

Editor's Notes

  1. One-sided confounding function