Causal Inference

The core challenge is that we can never observe the counterfactual outcome for a single individual. For a customer who received a discount, we see their purchase behavior, but we cannot simultaneously observe what they would have done without the discount. Causal inference methods are designed to estimate this missing counterfactual using statistical techniques like randomized control trials (RCTs) or observational study designs.

DAGs are visual and mathematical tools used to encode assumptions about the causal relationships between variables. They explicitly map out confounders, mediators, and colliders, preventing statistical paradoxes. By following the rules of d-separation, analysts can identify which variables must be controlled for to isolate a causal effect and which must be left alone to avoid introducing bias.

Also known as the Rubin Causal Model, this framework formalizes causality by defining a treatment effect as the difference between two potential outcomes for each unit: Y(1) under treatment and Y(0) under control. The Average Treatment Effect (ATE) is the population mean of these individual differences. This framework directly connects the definition of a causal effect to the missing data problem.

An instrumental variable is a tool used to estimate causal effects when a randomized experiment is impossible and unobserved confounding is present. A valid instrument must satisfy three conditions: it must be correlated with the treatment (relevance), have no direct effect on the outcome except through the treatment (exclusion restriction), and be independent of unobserved confounders (exchangeability). A classic example is using a randomized encouragement design as an instrument for actual treatment uptake.

DiD is a quasi-experimental design that estimates a treatment effect by comparing the change in an outcome over time between a treated group and an untreated control group. The key identifying assumption is parallel trends: in the absence of treatment, the difference between the groups would have remained constant. This method is widely used in policy evaluation and marketing to measure the impact of a regional campaign launch.

Developed by Judea Pearl, do-calculus is a formal symbolic language that distinguishes between passively observing a variable, P(Y|X), and actively intervening to set its value, P(Y|do(X)). This mathematical framework provides three rules for transforming expressions containing interventions into standard probabilistic expressions, allowing causal effects to be derived from observational data when a causal graph is known.

A causal ML technique that predicts the incremental impact of a treatment on an individual's behavior. Unlike propensity models that predict likelihood, uplift models isolate the true persuasion effect by subtracting the organic conversion rate from the treated conversion rate.

• Four-quadrant segmentation: Persuadables, Sure Things, Lost Causes, Sleeping Dogs
• Directly measures the Conditional Average Treatment Effect (CATE)
• Essential for avoiding wasted marketing spend on customers who would convert anyway

The variation in causal impact across different individuals or subgroups. A single intervention rarely affects all customers uniformly—HTE analysis reveals who responds and who doesn't.

• Drives personalization strategy by identifying responsive segments
• Estimated through methods like causal forests and meta-learners
• Critical insight: a null average effect may mask significant positive and negative subgroup effects

An off-policy evaluation method that corrects for selection bias in historical data. When actions were taken by a non-random logging policy, IPS re-weights observed outcomes by the inverse probability of the action being taken.

• Enables unbiased estimation of a new policy's value from old data
• Suffers from high variance when propensity scores are extreme
• Foundation for more advanced estimators like Doubly Robust

A statistical method combining inverse propensity scoring with a direct outcome model to estimate causal effects. It remains consistent if either the propensity model or the outcome model is correctly specified—not necessarily both.

• Provides two chances to get the estimate right
• Significantly reduces variance compared to pure IPS
• Standard approach for evaluating NBA policies in production

The average causal effect of a treatment for a specific subgroup defined by observed features. CATE estimation is the core task of personalized decision-making—determining which action works best for which individual.

• Estimated via S-Learners, T-Learners, and X-Learners
• Causal forests use recursive partitioning to discover effect heterogeneity
• Directly feeds into the reward function of contextual bandits

A suite of techniques for estimating how a new target policy would perform using only historical data collected by a different behavior policy. OPE is essential when online A/B testing is too costly, risky, or slow.

• Methods include IPS, Doubly Robust, and Direct Method
• Validates NBA models before production deployment
• Requires careful handling of covariate shift and concept drift