chapter seven

7 Interventions and Causal Effects

 

This chapter covers

  • Case studies of interventions in ML engineering contexts
  • How interventions relate to A/B tests and randomized experiments
  • Implementing interventions on causal models with intervention operators
  • Using a causal model to represent many interventional distributions
  • Causal effects as natural extensions of an intervention distribution

An intervention is something an agent does to cause other things to happen. Interventions change the data generating process.

Interventions are the most fundamental concept in how we define causality. An example is this definition from an influential textbook on experimental design:

The paradigmatic assertion in causal relationships is that manipulation of a cause will result in the manipulation of an effect… Causation implies that by varying one factor I can make another vary.

(Campbell, D.T. and Cook, T.D., 1979. Quasi-experimentation. Chicago, IL: Rand McNally. p36)

Interventions are how we go from correlation to causality. Correlation is symmetric; the statements “Amazon’s laptop sales correlate with Amazon’s laptop bag sales” and “Amazon’s laptop bag sales correlate with Amazon’s laptop sales” are equivalent. But interventions make causality a one-way street; if Amazon recommends the sale of laptops, laptop bag sales will increase, but if Amazon promotes the sale of laptop bags, we wouldn’t expect people to respond by buying new laptops to fill them.

7.1 Case studies

7.1.1 Predicting the weather vs. business performance

7.1.2 Case study: Credit fraud detection

7.1.3 Case Study: Statistical analysis for an online role-playing game

7.1.4 From randomized experiments to interventions

7.1.5 From observations to experiments

7.1.6 From experiments to interventions

7.1.7 Recap

7.2 The ideal intervention and intervention operator

7.2.1 Intervention operators

7.2.2 Ideal interventions in structural causal models

7.2.3 Graph mutilation: The ideal intervention in causal DAGs and causal graphical models

7.2.4 Graphs mutilation and d-separation

7.2.5 Ideal interventions and causal Markov kernels

7.2.6 Ideal interventions in a causal program

7.3 Intervention variables and distributions

7.3.1 “Do” and counterfactual notation

7.3.2 When causal notation reduces to traditional notation

7.3.3 Causal models represent all intervention distributions

7.4 Interventions and causal effects

7.4.1 Average treatment effects with binary causes

7.4.2 Average treatment effect with categorical causes

7.4.3 Average treatment effect for continuous causes

7.4.4 Conditional average treatment effect

7.4.5 Statistical measures of association and causality

7.4.6 Causality and regression models

7.5 Stochastic interventions

7.5.1 Random assignment in an experiment is a stochastic intervention

7.5.2 Intervention policies