The traditional aim of machine learning methods is to infer meaningful features of an underlying probability distribution from samples drawn of that distribution. With the help of such features, one can infer associations of interest and predict or classify yet unobserved samples. Causal analysis goes one step further; it aims at inferring features of the data-generating process, that is, of the invariant strategy by which Nature assigns values to the variables in the distribution. Process features enable us to predict, not merely relationships governed by the underlying distribution, but also how that distribution would CHANGE when conditions are altered, say, by deliberate interventions or by spontaneous transformations.

We will review concepts, principles, and mathematical tools that were found useful in reasoning about causal and counterfactual relations, and will demonstrate their applications in several data-intensive sciences. These include questions of confounding control, policy analysis, misspecification tests, mediation, heterogeneity, selection bias, missing data, and the integration of findings from diverse studies.

The following topics will be emphasized:

1. The 3-layer causal hierarchy: association, intervention and counterfactuals. http://ftp.cs.ucla.edu/pub/stat_ser/r350.pdf

2. What mathematics can tell us about "transfer learning" or "generalizing across domains" http://ftp.cs.ucla.edu/pub/statser/r372.pdf http://ftp.cs.ucla.edu/pub/statser/r387.pdf

3. What causal analysis tells us about recovery from selection bias and missing data. http://ftp.cs.ucla.edu/pub/statser/r381.pdf http://ftp.cs.ucla.edu/pub/statser/r410.pdf

4. The Mediation Formula, and what it tells us about “How nature works” http://ftp.cs.ucla.edu/pub/stat_ser/r379.pdf