Md. Asif Uddin

    Chapter 8 VI.8

    Causal Machine Learning

    Machine learning estimates the nuisance functions, and the estimator's structure is what makes the effect robust to getting them wrong.

    Machine learning estimates the nuisance functions; structure makes the effect robust.

    How this chapter is built

    M3Load-bearing

    The content is mathematics. Understanding is demonstrated by computation, not recall.

    basics2/11what the words mean
    concept2/2what to picture
    theory0/4why it works, and when it does not
    mathematics0/15derive it, then compute it
    practice0/9build it, break it, read the papers

    Five strands, not one. Mathematics is the spine; the other four are the body. A chapter cannot pay its way out of teaching with problems, nor out of problems with teaching.

    Before you start

    The problem

    Flexible models fit the outcome and the treatment better than any parametric form. Plugging them into an effect estimate introduces a bias that does not vanish with sample size, and the repair is a change of estimator rather than of model.

    Operators by the range they coverFour operator types striped through the model, each covering a different range: short and medium convolutions for local motifs, long implicit convolutions for domain-scale structure, and self-attention reserved for the sparse long-range relationships that need it.one megabase, single-nucleotide resolutionshort explicit convmotifs, splice sitesmedium regularized convlocal regulatory syntaxlong implicit convdomain-scale structureself-attentionenhancer to promoter, sparseAttention costs the square of the length, so you do not pay it across the whole sequence.
    Fig. 8 — Operators assigned by the range they cover, so attention is spent only on the sparse long-range relationships that need it. A megabase becomes affordable.

    What this chapter covers

    • Heterogeneous treatment effects
    • Causal forests
    • Representation learning
    • Neural causal models
    • Causal discovery

    Apparatus

    The mathematics this chapter leans on, held in Book 0 so it can be assumed here without being taught here. Not a gate — follow a link when a step stops making sense.

    Estimators, bias and variance 0.ST.01 · The bootstrap 0.ST.05 · The chain rule 0.MC.03

    Notation

    • 𝔼Expectation
    • VarVariance
    • θ̂An estimate, as against the quantity it estimates
    • θAll parameters of a model, taken together

    Propositions

    Not yet written. The topics above are the plan for this chapter; each will become a proposition with its own figure.

    Worked problems

    0/5 problems0/4 variants0/10 exercisesowes 15 more

    Not yet written. At M3 this chapter owes 5 worked problems across 4 distinct variants, and 10 exercises, every one with a published solution. The build enforces that from the day the chapter is marked published.