Jethro's Braindump

Causality, part 1 - Bernhard Schölkopf - MLSS 2020, Tübingen - YouTube


Background and Motivation

Consider a dataset of temperature \(t\) vs altitude \(a\). We typically see that the larger the altitude, the lower the temperature. How do we know if this is a causal effect?

  1. Intervention: we can raise the city, and find that the temperature changes
  2. Hypothetical intervention: expect that \(t\) changes, since we can think of a physical mechanism \(p(t|a)\) that is independent of \(p(a)\). We expect that \(p(t|a)\) is invariant across different countries in similar climate zone.

A “structural” relation not only explains the observed data; it captures a structure connecting the variables.

An equation becomes structural by virtue of invariance to a domain of modifications.

Structural Causal Model

A structural causal model satisfies the following conditions:

  1. It is a directed acyclic graph \(G\) with vertices \(X_{1}, \dots, X_{n}\)
  2. Vertices are observables, and arrows represent direct causation
  3. Each observable \(X_{i}\) is a density, with independent unexplained random variables \(U_{i}, \dots, U_{n}\).

The structural causal model satisfies the Reichenbach’s principle.

TODO Reichenbach’s principle