Jethro's Braindump

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

source
https://www.youtube.com/watch?v=btmJtThWmhA&feature=youtu.be

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 X1,…,Xn
  2. Vertices are observables, and arrows represent direct causation
  3. Each observable Xi is a density, with independent unexplained random variables Ui,…,Un.

The structural causal model satisfies the Reichenbach’s principle.

TODO Reichenbach’s principle