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?
- Intervention: we can raise the city, and find that the temperature changes
- 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:
- It is a directed acyclic graph \(G\) with vertices \(X_{1}, \dots, X_{n}\)
- Vertices are observables, and arrows represent direct causation
- 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.