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

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## 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.