Symmetric observations without symmetric causal explanations

TL;DR

This paper investigates whether symmetries in observed data can simplify causal inference, demonstrating that, in general, symmetries do not reduce the complexity of identifying causal explanations.

Contribution

It provides a formal proof showing that symmetries in observations do not necessarily correspond to symmetries in underlying causal models, challenging assumptions in causal inference.

Findings

Symmetries in observations often do not imply symmetries in causal explanations.

Explicit example with tripartite distribution shows limitations of exploiting symmetries.

Proves incompatibility of certain classical and relativistic causal assumptions.

Abstract

Inferring causal models from observed correlations is a challenging task, crucial to many areas of science. In order to alleviate the computational effort when sifting through possible causal explanations for some given observations, it is important to know whether symmetries in the observations correspond to symmetries in the underlying realization so that one can quickly discard impossible explanations. Via an explicit example, we demonstrate that, in general, symmetries cannot be exploited to reduce the hypothesis space. We use a tripartite probability distribution over binary events that is realized by using three (different) independent sources of classical randomness. We prove that even removing the condition that the sources distribute systems described by classical physics, the requirements that (i) the sources distribute the same physical systems, (ii) these physical systems respect relativistic causality, and (iii) the correlations are the observed ones are incompatible.