Causal Layering via Conditional Entropy

TL;DR

This paper introduces algorithms for recovering causal layerings in discrete distributions using conditional entropy, providing provably correct methods that operate efficiently under certain assumptions.

Contribution

It presents novel algorithms for causal layering recovery based on conditional entropy with proven correctness and quadratic runtime under specific assumptions.

Findings

Algorithms correctly recover causal layerings.

Methods operate in quadratic worst-case time.

Applicable under faithfulness and noise assumptions.

Abstract

Causal discovery aims to recover information about an unobserved causal graph from the observable data it generates. Layerings are orderings of the variables which place causes before effects. In this paper, we provide ways to recover layerings of a graph by accessing the data via a conditional entropy oracle, when distributions are discrete. Our algorithms work by repeatedly removing sources or sinks from the graph. Under appropriate assumptions and conditioning, we can separate the sources or sinks from the remainder of the nodes by comparing their conditional entropy to the unconditional entropy of their noise. Our algorithms are provably correct and run in worst-case quadratic time. The main assumptions are faithfulness and injective noise, and either known noise entropies or weakly monotonically increasing noise entropies along directed paths. In addition, we require one of either a very mild extension of faithfulness, or strictly monotonically increasing noise entropies, or expanding noise injectivity to include an additional single argument in the structural functions.