The Recovery of Causal Poly-Trees from Statistical Data

TL;DR

This paper presents a method for accurately reconstructing causal poly-trees from empirical data, determining both structure and causal directions with minimal external assumptions.

Contribution

It introduces a novel approach to recover the topology and causal directions of poly-trees from probability distributions, with guarantees of correctness under certain conditions.

Findings

Exact recovery of poly-tree structure from data

Determination of causal directions up to maximum extent

Identification of minimal external semantics needed

Abstract

Poly-trees are singly connected causal networks in which variables may arise from multiple causes. This paper develops a method of recovering ply-trees from empirically measured probability distributions of pairs of variables. The method guarantees that, if the measured distributions are generated by a causal process structured as a ply-tree then the topological structure of such tree can be recovered precisely and, in addition, the causal directionality of the branches can be determined up to the maximum extent possible. The method also pinpoints the minimum (if any) external semantics required to determine the causal relationships among the variables considered.