Efficient Symbolic Computations for Identifying Causal Effects

TL;DR

This paper introduces an efficient algorithm for symbolic computation that determines the identifiability of causal effects in linear models, overcoming computational challenges of traditional methods.

Contribution

The authors develop a quasi-polynomial time algorithm to find the lowest degree identifying formulas for causal effects, improving practical feasibility.

Findings

Algorithm finds the lowest degree formulas efficiently.

Decides rational identifiability in quasi-polynomial time.

Overcomes limitations of Gr"obner basis methods.

Abstract

Determining identifiability of causal effects from observational data under latent confounding is a central challenge in causal inference. For linear structural causal models, identifiability of causal effects is decidable through symbolic computation. However, standard approaches based on Gr\"obner bases become computationally infeasible beyond small settings due to their doubly exponential complexity. In this work, we study how to practically use symbolic computation for deciding rational identifiability. In particular, we present an efficient algorithm that provably finds the lowest degree identifying formulas. For a causal effect of interest, if there exists an identification formula of a prespecified maximal degree, our algorithm returns such a formula in quasi-polynomial time.