Graph-based Complexity for Causal Effect by Empirical Plug-in

TL;DR

This paper demonstrates that the computational complexity of evaluating empirical causal effect estimates can be efficiently bounded by the hypergraph structure of the estimand, often enabling linear-time evaluation depending on the estimand's properties.

Contribution

It introduces a graph-based framework linking the complexity of empirical causal effect estimation to hypergraph properties like treewidth and hypertree width.

Findings

Evaluation complexity is bounded by estimand hypergraph properties.

Hypertree width often provides tighter bounds due to data sparsity.

Efficient evaluation is possible even with high-dimensional data.

Abstract

This paper focuses on the computational complexity of computing empirical plug-in estimates for causal effect queries. Given a causal graph and observational data, any identifiable causal query can be estimated from an expression over the observed variables, called the estimand. The estimand can then be evaluated by plugging in probabilities computed empirically from data. In contrast to conventional wisdom, which assumes that high dimensional probabilistic functions will lead to exponential evaluation time of the estimand. We show that computation can be done efficiently, potentially in time linear in the data size, depending on the estimand's hypergraph. In particular, we show that both the treewidth and hypertree width of the estimand's structure bound the evaluation complexity of the plug-in estimands, analogous to their role in the complexity of probabilistic inference in graphical models. Often, the hypertree width provides a more effective bound, since the empirical distributions are sparse.