A Unified Experiment Design Approach for Cyclic and Acyclic Causal Models

TL;DR

This paper introduces a unified experiment design method capable of identifying both cyclic and acyclic causal graphs, addressing challenges posed by cycles and optimizing the number and size of experiments needed.

Contribution

It proposes a novel, order-optimal experiment design approach that unifies causal graph identification for both cyclic and acyclic structures, with bounds on experiments and their sizes.

Findings

The approach guarantees unique causal graph identification in the worst case.

It is order-optimal in the number of experiments required.

The method is also optimal when experiment size is bounded.

Abstract

We study experiment design for unique identification of the causal graph of a simple SCM, where the graph may contain cycles. The presence of cycles in the structure introduces major challenges for experiment design as, unlike acyclic graphs, learning the skeleton of causal graphs with cycles may not be possible from merely the observational distribution. Furthermore, intervening on a variable in such graphs does not necessarily lead to orienting all the edges incident to it. In this paper, we propose an experiment design approach that can learn both cyclic and acyclic graphs and hence, unifies the task of experiment design for both types of graphs. We provide a lower bound on the number of experiments required to guarantee the unique identification of the causal graph in the worst case, showing that the proposed approach is order-optimal in terms of the number of experiments up to an additive logarithmic term. Moreover, we extend our result to the setting where the size of each experiment is bounded by a constant. For this case, we show that our approach is optimal in terms of the size of the largest experiment required for uniquely identifying the causal graph in the worst case.