Disentangling Mixtures of Unknown Causal Interventions

TL;DR

This paper investigates the problem of identifying individual intervention components in mixtures affecting causal Bayesian Networks, providing conditions for identifiability, an efficient recovery algorithm, and empirical evaluation through simulations.

Contribution

It introduces conditions under which intervention components are identifiable and develops an efficient algorithm for their recovery in causal Bayesian networks.

Findings

Components are not identifiable in general without assumptions.

Under positivity and exclusion assumptions, components can be uniquely identified.

Simulation results demonstrate the algorithm's effectiveness in finite sample scenarios.

Abstract

In many real-world scenarios, such as gene knockout experiments, targeted interventions are often accompanied by unknown interventions at off-target sites. Moreover, different units can get randomly exposed to different unknown interventions, thereby creating a mixture of interventions. Identifying different components of this mixture can be very valuable in some applications. Motivated by such situations, in this work, we study the problem of identifying all components present in a mixture of interventions on a given causal Bayesian Network. We construct an example to show that, in general, the components are not identifiable from the mixture distribution. Next, assuming that the given network satisfies a positivity condition, we show that, if the set of mixture components satisfy a mild exclusion assumption, then they can be uniquely identified. Our proof gives an efficient algorithm to recover these targets from the exponentially large search space of possible targets. In the more realistic scenario, where distributions are given via finitely many samples, we conduct a simulation study to analyze the performance of an algorithm derived from our identifiability proof.