Matching a Desired Causal State via Shift Interventions

TL;DR

This paper introduces active learning strategies for identifying shift interventions in causal models to match a desired system mean, significantly reducing interventions compared to prior methods.

Contribution

It defines the identifiable class of shift interventions, proposes optimal active learning strategies, and provides theoretical and experimental evidence of their efficiency.

Findings

Strategies guarantee exact mean matching

Fewer interventions needed than previous methods

Strategies are optimal for certain graph classes

Abstract

Transforming a causal system from a given initial state to a desired target state is an important task permeating multiple fields including control theory, biology, and materials science. In causal models, such transformations can be achieved by performing a set of interventions. In this paper, we consider the problem of identifying a shift intervention that matches the desired mean of a system through active learning. We define the Markov equivalence class that is identifiable from shift interventions and propose two active learning strategies that are guaranteed to exactly match a desired mean. We then derive a worst-case lower bound for the number of interventions required and show that these strategies are optimal for certain classes of graphs. In particular, we show that our strategies may require exponentially fewer interventions than the previously considered approaches, which optimize for structure learning in the underlying causal graph. In line with our theoretical results, we also demonstrate experimentally that our proposed active learning strategies require fewer interventions compared to several baselines.