New metrics and search algorithms for weighted causal DAGs

TL;DR

This paper explores the limits of causal graph discovery using adaptive interventions with node-dependent costs, establishing theoretical bounds and proposing algorithms with logarithmic approximation guarantees.

Contribution

It introduces a new benchmark for interventional cost and provides adaptive search algorithms with logarithmic approximation guarantees under various settings.

Findings

No algorithm can surpass linear approximation in the worst case.

A new benchmark for interventional cost is proposed.

Algorithms achieve logarithmic approximation under certain conditions.

Abstract

Recovering causal relationships from data is an important problem. Using observational data, one can typically only recover causal graphs up to a Markov equivalence class and additional assumptions or interventional data are needed for complete recovery. In this work, under some standard assumptions, we study causal graph discovery via adaptive interventions with node-dependent interventional costs. For this setting, we show that no algorithm can achieve an approximation guarantee that is asymptotically better than linear in the number of vertices with respect to the verification number; a well-established benchmark for adaptive search algorithms. Motivated by this negative result, we define a new benchmark that captures the worst-case interventional cost for any search algorithm. Furthermore, with respect to this new benchmark, we provide adaptive search algorithms that achieve logarithmic approximations under various settings: atomic, bounded size interventions and generalized cost objectives.