Functional Causal Bayesian Optimization

TL;DR

The paper introduces functional causal Bayesian optimization (fCBO), a novel method for optimizing target variables through deterministic functional interventions within known causal graphs, leveraging Gaussian processes in a reproducing kernel Hilbert space.

Contribution

fCBO extends causal Bayesian optimization to enable functional interventions, providing a new approach to optimize targets in causal graphs with theoretical criteria and practical demonstrations.

Findings

fCBO can identify better interventions in synthetic and real-world causal graphs.

The method models vector-valued objectives with Gaussian processes in RKHS.

Graphical criteria determine when functional interventions outperform traditional methods.

Abstract

We propose functional causal Bayesian optimization (fCBO), a method for finding interventions that optimize a target variable in a known causal graph. fCBO extends the CBO family of methods to enable functional interventions, which set a variable to be a deterministic function of other variables in the graph. fCBO models the unknown objectives with Gaussian processes whose inputs are defined in a reproducing kernel Hilbert space, thus allowing to compute distances among vector-valued functions. In turn, this enables to sequentially select functions to explore by maximizing an expected improvement acquisition functional while keeping the typical computational tractability of standard BO settings. We introduce graphical criteria that establish when considering functional interventions allows attaining better target effects, and conditions under which selected interventions are also optimal for conditional target effects. We demonstrate the benefits of the method in a synthetic and in a real-world causal graph.