Functional causal Bayesian optimization

Limor Gultchin, Virginia Aglietti, Alexis Bellot, Silvia Chiappa
Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, PMLR 216:756-765, 2023.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v216-gultchin23a, title = {Functional causal {B}ayesian optimization}, author = {Gultchin, Limor and Aglietti, Virginia and Bellot, Alexis and Chiappa, Silvia}, booktitle = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence}, pages = {756--765}, year = {2023}, editor = {Evans, Robin J. and Shpitser, Ilya}, volume = {216}, series = {Proceedings of Machine Learning Research}, month = {31 Jul--04 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v216/gultchin23a/gultchin23a.pdf}, url = {https://proceedings.mlr.press/v216/gultchin23a.html}, 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.} }
Endnote
%0 Conference Paper %T Functional causal Bayesian optimization %A Limor Gultchin %A Virginia Aglietti %A Alexis Bellot %A Silvia Chiappa %B Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2023 %E Robin J. Evans %E Ilya Shpitser %F pmlr-v216-gultchin23a %I PMLR %P 756--765 %U https://proceedings.mlr.press/v216/gultchin23a.html %V 216 %X 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.
APA
Gultchin, L., Aglietti, V., Bellot, A. & Chiappa, S.. (2023). Functional causal Bayesian optimization. Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 216:756-765 Available from https://proceedings.mlr.press/v216/gultchin23a.html.

Related Material