Active causal structure learning with advice

Davin Choo, Themistoklis Gouleakis, Arnab Bhattacharyya
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:5838-5867, 2023.

Abstract

We introduce the problem of active causal structure learning with advice. In the typical well-studied setting, the learning algorithm is given the essential graph for the observational distribution and is asked to recover the underlying causal directed acyclic graph (DAG) G∗ while minimizing the number of interventions made. In our setting, we are additionally given side information about G∗ as advice, e.g. a DAG G purported to be G∗. We ask whether the learning algorithm can benefit from the advice when it is close to being correct, while still having worst-case guarantees even when the advice is arbitrarily bad. Our work is in the same space as the growing body of research on algorithms with predictions. When the advice is a DAG G, we design an adaptive search algorithm to recover G∗ whose intervention cost is at most O(max times the cost for verifying G^*; here, \psi is a distance measure between G and G^* that is upper bounded by the number of variables n, and is exactly 0 when G=G^*. Our approximation factor matches the state-of-the-art for the advice-less setting.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-choo23a, title = {Active causal structure learning with advice}, author = {Choo, Davin and Gouleakis, Themistoklis and Bhattacharyya, Arnab}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {5838--5867}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/choo23a/choo23a.pdf}, url = {https://proceedings.mlr.press/v202/choo23a.html}, abstract = {We introduce the problem of active causal structure learning with advice. In the typical well-studied setting, the learning algorithm is given the essential graph for the observational distribution and is asked to recover the underlying causal directed acyclic graph (DAG) $G^*$ while minimizing the number of interventions made. In our setting, we are additionally given side information about $G^*$ as advice, e.g. a DAG $G$ purported to be $G^*$. We ask whether the learning algorithm can benefit from the advice when it is close to being correct, while still having worst-case guarantees even when the advice is arbitrarily bad. Our work is in the same space as the growing body of research on algorithms with predictions. When the advice is a DAG $G$, we design an adaptive search algorithm to recover $G^*$ whose intervention cost is at most $\mathcal{O}(\max\{1, \log \psi\})$ times the cost for verifying $G^*$; here, $\psi$ is a distance measure between $G$ and $G^*$ that is upper bounded by the number of variables $n$, and is exactly 0 when $G=G^*$. Our approximation factor matches the state-of-the-art for the advice-less setting.} }
Endnote
%0 Conference Paper %T Active causal structure learning with advice %A Davin Choo %A Themistoklis Gouleakis %A Arnab Bhattacharyya %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-choo23a %I PMLR %P 5838--5867 %U https://proceedings.mlr.press/v202/choo23a.html %V 202 %X We introduce the problem of active causal structure learning with advice. In the typical well-studied setting, the learning algorithm is given the essential graph for the observational distribution and is asked to recover the underlying causal directed acyclic graph (DAG) $G^*$ while minimizing the number of interventions made. In our setting, we are additionally given side information about $G^*$ as advice, e.g. a DAG $G$ purported to be $G^*$. We ask whether the learning algorithm can benefit from the advice when it is close to being correct, while still having worst-case guarantees even when the advice is arbitrarily bad. Our work is in the same space as the growing body of research on algorithms with predictions. When the advice is a DAG $G$, we design an adaptive search algorithm to recover $G^*$ whose intervention cost is at most $\mathcal{O}(\max\{1, \log \psi\})$ times the cost for verifying $G^*$; here, $\psi$ is a distance measure between $G$ and $G^*$ that is upper bounded by the number of variables $n$, and is exactly 0 when $G=G^*$. Our approximation factor matches the state-of-the-art for the advice-less setting.
APA
Choo, D., Gouleakis, T. & Bhattacharyya, A.. (2023). Active causal structure learning with advice. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:5838-5867 Available from https://proceedings.mlr.press/v202/choo23a.html.

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