Intervention Efficient Algorithms for Approximate Learning of Causal Graphs

Raghavendra Addanki, Andrew McGregor, Cameron Musco
Proceedings of the 32nd International Conference on Algorithmic Learning Theory, PMLR 132:151-184, 2021.

Abstract

We study the problem of learning the causal relationships between a set of observed variables in the presence of latents, while minimizing the cost of interventions on the observed variables. We assume access to an undirected graph $G$ on the observed variables whose edges represent either all direct causal relationships or, less restrictively, a superset of causal relationships (identified, e.g., via conditional independence tests or a domain expert). Our goal is to recover the directions of all causal or ancestral relations in $G$, via a minimum cost set of interventions. It is known that constructing an exact minimum cost intervention set for an arbitrary graph $G$ is NP-hard. We further argue that, conditioned on the hardness of approximate graph coloring, no polynomial time algorithm can achieve an approximation factor better than $\Theta(\log n)$, where $n$ is the number of observed variables in $G$. To overcome this limitation, we introduce a bi-criteria approximation goal that lets us recover the directions of all but $\epsilon n^2$ edges in $G$, for some specified error parameter $\epsilon > 0$. Under this relaxed goal, we give polynomial time algorithms that achieve intervention cost within a small constant factor of the optimal. Our algorithms combine work on efficient intervention design and the design of low-cost separating set systems, with ideas from the literature on graph property testing.

Cite this Paper

BibTeX
@InProceedings{pmlr-v132-addanki21a, title = {Intervention Efficient Algorithms for Approximate Learning of Causal Graphs}, author = {Addanki, Raghavendra and McGregor, Andrew and Musco, Cameron}, booktitle = {Proceedings of the 32nd International Conference on Algorithmic Learning Theory}, pages = {151--184}, year = {2021}, editor = {Feldman, Vitaly and Ligett, Katrina and Sabato, Sivan}, volume = {132}, series = {Proceedings of Machine Learning Research}, month = {16--19 Mar}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v132/addanki21a/addanki21a.pdf}, url = {https://proceedings.mlr.press/v132/addanki21a.html}, abstract = {We study the problem of learning the causal relationships between a set of observed variables in the presence of latents, while minimizing the cost of interventions on the observed variables. We assume access to an undirected graph $G$ on the observed variables whose edges represent either all direct causal relationships or, less restrictively, a superset of causal relationships (identified, e.g., via conditional independence tests or a domain expert). Our goal is to recover the directions of all causal or ancestral relations in $G$, via a minimum cost set of interventions. It is known that constructing an exact minimum cost intervention set for an arbitrary graph $G$ is NP-hard. We further argue that, conditioned on the hardness of approximate graph coloring, no polynomial time algorithm can achieve an approximation factor better than $\Theta(\log n)$, where $n$ is the number of observed variables in $G$. To overcome this limitation, we introduce a bi-criteria approximation goal that lets us recover the directions of all but $\epsilon n^2$ edges in $G$, for some specified error parameter $\epsilon > 0$. Under this relaxed goal, we give polynomial time algorithms that achieve intervention cost within a small constant factor of the optimal. Our algorithms combine work on efficient intervention design and the design of low-cost separating set systems, with ideas from the literature on graph property testing.} }
Endnote
%0 Conference Paper %T Intervention Efficient Algorithms for Approximate Learning of Causal Graphs %A Raghavendra Addanki %A Andrew McGregor %A Cameron Musco %B Proceedings of the 32nd International Conference on Algorithmic Learning Theory %C Proceedings of Machine Learning Research %D 2021 %E Vitaly Feldman %E Katrina Ligett %E Sivan Sabato %F pmlr-v132-addanki21a %I PMLR %P 151--184 %U https://proceedings.mlr.press/v132/addanki21a.html %V 132 %X We study the problem of learning the causal relationships between a set of observed variables in the presence of latents, while minimizing the cost of interventions on the observed variables. We assume access to an undirected graph $G$ on the observed variables whose edges represent either all direct causal relationships or, less restrictively, a superset of causal relationships (identified, e.g., via conditional independence tests or a domain expert). Our goal is to recover the directions of all causal or ancestral relations in $G$, via a minimum cost set of interventions. It is known that constructing an exact minimum cost intervention set for an arbitrary graph $G$ is NP-hard. We further argue that, conditioned on the hardness of approximate graph coloring, no polynomial time algorithm can achieve an approximation factor better than $\Theta(\log n)$, where $n$ is the number of observed variables in $G$. To overcome this limitation, we introduce a bi-criteria approximation goal that lets us recover the directions of all but $\epsilon n^2$ edges in $G$, for some specified error parameter $\epsilon > 0$. Under this relaxed goal, we give polynomial time algorithms that achieve intervention cost within a small constant factor of the optimal. Our algorithms combine work on efficient intervention design and the design of low-cost separating set systems, with ideas from the literature on graph property testing.
APA
Addanki, R., McGregor, A. & Musco, C.. (2021). Intervention Efficient Algorithms for Approximate Learning of Causal Graphs. Proceedings of the 32nd International Conference on Algorithmic Learning Theory, in Proceedings of Machine Learning Research 132:151-184 Available from https://proceedings.mlr.press/v132/addanki21a.html.

Related Material