Disentangling mixtures of unknown causal interventions

Abhinav Kumar, Gaurav Sinha
Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, PMLR 161:2093-2102, 2021.

Abstract

In many real-world scenarios, such as gene knockout experiments, targeted interventions are often accompanied by unknown interventions at off-target sites. Moreover, different units can get randomly exposed to different unknown interventions, thereby creating a mixture of interventions. Identifying different components of this mixture can be very valuable in some applications. Motivated by such situations, in this work, we study the problem of identifying all components present in a mixture of interventions on a given causal Bayesian Network. We construct examples to show that, in general, the components are not identifiable from the mixture distribution. Next, assuming that the given network satisfies a positivity condition, we show that, if the set of mixture components satisfy a mild exclusion assumption, then they can be uniquely identified. Our proof gives an efficient algorithm to recover these targets from the exponentially large search space of possible targets. In the more realistic scenario, where distributions are given via finitely many samples, we conduct a simulation study to analyze the performance of an algorithm derived from our identifiability proof.

Cite this Paper

BibTeX
@InProceedings{pmlr-v161-kumar21a, title = {Disentangling mixtures of unknown causal interventions}, author = {Kumar, Abhinav and Sinha, Gaurav}, booktitle = {Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence}, pages = {2093--2102}, year = {2021}, editor = {de Campos, Cassio and Maathuis, Marloes H.}, volume = {161}, series = {Proceedings of Machine Learning Research}, month = {27--30 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v161/kumar21a/kumar21a.pdf}, url = {https://proceedings.mlr.press/v161/kumar21a.html}, abstract = {In many real-world scenarios, such as gene knockout experiments, targeted interventions are often accompanied by unknown interventions at off-target sites. Moreover, different units can get randomly exposed to different unknown interventions, thereby creating a mixture of interventions. Identifying different components of this mixture can be very valuable in some applications. Motivated by such situations, in this work, we study the problem of identifying all components present in a mixture of interventions on a given causal Bayesian Network. We construct examples to show that, in general, the components are not identifiable from the mixture distribution. Next, assuming that the given network satisfies a positivity condition, we show that, if the set of mixture components satisfy a mild exclusion assumption, then they can be uniquely identified. Our proof gives an efficient algorithm to recover these targets from the exponentially large search space of possible targets. In the more realistic scenario, where distributions are given via finitely many samples, we conduct a simulation study to analyze the performance of an algorithm derived from our identifiability proof.} }
Endnote
%0 Conference Paper %T Disentangling mixtures of unknown causal interventions %A Abhinav Kumar %A Gaurav Sinha %B Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2021 %E Cassio de Campos %E Marloes H. Maathuis %F pmlr-v161-kumar21a %I PMLR %P 2093--2102 %U https://proceedings.mlr.press/v161/kumar21a.html %V 161 %X In many real-world scenarios, such as gene knockout experiments, targeted interventions are often accompanied by unknown interventions at off-target sites. Moreover, different units can get randomly exposed to different unknown interventions, thereby creating a mixture of interventions. Identifying different components of this mixture can be very valuable in some applications. Motivated by such situations, in this work, we study the problem of identifying all components present in a mixture of interventions on a given causal Bayesian Network. We construct examples to show that, in general, the components are not identifiable from the mixture distribution. Next, assuming that the given network satisfies a positivity condition, we show that, if the set of mixture components satisfy a mild exclusion assumption, then they can be uniquely identified. Our proof gives an efficient algorithm to recover these targets from the exponentially large search space of possible targets. In the more realistic scenario, where distributions are given via finitely many samples, we conduct a simulation study to analyze the performance of an algorithm derived from our identifiability proof.
APA
Kumar, A. & Sinha, G.. (2021). Disentangling mixtures of unknown causal interventions. Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 161:2093-2102 Available from https://proceedings.mlr.press/v161/kumar21a.html.

Related Material