Directed Graphical Models and Causal Discovery for Zero-Inflated Data

Shiqing Yu, Mathias Drton, Ali Shojaie
Proceedings of the Second Conference on Causal Learning and Reasoning, PMLR 213:27-67, 2023.

Abstract

With advances in technology, gene expression measurements from single cells can be used to gain refined insights into regulatory relationships among genes. Directed graphical models are well-suited to explore such (cause-effect) relationships. However, statistical analyses of single cell data are complicated by the fact that the data often show zero-inflated expression patterns. To address this challenge, we propose directed graphical models that are based on Hurdle conditional distributions parametrized in terms of polynomials in parent variables and their $0/1$ indicators of being zero or nonzero. While directed graphs for Gaussian models are only identifiable up to an equivalence class in general, we show that, under a natural and weak assumption, the exact directed acyclic graph of our zero-inflated models can be identified. We propose methods for graph recovery, apply our model to real single-cell gene expression data on T helper cells, and show simulated experiments that validate the identifiability and graph estimation methods in practice.

Cite this Paper

BibTeX
@InProceedings{pmlr-v213-yu23a, title = {Directed Graphical Models and Causal Discovery for Zero-Inflated Data}, author = {Yu, Shiqing and Drton, Mathias and Shojaie, Ali}, booktitle = {Proceedings of the Second Conference on Causal Learning and Reasoning}, pages = {27--67}, year = {2023}, editor = {van der Schaar, Mihaela and Zhang, Cheng and Janzing, Dominik}, volume = {213}, series = {Proceedings of Machine Learning Research}, month = {11--14 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v213/yu23a/yu23a.pdf}, url = {https://proceedings.mlr.press/v213/yu23a.html}, abstract = {With advances in technology, gene expression measurements from single cells can be used to gain refined insights into regulatory relationships among genes. Directed graphical models are well-suited to explore such (cause-effect) relationships. However, statistical analyses of single cell data are complicated by the fact that the data often show zero-inflated expression patterns. To address this challenge, we propose directed graphical models that are based on Hurdle conditional distributions parametrized in terms of polynomials in parent variables and their $0/1$ indicators of being zero or nonzero. While directed graphs for Gaussian models are only identifiable up to an equivalence class in general, we show that, under a natural and weak assumption, the exact directed acyclic graph of our zero-inflated models can be identified. We propose methods for graph recovery, apply our model to real single-cell gene expression data on T helper cells, and show simulated experiments that validate the identifiability and graph estimation methods in practice.} }
Endnote
%0 Conference Paper %T Directed Graphical Models and Causal Discovery for Zero-Inflated Data %A Shiqing Yu %A Mathias Drton %A Ali Shojaie %B Proceedings of the Second Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2023 %E Mihaela van der Schaar %E Cheng Zhang %E Dominik Janzing %F pmlr-v213-yu23a %I PMLR %P 27--67 %U https://proceedings.mlr.press/v213/yu23a.html %V 213 %X With advances in technology, gene expression measurements from single cells can be used to gain refined insights into regulatory relationships among genes. Directed graphical models are well-suited to explore such (cause-effect) relationships. However, statistical analyses of single cell data are complicated by the fact that the data often show zero-inflated expression patterns. To address this challenge, we propose directed graphical models that are based on Hurdle conditional distributions parametrized in terms of polynomials in parent variables and their $0/1$ indicators of being zero or nonzero. While directed graphs for Gaussian models are only identifiable up to an equivalence class in general, we show that, under a natural and weak assumption, the exact directed acyclic graph of our zero-inflated models can be identified. We propose methods for graph recovery, apply our model to real single-cell gene expression data on T helper cells, and show simulated experiments that validate the identifiability and graph estimation methods in practice.
APA
Yu, S., Drton, M. & Shojaie, A.. (2023). Directed Graphical Models and Causal Discovery for Zero-Inflated Data. Proceedings of the Second Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 213:27-67 Available from https://proceedings.mlr.press/v213/yu23a.html.

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