Estimating Causal Effects with Ancestral Graph Markov Models

Daniel Malinsky, Peter Spirtes
Proceedings of the Eighth International Conference on Probabilistic Graphical Models, PMLR 52:299-309, 2016.

Abstract

We present an algorithm for estimating bounds on causal effects from observational data which combines graphical model search with simple linear regression. We assume that the underlying system can be represented by a linear structural equation model with no feedback, and we allow for the possibility of latent variables. Under assumptions standard in the causal search literature, we use conditional independence constraints to search for an equivalence class of ancestral graphs. Then, for each model in the equivalence class, we perform the appropriate regression (using causal structure information to determine which covariates to include in the regression) to estimate a set of possible causal effects. Our approach is based on the “IDA” procedure of Maathuis et al. (2009), which assumes that all relevant variables have been measured (i.e., no unmeasured confounders). We generalize their work by relaxing this assumption, which is often violated in applied contexts. We validate the performance of our algorithm on simulated data and demonstrate improved precision over IDA when latent variables are present.

Cite this Paper

BibTeX
@InProceedings{pmlr-v52-malinsky16, title = {Estimating Causal Effects with Ancestral Graph {M}arkov Models}, author = {Malinsky, Daniel and Spirtes, Peter}, booktitle = {Proceedings of the Eighth International Conference on Probabilistic Graphical Models}, pages = {299--309}, year = {2016}, editor = {Antonucci, Alessandro and Corani, Giorgio and Campos}, Cassio Polpo}, volume = {52}, series = {Proceedings of Machine Learning Research}, address = {Lugano, Switzerland}, month = {06--09 Sep}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v52/malinsky16.pdf}, url = {https://proceedings.mlr.press/v52/malinsky16.html}, abstract = {We present an algorithm for estimating bounds on causal effects from observational data which combines graphical model search with simple linear regression. We assume that the underlying system can be represented by a linear structural equation model with no feedback, and we allow for the possibility of latent variables. Under assumptions standard in the causal search literature, we use conditional independence constraints to search for an equivalence class of ancestral graphs. Then, for each model in the equivalence class, we perform the appropriate regression (using causal structure information to determine which covariates to include in the regression) to estimate a set of possible causal effects. Our approach is based on the “IDA” procedure of Maathuis et al. (2009), which assumes that all relevant variables have been measured (i.e., no unmeasured confounders). We generalize their work by relaxing this assumption, which is often violated in applied contexts. We validate the performance of our algorithm on simulated data and demonstrate improved precision over IDA when latent variables are present.} }
Endnote
%0 Conference Paper %T Estimating Causal Effects with Ancestral Graph Markov Models %A Daniel Malinsky %A Peter Spirtes %B Proceedings of the Eighth International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2016 %E Alessandro Antonucci %E Giorgio Corani %E Cassio Polpo Campos} %F pmlr-v52-malinsky16 %I PMLR %P 299--309 %U https://proceedings.mlr.press/v52/malinsky16.html %V 52 %X We present an algorithm for estimating bounds on causal effects from observational data which combines graphical model search with simple linear regression. We assume that the underlying system can be represented by a linear structural equation model with no feedback, and we allow for the possibility of latent variables. Under assumptions standard in the causal search literature, we use conditional independence constraints to search for an equivalence class of ancestral graphs. Then, for each model in the equivalence class, we perform the appropriate regression (using causal structure information to determine which covariates to include in the regression) to estimate a set of possible causal effects. Our approach is based on the “IDA” procedure of Maathuis et al. (2009), which assumes that all relevant variables have been measured (i.e., no unmeasured confounders). We generalize their work by relaxing this assumption, which is often violated in applied contexts. We validate the performance of our algorithm on simulated data and demonstrate improved precision over IDA when latent variables are present.
RIS
TY - CPAPER TI - Estimating Causal Effects with Ancestral Graph Markov Models AU - Daniel Malinsky AU - Peter Spirtes BT - Proceedings of the Eighth International Conference on Probabilistic Graphical Models DA - 2016/08/15 ED - Alessandro Antonucci ED - Giorgio Corani ED - Cassio Polpo Campos} ID - pmlr-v52-malinsky16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 52 SP - 299 EP - 309 L1 - http://proceedings.mlr.press/v52/malinsky16.pdf UR - https://proceedings.mlr.press/v52/malinsky16.html AB - We present an algorithm for estimating bounds on causal effects from observational data which combines graphical model search with simple linear regression. We assume that the underlying system can be represented by a linear structural equation model with no feedback, and we allow for the possibility of latent variables. Under assumptions standard in the causal search literature, we use conditional independence constraints to search for an equivalence class of ancestral graphs. Then, for each model in the equivalence class, we perform the appropriate regression (using causal structure information to determine which covariates to include in the regression) to estimate a set of possible causal effects. Our approach is based on the “IDA” procedure of Maathuis et al. (2009), which assumes that all relevant variables have been measured (i.e., no unmeasured confounders). We generalize their work by relaxing this assumption, which is often violated in applied contexts. We validate the performance of our algorithm on simulated data and demonstrate improved precision over IDA when latent variables are present. ER -
APA
Malinsky, D. & Spirtes, P.. (2016). Estimating Causal Effects with Ancestral Graph Markov Models. Proceedings of the Eighth International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 52:299-309 Available from https://proceedings.mlr.press/v52/malinsky16.html.

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