Sparse Nested Markov models with Log-linear Parameters

Ilya Shpitser, Robin Evans, Thomas Richardson, James Robins
Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence, PMLR R11:203-212, 2013.

Abstract

Hidden variables are ubiquitous in practi- cal data analysis, and therefore modeling marginal densities and doing inference with the resulting models is an important problem in statistics, machine learning, and causal inference. Recently, a new type of graphi- cal model, called the nested Markov model, was developed which captures equality con- straints found in marginals of directed acyclic graph (DAG) models. Some of these con- straints, such as the so called ‘Verma con- straint’, strictly generalize conditional inde- pendence. To make modeling and inference with nested Markov models practical, it is necessary to limit the number of parameters in the model, while still correctly capturing the constraints in the marginal of a DAG model. Placing such limits is similar in spirit to sparsity methods for undirected graphical models, and regression models. In this paper, we give a log-linear parameterization which allows sparse modeling with nested Markov models. We illustrate the advantages of this parameterization with a simulation study.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR11-shpitser13a, title = {Sparse Nested {M}arkov models with Log-linear Parameters}, author = {Shpitser, Ilya and Evans, Robin and Richardson, Thomas and Robins, James}, booktitle = {Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence}, pages = {203--212}, year = {2013}, editor = {Nicholson, Ann and Smyth, Padhraic}, volume = {R11}, series = {Proceedings of Machine Learning Research}, month = {12--14 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r11/main/assets/shpitser13a/shpitser13a.pdf}, url = {https://proceedings.mlr.press/r11/shpitser13a.html}, abstract = {Hidden variables are ubiquitous in practi- cal data analysis, and therefore modeling marginal densities and doing inference with the resulting models is an important problem in statistics, machine learning, and causal inference. Recently, a new type of graphi- cal model, called the nested Markov model, was developed which captures equality con- straints found in marginals of directed acyclic graph (DAG) models. Some of these con- straints, such as the so called ‘Verma con- straint’, strictly generalize conditional inde- pendence. To make modeling and inference with nested Markov models practical, it is necessary to limit the number of parameters in the model, while still correctly capturing the constraints in the marginal of a DAG model. Placing such limits is similar in spirit to sparsity methods for undirected graphical models, and regression models. In this paper, we give a log-linear parameterization which allows sparse modeling with nested Markov models. We illustrate the advantages of this parameterization with a simulation study.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Sparse Nested Markov models with Log-linear Parameters %A Ilya Shpitser %A Robin Evans %A Thomas Richardson %A James Robins %B Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2013 %E Ann Nicholson %E Padhraic Smyth %F pmlr-vR11-shpitser13a %I PMLR %P 203--212 %U https://proceedings.mlr.press/r11/shpitser13a.html %V R11 %X Hidden variables are ubiquitous in practi- cal data analysis, and therefore modeling marginal densities and doing inference with the resulting models is an important problem in statistics, machine learning, and causal inference. Recently, a new type of graphi- cal model, called the nested Markov model, was developed which captures equality con- straints found in marginals of directed acyclic graph (DAG) models. Some of these con- straints, such as the so called ‘Verma con- straint’, strictly generalize conditional inde- pendence. To make modeling and inference with nested Markov models practical, it is necessary to limit the number of parameters in the model, while still correctly capturing the constraints in the marginal of a DAG model. Placing such limits is similar in spirit to sparsity methods for undirected graphical models, and regression models. In this paper, we give a log-linear parameterization which allows sparse modeling with nested Markov models. We illustrate the advantages of this parameterization with a simulation study. %Z Reissued by PMLR on 04 October 2026.
APA
Shpitser, I., Evans, R., Richardson, T. & Robins, J.. (2013). Sparse Nested Markov models with Log-linear Parameters. Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R11:203-212 Available from https://proceedings.mlr.press/r11/shpitser13a.html. Reissued by PMLR on 04 October 2026.

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