Semiparametric Pseudo-Likelihood Estimation in Markov Random Fields

Antonino Freno
Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, PMLR 22:391-399, 2012.

Abstract

Probabilistic graphical models for continuous variables can be built out of either parametric or nonparametric conditional density estimators. While several research efforts have been focusing on parametric approaches (such as Gaussian models), kernel-based estimators are still the only viable and well-understood option for nonparametric density estimation. This paper develops a semiparametric estimator of probability density functions based on the nonparanormal transformation, which has been recently proposed for mapping arbitrarily distributed data samples onto normally distributed datasets. Pointwise and uniform consistency properties are established for the developed method. The resulting density model is then applied to pseudo-likelihood estimation in Markov random fields. An experimental evaluation on data distributed according to a variety of density functions indicates that such semiparametric Markov random field models significantly outperform both their Gaussian and kernel-based alternatives in terms of prediction accuracy.

Cite this Paper

BibTeX
@InProceedings{pmlr-v22-freno12, title = {Semiparametric Pseudo-Likelihood Estimation in Markov Random Fields}, author = {Freno, Antonino}, booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics}, pages = {391--399}, year = {2012}, editor = {Lawrence, Neil D. and Girolami, Mark}, volume = {22}, series = {Proceedings of Machine Learning Research}, address = {La Palma, Canary Islands}, month = {21--23 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v22/freno12/freno12.pdf}, url = {https://proceedings.mlr.press/v22/freno12.html}, abstract = {Probabilistic graphical models for continuous variables can be built out of either parametric or nonparametric conditional density estimators. While several research efforts have been focusing on parametric approaches (such as Gaussian models), kernel-based estimators are still the only viable and well-understood option for nonparametric density estimation. This paper develops a semiparametric estimator of probability density functions based on the nonparanormal transformation, which has been recently proposed for mapping arbitrarily distributed data samples onto normally distributed datasets. Pointwise and uniform consistency properties are established for the developed method. The resulting density model is then applied to pseudo-likelihood estimation in Markov random fields. An experimental evaluation on data distributed according to a variety of density functions indicates that such semiparametric Markov random field models significantly outperform both their Gaussian and kernel-based alternatives in terms of prediction accuracy.} }
Endnote
%0 Conference Paper %T Semiparametric Pseudo-Likelihood Estimation in Markov Random Fields %A Antonino Freno %B Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2012 %E Neil D. Lawrence %E Mark Girolami %F pmlr-v22-freno12 %I PMLR %P 391--399 %U https://proceedings.mlr.press/v22/freno12.html %V 22 %X Probabilistic graphical models for continuous variables can be built out of either parametric or nonparametric conditional density estimators. While several research efforts have been focusing on parametric approaches (such as Gaussian models), kernel-based estimators are still the only viable and well-understood option for nonparametric density estimation. This paper develops a semiparametric estimator of probability density functions based on the nonparanormal transformation, which has been recently proposed for mapping arbitrarily distributed data samples onto normally distributed datasets. Pointwise and uniform consistency properties are established for the developed method. The resulting density model is then applied to pseudo-likelihood estimation in Markov random fields. An experimental evaluation on data distributed according to a variety of density functions indicates that such semiparametric Markov random field models significantly outperform both their Gaussian and kernel-based alternatives in terms of prediction accuracy.
RIS
TY - CPAPER TI - Semiparametric Pseudo-Likelihood Estimation in Markov Random Fields AU - Antonino Freno BT - Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics DA - 2012/03/21 ED - Neil D. Lawrence ED - Mark Girolami ID - pmlr-v22-freno12 PB - PMLR DP - Proceedings of Machine Learning Research VL - 22 SP - 391 EP - 399 L1 - http://proceedings.mlr.press/v22/freno12/freno12.pdf UR - https://proceedings.mlr.press/v22/freno12.html AB - Probabilistic graphical models for continuous variables can be built out of either parametric or nonparametric conditional density estimators. While several research efforts have been focusing on parametric approaches (such as Gaussian models), kernel-based estimators are still the only viable and well-understood option for nonparametric density estimation. This paper develops a semiparametric estimator of probability density functions based on the nonparanormal transformation, which has been recently proposed for mapping arbitrarily distributed data samples onto normally distributed datasets. Pointwise and uniform consistency properties are established for the developed method. The resulting density model is then applied to pseudo-likelihood estimation in Markov random fields. An experimental evaluation on data distributed according to a variety of density functions indicates that such semiparametric Markov random field models significantly outperform both their Gaussian and kernel-based alternatives in terms of prediction accuracy. ER -
APA
Freno, A.. (2012). Semiparametric Pseudo-Likelihood Estimation in Markov Random Fields. Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 22:391-399 Available from https://proceedings.mlr.press/v22/freno12.html.

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