Sparse Learning in Gaussian Chain Graphs for State Space Models

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt

Standard

Sparse Learning in Gaussian Chain Graphs for State Space Models. / Petersen, Lasse.

Proceedings of the 9th International Conference on Probabilistic Graphical Models. red. / Václav Kratochvíl; Milan Studený. PMLR, 2018. s. 333-343 (Proceedings of Machine Learning Research, Bind 72).

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt

Harvard

Petersen, L 2018, Sparse Learning in Gaussian Chain Graphs for State Space Models. i V Kratochvíl & M Studený (red), Proceedings of the 9th International Conference on Probabilistic Graphical Models. PMLR, Proceedings of Machine Learning Research, bind 72, s. 333-343, 9th International Conference on Probabilistic Graphical Models, Prague, Tjekkiet, 11/09/2018.

APA

Petersen, L. (2018). Sparse Learning in Gaussian Chain Graphs for State Space Models. I V. Kratochvíl, & M. Studený (red.), Proceedings of the 9th International Conference on Probabilistic Graphical Models (s. 333-343). PMLR. Proceedings of Machine Learning Research Bind 72

Vancouver

Petersen L. Sparse Learning in Gaussian Chain Graphs for State Space Models. I Kratochvíl V, Studený M, red., Proceedings of the 9th International Conference on Probabilistic Graphical Models. PMLR. 2018. s. 333-343. (Proceedings of Machine Learning Research, Bind 72).

Author

Petersen, Lasse. / Sparse Learning in Gaussian Chain Graphs for State Space Models. Proceedings of the 9th International Conference on Probabilistic Graphical Models. red. / Václav Kratochvíl ; Milan Studený. PMLR, 2018. s. 333-343 (Proceedings of Machine Learning Research, Bind 72).

Bibtex

@inproceedings{b0ee36b832c349edbdef3a1abad7b84e,
title = "Sparse Learning in Gaussian Chain Graphs for State Space Models",
abstract = "The graphical lasso is a popular method for estimating the structure of undirected Gaussian graphical models from data by penalized maximum likelihood. This paper extends the idea of structure estimation of graphical models by penalized maximum likelihood to Gaussian chain graph models for state space models. First we show how the class of linear Gaussian state space models can be interpreted in the chain graph set-up under both the LWF and AMP Markov properties, and we demonstrate how sparsity of the chain graph structure relates to sparsity of the model parameters. Exploiting this relation we propose two different penalized maximum likelihood estimators for recovering the chain graph structure from data depending on the Markov interpretation at hand. We frame the penalized maximum likelihood problem in a missing data set-up and carry out estimation in each of the two cases using the EM algorithm. The common E-step is solved by smoothing, and we solve the two different M-steps by utilizing existing methods from high dimensional statistics and convex optimization. ",
author = "Lasse Petersen",
year = "2018",
language = "English",
series = "Proceedings of Machine Learning Research",
pages = "333--343",
editor = "V{\'a}clav Kratochv{\'i}l and Studen{\'y}, {Milan }",
booktitle = "Proceedings of the 9th International Conference on Probabilistic Graphical Models",
publisher = "PMLR",
note = "9th International Conference on Probabilistic Graphical Models ; Conference date: 11-09-2018 Through 14-09-2018",

}

RIS

TY - GEN

T1 - Sparse Learning in Gaussian Chain Graphs for State Space Models

AU - Petersen, Lasse

PY - 2018

Y1 - 2018

N2 - The graphical lasso is a popular method for estimating the structure of undirected Gaussian graphical models from data by penalized maximum likelihood. This paper extends the idea of structure estimation of graphical models by penalized maximum likelihood to Gaussian chain graph models for state space models. First we show how the class of linear Gaussian state space models can be interpreted in the chain graph set-up under both the LWF and AMP Markov properties, and we demonstrate how sparsity of the chain graph structure relates to sparsity of the model parameters. Exploiting this relation we propose two different penalized maximum likelihood estimators for recovering the chain graph structure from data depending on the Markov interpretation at hand. We frame the penalized maximum likelihood problem in a missing data set-up and carry out estimation in each of the two cases using the EM algorithm. The common E-step is solved by smoothing, and we solve the two different M-steps by utilizing existing methods from high dimensional statistics and convex optimization.

AB - The graphical lasso is a popular method for estimating the structure of undirected Gaussian graphical models from data by penalized maximum likelihood. This paper extends the idea of structure estimation of graphical models by penalized maximum likelihood to Gaussian chain graph models for state space models. First we show how the class of linear Gaussian state space models can be interpreted in the chain graph set-up under both the LWF and AMP Markov properties, and we demonstrate how sparsity of the chain graph structure relates to sparsity of the model parameters. Exploiting this relation we propose two different penalized maximum likelihood estimators for recovering the chain graph structure from data depending on the Markov interpretation at hand. We frame the penalized maximum likelihood problem in a missing data set-up and carry out estimation in each of the two cases using the EM algorithm. The common E-step is solved by smoothing, and we solve the two different M-steps by utilizing existing methods from high dimensional statistics and convex optimization.

M3 - Article in proceedings

T3 - Proceedings of Machine Learning Research

SP - 333

EP - 343

BT - Proceedings of the 9th International Conference on Probabilistic Graphical Models

A2 - Kratochvíl, Václav

A2 - Studený, Milan

PB - PMLR

T2 - 9th International Conference on Probabilistic Graphical Models

Y2 - 11 September 2018 through 14 September 2018

ER -

ID: 215088871