Sparse Submodular Probabilistic PCA

Rajiv Khanna, Joydeep Ghosh, Russell Poldrack, Oluwasanmi Koyejo
Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, PMLR 38:453-461, 2015.

Abstract

We propose a novel approach for sparse probabilistic principal component analysis, that combines a low rank representation for the latent factors and loadings with a novel sparse variational inference approach for estimating distributions of latent variables subject to sparse support constraints. Inference and parameter estimation for the resulting model is achieved via expectation maximization with a novel variational inference method for the E-step that induces sparsity. We show that this inference problem can be reduced to discrete optimal support selection. The discrete optimization is submodular, hence, greedy selection is guaranteed to achieve 1-1/e fraction of the optimal. Empirical studies indicate effectiveness of the proposed approach for the recovery of a parsimonious decomposition as compared to established baseline methods. We also evaluate our method against state-of-the-art methods on high dimensional fMRI data, and show that the method performs as good as or better than other methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v38-khanna15, title = {{Sparse Submodular Probabilistic PCA}}, author = {Khanna, Rajiv and Ghosh, Joydeep and Poldrack, Russell and Koyejo, Oluwasanmi}, booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics}, pages = {453--461}, year = {2015}, editor = {Lebanon, Guy and Vishwanathan, S. V. N.}, volume = {38}, series = {Proceedings of Machine Learning Research}, address = {San Diego, California, USA}, month = {09--12 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v38/khanna15.pdf}, url = {https://proceedings.mlr.press/v38/khanna15.html}, abstract = {We propose a novel approach for sparse probabilistic principal component analysis, that combines a low rank representation for the latent factors and loadings with a novel sparse variational inference approach for estimating distributions of latent variables subject to sparse support constraints. Inference and parameter estimation for the resulting model is achieved via expectation maximization with a novel variational inference method for the E-step that induces sparsity. We show that this inference problem can be reduced to discrete optimal support selection. The discrete optimization is submodular, hence, greedy selection is guaranteed to achieve 1-1/e fraction of the optimal. Empirical studies indicate effectiveness of the proposed approach for the recovery of a parsimonious decomposition as compared to established baseline methods. We also evaluate our method against state-of-the-art methods on high dimensional fMRI data, and show that the method performs as good as or better than other methods.} }
Endnote
%0 Conference Paper %T Sparse Submodular Probabilistic PCA %A Rajiv Khanna %A Joydeep Ghosh %A Russell Poldrack %A Oluwasanmi Koyejo %B Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2015 %E Guy Lebanon %E S. V. N. Vishwanathan %F pmlr-v38-khanna15 %I PMLR %P 453--461 %U https://proceedings.mlr.press/v38/khanna15.html %V 38 %X We propose a novel approach for sparse probabilistic principal component analysis, that combines a low rank representation for the latent factors and loadings with a novel sparse variational inference approach for estimating distributions of latent variables subject to sparse support constraints. Inference and parameter estimation for the resulting model is achieved via expectation maximization with a novel variational inference method for the E-step that induces sparsity. We show that this inference problem can be reduced to discrete optimal support selection. The discrete optimization is submodular, hence, greedy selection is guaranteed to achieve 1-1/e fraction of the optimal. Empirical studies indicate effectiveness of the proposed approach for the recovery of a parsimonious decomposition as compared to established baseline methods. We also evaluate our method against state-of-the-art methods on high dimensional fMRI data, and show that the method performs as good as or better than other methods.
RIS
TY - CPAPER TI - Sparse Submodular Probabilistic PCA AU - Rajiv Khanna AU - Joydeep Ghosh AU - Russell Poldrack AU - Oluwasanmi Koyejo BT - Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics DA - 2015/02/21 ED - Guy Lebanon ED - S. V. N. Vishwanathan ID - pmlr-v38-khanna15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 38 SP - 453 EP - 461 L1 - http://proceedings.mlr.press/v38/khanna15.pdf UR - https://proceedings.mlr.press/v38/khanna15.html AB - We propose a novel approach for sparse probabilistic principal component analysis, that combines a low rank representation for the latent factors and loadings with a novel sparse variational inference approach for estimating distributions of latent variables subject to sparse support constraints. Inference and parameter estimation for the resulting model is achieved via expectation maximization with a novel variational inference method for the E-step that induces sparsity. We show that this inference problem can be reduced to discrete optimal support selection. The discrete optimization is submodular, hence, greedy selection is guaranteed to achieve 1-1/e fraction of the optimal. Empirical studies indicate effectiveness of the proposed approach for the recovery of a parsimonious decomposition as compared to established baseline methods. We also evaluate our method against state-of-the-art methods on high dimensional fMRI data, and show that the method performs as good as or better than other methods. ER -
APA
Khanna, R., Ghosh, J., Poldrack, R. & Koyejo, O.. (2015). Sparse Submodular Probabilistic PCA. Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 38:453-461 Available from https://proceedings.mlr.press/v38/khanna15.html.

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