Sparse Submodular Probabilistic PCA

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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.

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