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A Pseudo-Bayesian Algorithm for Robust PCA

Tae-Hyun Oh · Yasuyuki Matsushita · In So Kweon · David Wipf

Area 5+6+7+8 #82

Keywords: [ (Other) Bayesian Inference ] [ Sparsity and Feature Selection ] [ (Other) Probabilistic Models and Methods ] [ Matrix Factorization ]


Commonly used in many applications, robust PCA represents an algorithmic attempt to reduce the sensitivity of classical PCA to outliers. The basic idea is to learn a decomposition of some data matrix of interest into low rank and sparse components, the latter representing unwanted outliers. Although the resulting problem is typically NP-hard, convex relaxations provide a computationally-expedient alternative with theoretical support. However, in practical regimes performance guarantees break down and a variety of non-convex alternatives, including Bayesian-inspired models, have been proposed to boost estimation quality. Unfortunately though, without additional a priori knowledge none of these methods can significantly expand the critical operational range such that exact principal subspace recovery is possible. Into this mix we propose a novel pseudo-Bayesian algorithm that explicitly compensates for design weaknesses in many existing non-convex approaches leading to state-of-the-art performance with a sound analytical foundation.

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