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Sparse Bayesian binary logistic regression using the split-and-augmented Gibbs sampler

Vono, Maxime and Dobigeon, Nicolas and Chainais, Pierre Sparse Bayesian binary logistic regression using the split-and-augmented Gibbs sampler. (2018) In: IEEE International Workshop on Machine Learning for Signal Processing (MLSP 2018), 17 September 2018 - 20 September 2018 (Aalborg, Denmark).

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Official URL: https://doi.org/10.1109/MLSP.2018.8516963

Abstract

Logistic regression has been extensively used to perform classification in machine learning and signal/image processing. Bayesian formulations of this model with sparsity-inducing priors are particularly relevant when one is interested in drawing credibility intervals with few active coefficients. Along these lines, the derivation of efficient simulation-based methods is still an active research area because of the analytically challenging form of the binomial likelihood. This paper tackles the sparse Bayesian binary logistic regression problem by relying on the recent split-and-augmented Gibbs sampler (SPA). Contrary to usual data augmentation strategies, this Markov chain Monte Carlo (MCMC) algorithm scales in high dimension and divides the initial sampling problem into simpler ones. These sampling steps are then addressed with efficient state-of-the-art methods, namely proximal MCMC algorithms that can benefit from the recent closed-form expression of the proximal operator of the logistic cost function. SPA appears to be faster than efficient proximal MCMC algorithms and presents a reasonable computational cost compared to optimization-based methods with the advantage of producing credibility intervals. Experiments on handwritten digits classification problems illustrate the performances of the proposed approach.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to IEEE editor. The definitive version is available at http://ieeexplore.ieee.org This papers appears in Proceedings of MLSP 2018 Electronic ISBN: 978-1-5386-5477-4 The original PDF of the article can be found at: https://ieeexplore.ieee.org/document/8516963 Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
HAL Id:hal-02279425
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Ecole Centrale de Lille (FRANCE)
Other partners > Université de Lille (FRANCE)
Laboratory name:
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Deposited By: IRIT IRIT
Deposited On:26 Jun 2019 09:48

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