Block Majorization Minimization with Extrapolation and Application to $\beta$-NMF

• URL: http://arxiv.org/abs/2401.06646v1
• Date: Fri, 12 Jan 2024 15:52:02 GMT
• Title: Block Majorization Minimization with Extrapolation and Application to $\beta$-NMF
• Authors: Le Thi Khanh Hien, Valentin Leplat, Nicolas Gillis
• Abstract summary: We propose a Block Majorization Minimization method with Extrapolation (BMMe) for solving a class of multi- optimization problems. We show that block majorization parameters of BMMe can be reformulated as a block mirror method with the Bregman divergence adaptively updated. We empirically illustrate the significant acceleration BM for $beta$NMF through extensive experiments.
• Score: 17.97403029273243
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a Block Majorization Minimization method with Extrapolation (BMMe) for solving a class of multi-convex optimization problems. The extrapolation parameters of BMMe are updated using a novel adaptive update rule. By showing that block majorization minimization can be reformulated as a block mirror descent method, with the Bregman divergence adaptively updated at each iteration, we establish subsequential convergence for BMMe. We use this method to design efficient algorithms to tackle nonnegative matrix factorization problems with the $\beta$-divergences ($\beta$-NMF) for $\beta\in [1,2]$. These algorithms, which are multiplicative updates with extrapolation, benefit from our novel results that offer convergence guarantees. We also empirically illustrate the significant acceleration of BMMe for $\beta$-NMF through extensive experiments.

Related papers

• Smoothed Normalization for Efficient Distributed Private Optimization [54.197255548244705]
  Federated learning enables machine learning models with privacy of participants. There is no differentially private distributed method for training, non-feedback problems. We introduce a new distributed algorithm $alpha$-$sf NormEC$ with provable convergence guarantees.
  arXiv  Detail & Related papers  (2025-02-19T07:10:32Z)
• Strictly Low Rank Constraint Optimization -- An Asymptotically $\mathcal{O}(\frac{1}{t^2})$ Method [5.770309971945476]
  We propose a class of non-text and non-smooth problems with textitrank regularization to promote sparsity in optimal solution. We show that our algorithms are able to achieve a singular convergence of $Ofrac(t2)$, which is exactly same as Nesterov's optimal convergence for first-order methods on smooth convex problems.
  arXiv  Detail & Related papers  (2023-07-04T16:55:41Z)
• Extra-Newton: A First Approach to Noise-Adaptive Accelerated Second-Order Methods [57.050204432302195]
  This work proposes a universal and adaptive second-order method for minimizing second-order smooth, convex functions. Our algorithm achieves $O(sigma / sqrtT)$ convergence when the oracle feedback is with variance $sigma2$, and improves its convergence to $O( 1 / T3)$ with deterministic oracles.
  arXiv  Detail & Related papers  (2022-11-03T14:12:51Z)
• Majorization-minimization for Sparse Nonnegative Matrix Factorization with the $\beta$-divergence [2.3787352248749376]
  It is well known that the norm of the other factor (the dictionary matrix) needs to be controlled in order to avoid an ill-posed formulation. Standard practice consists in constraining the columns of the dictionary to have unit norm, which leads to a nontrivial optimization problem. We derive block-descent majorization-minimization algorithms that result in simple multiplicative updates for either $ell_1$-regularization or the more "aggressive" log-regularization.
  arXiv  Detail & Related papers  (2022-07-13T16:09:29Z)
• Meta-Learning Adversarial Bandits [49.094361442409785]
  We study online learning with bandit feedback across multiple tasks, with the goal of improving average performance across tasks if they are similar according to some natural task-similarity measure. As the first to target the adversarial setting, we design a meta-algorithm that setting-specific guarantees for two important cases: multi-armed bandits (MAB) and bandit optimization (BLO) Our guarantees rely on proving that unregularized follow-the-leader combined with multiplicative weights is enough to online learn a non-smooth and non-B sequence.
  arXiv  Detail & Related papers  (2022-05-27T17:40:32Z)
• Log-based Sparse Nonnegative Matrix Factorization for Data Representation [55.72494900138061]
  Nonnegative matrix factorization (NMF) has been widely studied in recent years due to its effectiveness in representing nonnegative data with parts-based representations. We propose a new NMF method with log-norm imposed on the factor matrices to enhance the sparseness. A novel column-wisely sparse norm, named $ell_2,log$-(pseudo) norm, is proposed to enhance the robustness of the proposed method.
  arXiv  Detail & Related papers  (2022-04-22T11:38:10Z)
• Block Alternating Bregman Majorization Minimization with Extrapolation [16.04690575393738]
  We consider a class of nonsmooth non optimization problems whose objective is the sum of a block relative smooth function and a proper separable function. We propose a block alternating Bregman Majorization-Minimization framework with Extrapolation (BMME) We prove the effectiveness of BMME on the penalized nonnegative matrix under stronger conditions.
  arXiv  Detail & Related papers  (2021-07-09T12:47:00Z)
• Momentum Accelerates the Convergence of Stochastic AUPRC Maximization [80.8226518642952]
  We study optimization of areas under precision-recall curves (AUPRC), which is widely used for imbalanced tasks. We develop novel momentum methods with a better iteration of $O (1/epsilon4)$ for finding an $epsilon$stationary solution. We also design a novel family of adaptive methods with the same complexity of $O (1/epsilon4)$, which enjoy faster convergence in practice.
  arXiv  Detail & Related papers  (2021-07-02T16:21:52Z)
• Joint Majorization-Minimization for Nonnegative Matrix Factorization with the $\beta$-divergence [4.468952886990851]
  This article proposes new multiplicative updates for nonnegative matrix factorization (NMF) with the $beta$-divergence objective function. We report experimental results using diverse datasets: face images, an audio spectrogram, hyperspectral data and song play counts.
  arXiv  Detail & Related papers  (2021-06-29T09:58:21Z)
• Self-supervised Symmetric Nonnegative Matrix Factorization [82.59905231819685]
  Symmetric nonnegative factor matrix (SNMF) has demonstrated to be a powerful method for data clustering. Inspired by ensemble clustering that aims to seek better clustering results, we propose self-supervised SNMF (S$3$NMF) We take advantage of the sensitivity to code characteristic of SNMF, without relying on any additional information.
  arXiv  Detail & Related papers  (2021-03-02T12:47:40Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.