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In this paper, we propose a successive pseudo-convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of…

Optimization and Control · Mathematics 2018-12-17 Yang Yang , Marius Pesavento

The stabilization of a quantum computer by repeated error correction can be reduced almost entirely to repeated preparation of blocks of qubits in quantum codeword states. These are multi-particle entangled states with a high degree of…

Quantum Physics · Physics 2007-05-23 Andrew M. Steane

We consider a regularized least squares problem, with regularization by structured sparsity-inducing norms, which extend the usual $\ell_1$ and the group lasso penalty, by allowing the subsets to overlap. Such regularizations lead to…

Optimization and Control · Mathematics 2012-09-04 Silvia Villa , Lorenzo Rosasco , Sofia Mosci , Alessandro Verri

We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…

Machine Learning · Statistics 2009-06-12 Rahul Mazumder , Trevor Hastie , Rob Tibshirani

This paper focuses on the noiseless complete dictionary learning problem, where the goal is to represent a set of given signals as linear combinations of a small number of atoms from a learned dictionary. There are two main challenges faced…

Machine Learning · Computer Science 2025-03-06 Geyu Liang , Gavin Zhang , Salar Fattahi , Richard Y. Zhang

Iterative sketching and sketch-and-precondition are randomized algorithms used for solving overdetermined linear least-squares problems. When implemented in exact arithmetic, these algorithms produce high-accuracy solutions to least-squares…

Numerical Analysis · Mathematics 2024-04-15 Ethan N. Epperly

Sparse optimization problems are ubiquitous in many fields such as statistics, signal/image processing and machine learning. This has led to the birth of many iterative algorithms to solve them. A powerful strategy to boost the performance…

Machine Learning · Computer Science 2023-01-09 Cassio F. Dantas , Emmanuel Soubies , Cédric Févotte

Non-negative and bounded-variable linear regression problems arise in a variety of applications in machine learning and signal processing. In this paper, we propose a technique to accelerate existing solvers for these problems by…

Machine Learning · Computer Science 2023-06-27 Cassio F. Dantas , Emmanuel Soubies , Cédric Févotte

Sparse learning techniques have been routinely used for feature selection as the resulting model usually has a small number of non-zero entries. Safe screening, which eliminates the features that are guaranteed to have zero coefficients for…

Machine Learning · Computer Science 2014-05-13 Jun Liu , Zheng Zhao , Jie Wang , Jieping Ye

We study first-order algorithms that are uniformly stable for empirical risk minimization (ERM) problems that are convex and smooth with respect to $p$-norms, $p \geq 1$. We propose a black-box reduction method that, by employing properties…

Machine Learning · Computer Science 2024-12-23 Simon Vary , David Martínez-Rubio , Patrick Rebeschini

Recently dictionary screening has been proposed as an effective way to improve the computational efficiency of solving the lasso problem, which is one of the most commonly used method for learning sparse representations. To address today's…

Machine Learning · Computer Science 2016-08-29 Yun Wang , Peter J. Ramadge

In this paper, we discuss the acceleration of the regularized alternating least square (RALS) algorithm for tensor approximation. We propose a fast iterative method using a Aitken-Stefensen like updates for the regularized algorithm.…

Numerical Analysis · Mathematics 2017-07-25 Xiaofei Wang , Carmeliza Navasca , Stefan Kindermann

Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…

Machine Learning · Computer Science 2024-01-24 Alexandre d'Aspremont , Cristóbal Guzmán , Clément Lezane

We analyzed the performance of a biologically inspired algorithm called the Corrected Projections Algorithm (CPA) when a sparseness constraint is required to unambiguously reconstruct an observed signal using atoms from an overcomplete…

Numerical Analysis · Computer Science 2017-03-24 Gonzalo H Otazu

We design simple screening tests to automatically discard data samples in empirical risk minimization without losing optimization guarantees. We derive loss functions that produce dual objectives with a sparse solution. We also show how to…

Machine Learning · Computer Science 2020-06-15 Grégoire Mialon , Alexandre d'Aspremont , Julien Mairal

We study approximation algorithms for the following three string measures that are widely used in practice: edit distance (ED), longest common subsequence (LCS), and longest increasing sequence (LIS). All three problems can be solved…

Data Structures and Algorithms · Computer Science 2020-07-28 Kuan Cheng , Zhengzhong Jin , Xin Li , Yu Zheng

We consider the problem of designing uniformly stable first-order optimization algorithms for empirical risk minimization. Uniform stability is often used to obtain generalization error bounds for optimization algorithms, and we are…

Machine Learning · Computer Science 2022-07-19 Amit Attia , Tomer Koren

Distributed optimization has been widely used as one of the most efficient approaches for model training with massive samples. However, large-scale learning problems with both massive samples and high-dimensional features widely exist in…

Machine Learning · Computer Science 2022-04-26 Runxue Bao , Xidong Wu , Wenhan Xian , Heng Huang

The sparsity of natural signals and images in a transform domain or dictionary has been extensively exploited in several applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis…

Machine Learning · Computer Science 2017-04-24 Saiprasad Ravishankar , Raj Rao Nadakuditi , Jeffrey A. Fessler

Iterative sketching and sketch-and-precondition are well-established randomized algorithms for solving large-scale, over-determined linear least-squares problems. In this paper, we introduce a new perspective that interprets Iterative…

Numerical Analysis · Mathematics 2024-10-18 Ruihan Xu , Yiping Lu