English
Related papers

Related papers: Inverse Quadratic Decay in Random Subset Sum

200 papers

We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…

Numerical Analysis · Mathematics 2022-03-24 Darko Volkov

We present an efficient learning algorithm for the problem of training neural networks with discrete synapses, a well-known hard (NP-complete) discrete optimization problem. The algorithm is a variant of the so-called Max-Sum (MS)…

Disordered Systems and Neural Networks · Physics 2015-08-14 Carlo Baldassi , Alfredo Braunstein

Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…

Nuclear Theory · Physics 2023-04-05 Caleb Hicks , Dean Lee

We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast…

Information Theory · Computer Science 2022-09-14 Jean Barbier , Nicolas Macris

We propose a new randomized algorithm for solving L2-regularized least-squares problems based on sketching. We consider two of the most popular random embeddings, namely, Gaussian embeddings and the Subsampled Randomized Hadamard Transform…

Machine Learning · Computer Science 2020-10-26 Jonathan Lacotte , Mert Pilanci

Unbounded SubsetSum is a classical textbook problem: given integers $w_1,w_2,\cdots,w_n\in [1,u],~c,u$, we need to find if there exists $m_1,m_2,\cdots,m_n\in \mathbb{N}$ satisfying $c=\sum_{i=1}^n w_im_i$. In its all-target version, $t\in…

Data Structures and Algorithms · Computer Science 2022-03-01 Mingyang Deng , Xiao Mao , Ziqian Zhong

We present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set…

Optimization and Control · Mathematics 2014-08-14 Sanjay Mehrotra , David Papp

Sum-of-squares (SOS) optimization provides a computationally tractable framework for certifying polynomial nonnegativity. If the considered problem is convex, the SOS problem can be transcribed into and solved by semi-definite programs.…

Optimization and Control · Mathematics 2026-04-14 Jan Olucak , Torbjørn Cunis

Linear regression is a fundamental and primitive problem in supervised machine learning, with applications ranging from epidemiology to finance. In this work, we propose methods for speeding up distributed linear regression. We do so by…

Information Theory · Computer Science 2024-04-02 Neophytos Charalambides , Hessam Mahdavifar , Mert Pilanci , Alfred O. Hero

Sparse Blind Source Separation (sparse BSS) is a key method to analyze multichannel data in fields ranging from medical imaging to astrophysics. However, since it relies on seeking the solution of a non-convex penalized matrix factorization…

Machine Learning · Computer Science 2018-12-18 Christophe Kervazo , Jerome Bobin , Cecile Chenot

In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…

Information Theory · Computer Science 2017-03-24 Boshra Rajaei , Sylvain Gigan , Florent Krzakala , Laurent Daudet

Reconfigurable intelligent surfaces (RIS) is a promising solution to build a programmable wireless environment via steering the incident signal in fully customizable ways with reconfigurable passive elements. In this paper, we consider a…

Signal Processing · Electrical Eng. & Systems 2019-12-30 Huayan Guo , Ying-Chang Liang , Jie Chen , Erik G. Larsson

We initiate the study of numerical linear algebra in the sliding window model, where only the most recent $W$ updates in a stream form the underlying data set. We first introduce a unified row-sampling based framework that gives randomized…

Data Structures and Algorithms · Computer Science 2023-04-12 Vladimir Braverman , Petros Drineas , Cameron Musco , Christopher Musco , Jalaj Upadhyay , David P. Woodruff , Samson Zhou

We present a faster interior-point method for optimizing sum-of-squares (SOS) polynomials, which are a central tool in polynomial optimization and capture convex programming in the Lasserre hierarchy. Let $p = \sum_i q^2_i$ be an…

Optimization and Control · Mathematics 2022-02-18 Shunhua Jiang , Bento Natura , Omri Weinstein

In recent years, randomized methods for numerical linear algebra have received growing interest as a general approach to large-scale problems. Typically, the essential ingredient of these methods is some form of randomized dimension…

Machine Learning · Statistics 2019-04-05 Miles E. Lopes , Shusen Wang , Michael W. Mahoney

Optimization algorithms appear in the core calculations of numerous Artificial Intelligence (AI) and Machine Learning methods, as well as Engineering and Business applications. Following recent works on the theoretical deficiencies of AI, a…

Optimization and Control · Mathematics 2024-10-29 Nikolaos P. Bakas , Vagelis Plevris , Andreas Langousis , Savvas A. Chatzichristofis

This paper builds on classical distributionally robust optimization techniques to construct a comprehensive framework that can be used for solving inverse problems. Given an estimated distribution of inputs in $X$ and outputs in $Y$, an…

Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming…

Machine Learning · Statistics 2020-09-04 Young Woong Park , Diego Klabjan

We present an efficient algorithm to solve semirandom planted instances of any Boolean constraint satisfaction problem (CSP). The semirandom model is a hybrid between worst-case and average-case input models, where the input is generated by…

Computational Complexity · Computer Science 2023-10-02 Venkatesan Guruswami , Jun-Ting Hsieh , Pravesh K. Kothari , Peter Manohar

As one popular modeling approach for end-to-end speech recognition, attention-based encoder-decoder models are known to suffer the length bias and corresponding beam problem. Different approaches have been applied in simple beam search to…

Audio and Speech Processing · Electrical Eng. & Systems 2023-10-24 Wei Zhou , Ralf Schlüter , Hermann Ney