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Related papers: Discrepancy Algorithms for the Binary Perceptron

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We present an analysis of the Locally Competitive Algorithm (LCA), a Hopfield-style neural network that efficiently solves sparse approximation problems (e.g., approximating a vector from a dictionary using just a few non-zero…

Dynamical Systems · Mathematics 2015-03-19 Aurèle Balavoine , Justin Romberg , Christopher J. Rozell

This article investigates the interplay of rounding objective coefficients in binary programs and almost symmetries. Empirically, reducing the number of significant bits through rounding often leads to instances that are easier to solve.…

Optimization and Control · Mathematics 2025-12-12 Dominik Kuzinowicz , Paweł Lichocki , Gioni Mexi , Marc E. Pfetsch , Sebastian Pokutta , Max Zimmer

We consider chance-constrained binary knapsack problems, where the weights of items are independent random variables with the means and standard deviations known. The chance constraint can be reformulated as a second-order cone constraint…

Optimization and Control · Mathematics 2021-05-26 Jaehyeon Ryu , Sungsoo Park

We address the problem of detection and estimation of one or two change-points in the mean of a series of random variables. We use the formalism of set estimation in regression: To each point of a design is attached a binary label that…

Statistics Theory · Mathematics 2018-09-07 Victor-Emmanuel Brunel

The problem of classification in machine learning has often been approached in terms of function approximation. In this paper, we propose an alternative approach for classification in arbitrary compact metric spaces which, in theory, yields…

Machine Learning · Computer Science 2026-03-26 H. N. Mhaskar , Ryan O'Dowd

This paper investigates the problem of simultaneously predicting multiple binary responses by utilizing a shared set of covariates. Our approach incorporates machine learning techniques for binary classification, without making assumptions…

Methodology · Statistics 2024-03-07 The Tien Mai

In supervised learning, we often face with ambiguous (A) samples that are difficult to label even by domain experts. In this paper, we consider a binary classification problem in the presence of such A samples. This problem is substantially…

Machine Learning · Computer Science 2020-11-25 Naoya Otani , Yosuke Otsubo , Tetsuya Koike , Masashi Sugiyama

Let A be a matrix, c be any linear objective function and x be a fractional vector, say an LP solution to some discrete optimization problem. Then a recurring task in theoretical computer science (and in approximation algorithms in…

Data Structures and Algorithms · Computer Science 2011-04-26 Thomas Rothvoss

We study embedding a subset $K$ of the unit sphere to the Hamming cube $\{-1,+1\}^m$. We characterize the tradeoff between distortion and sample complexity $m$ in terms of the Gaussian width $\omega(K)$ of the set. For subspaces and several…

Machine Learning · Computer Science 2015-12-15 Samet Oymak , Ben Recht

In this chapter, we introduce the relaxed inertial proximal splitting algorithm (RIPSA) for hierarchical equilibrium problems. Using Opial-Passty's lemma, we first establish weak ergodic and weak convergence of the sequence generated by the…

Optimization and Control · Mathematics 2025-09-30 Zakaria Mazgouri , Hassan Riahi , Michel Théra

We unify f-divergences, Bregman divergences, surrogate loss bounds (regret bounds), proper scoring rules, matching losses, cost curves, ROC-curves and information. We do this by systematically studying integral and variational…

Machine Learning · Statistics 2009-01-06 Mark D. Reid , Robert C. Williamson

Given a heterogeneous Gaussian sequence model with unknown mean $\theta \in \mathbb R^d$ and known covariance matrix $\Sigma = \operatorname{diag}(\sigma_1^2,\dots, \sigma_d^2)$, we study the signal detection problem against sparse…

Statistics Theory · Mathematics 2023-08-03 Julien Chhor , Rajarshi Mukherjee , Subhabrata Sen

We consider the problem of partitioning $n$ integers into two subsets of given cardinalities such that the discrepancy, the absolute value of the difference of their sums, is minimized. The integers are i.i.d. random variables chosen…

Disordered Systems and Neural Networks · Physics 2007-05-23 C. Borgs , J. T. Chayes , S. Mertens , B. Pittel

Suppose we know that an object is in a sorted table and we want to determine the index of that object. To achieve this goal we could perform a binary search. However, suppose it is time-consuming to determine the relative position of that…

Data Structures and Algorithms · Computer Science 2017-11-07 Haoze Wu

With the growing interest in quantum machine learning, the perceptron -- a fundamental building block in traditional machine learning -- has emerged as a valuable model for exploring quantum advantages. Two quantum perceptron algorithms…

Quantum Physics · Physics 2025-03-24 Xiaoyu Sun , Mathieu Roget , Giuseppe Di Molfetta , Hachem Kadri

We extend a primal-dual fixed point algorithm (PDFP) proposed in [5] to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP…

Optimization and Control · Mathematics 2016-02-02 Peijun Chen , Jianguo Huang , Xiaoqun Zhang

We consider stochastic gradient methods under the interpolation regime where a perfect fit can be obtained (minimum loss at each observation). While previous work highlighted the implicit regularization of such algorithms, we consider an…

Optimization and Control · Mathematics 2020-04-01 Anant Raj , Francis Bach

Least squares form one of the most prominent classes of optimization problems, with numerous applications in scientific computing and data fitting. When such formulations aim at modeling complex systems, the optimization process must…

Optimization and Control · Mathematics 2021-05-31 E. Bergou , Y. Diouane , V. Kungurtsev , C. W. Royer

In this paper, we consider a class of difference-of-convex (DC) optimization problems, which require only a weaker restricted $L$-smooth adaptable property on the smooth part of the objective function, instead of the standard global…

Optimization and Control · Mathematics 2025-04-30 Lei Yang , Jingjing Hu , Kim-Chuan Toh

We revisit Matrix Balancing, a pre-conditioning task used ubiquitously for computing eigenvalues and matrix exponentials. Since 1960, Osborne's algorithm has been the practitioners' algorithm of choice and is now implemented in most…

Optimization and Control · Mathematics 2021-07-06 Jason M. Altschuler , Pablo A. Parrilo
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