English
Related papers

Related papers: Improved invariant polytope algorithm and applicat…

200 papers

We propose an inexact optimization algorithm on Riemannian manifolds, motivated by quadratic discrimination tasks in high-dimensional, low-sample-size (HDLSS) imaging settings. In such applications, gradient evaluations are often biased due…

Optimization and Control · Mathematics 2025-07-08 Uday Talwar , Meredith K. Kupinski , Afrooz Jalilzadeh

We present a faster direct sampling algorithm for random equilateral closed polygons in three-dimensional space. This method improves on the moment polytope sampling algorithm of Cantarella, Duplantier, Shonkwiler, and Uehara (2016) and has…

Statistical Mechanics · Physics 2025-06-02 Jason Cantarella , Henrik Schumacher , Clayton Shonkwiler

In this paper we provide new quantum algorithms with polynomial speed-up for a range of problems for which no such results were known, or we improve previous algorithms. First, we consider the approximation of the frequency moments $F_k$ of…

Quantum Physics · Physics 2019-07-08 Yassine Hamoudi , Frédéric Magniez

We study the computation of local approximations of invariant manifolds of parabolic fixed points and parabolic periodic orbits of periodic vector fields. If the dimension of these manifolds is two or greater, in general, it is not possible…

Dynamical Systems · Mathematics 2016-03-09 Inmaculada Baldomá , Ernest Fontich , Pau Martín

Geometric hitting set problems, in which we seek a smallest set of points that collectively hit a given set of ranges, are ubiquitous in computational geometry. Most often, the set is discrete and is given explicitly. We propose new…

Computational Geometry · Computer Science 2025-04-24 Jean Cardinal , Xavier Goaoc , Sarah Wajsbrot

The existing research on spectral algorithms, applied within a Reproducing Kernel Hilbert Space (RKHS), has primarily focused on general kernel functions, often neglecting the inherent structure of the input feature space. Our paper…

Machine Learning · Statistics 2024-03-08 Weichun Xia , Lei Shi

Polyhedral estimate is a generic efficiently computable nonlinear in observations routine for recovering unknown signal belonging to a given convex compact set from noisy observation of signal's linear image. Risk analysis and optimal…

Statistics Theory · Mathematics 2022-12-26 Anatoli Juditsky , Arkadi Nemirovski

In this paper we combine an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM). The resulting algorithm (IP-PMM) is interpreted as a primal-dual regularized IPM, suitable for solving linearly constrained…

Optimization and Control · Mathematics 2021-02-01 Spyridon Pougkakiotis , Jacek Gondzio

We make a convergence analysis of the harmonic and refined harmonic extraction versions of Jacobi-Davidson SVD (JDSVD) type methods for computing one or more interior singular triplets of a large matrix $A$. At each outer iteration of these…

Numerical Analysis · Mathematics 2019-09-24 Jinzhi Huang , Zhongxiao Jia

In the Upper Degree-Constrained Partial Orientation problem we are given an undirected graph $G=(V,E)$, together with two degree constraint functions $d^-,d^+ : V \to \mathbb{N}$. The goal is to orient as many edges as possible, in such a…

Data Structures and Algorithms · Computer Science 2014-10-13 Marek Cygan , Tomasz Kociumaka

In this work, a new algorithm for solving symmetric indefinite systems of linear equations is presented. It factorizes the matrix into the form LDLt using Jacobi rotations in order to increase the pivot's absolute value. Furthermore, Rook's…

Numerical Analysis · Mathematics 2025-01-30 Ibai Coria , Gorka Urkullu , Haritz Uriarte , Igor Fernández de Bustos

Although deep learning-based methods have dominated stereo matching leaderboards by yielding unprecedented disparity accuracy, their inference time is typically slow, on the order of seconds for a pair of 540p images. The main reason is…

Computer Vision and Pattern Recognition · Computer Science 2020-12-03 Yiran Zhong , Charles Loop , Wonmin Byeon , Stan Birchfield , Yuchao Dai , Kaihao Zhang , Alexey Kamenev , Thomas Breuel , Hongdong Li , Jan Kautz

We present improved algorithms for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithms are much more accurate than the famous fast inverse square root algorithm and have the same or…

Numerical Analysis · Computer Science 2018-02-22 Cezary J. Walczyk , Leonid V. Moroz , Jan L. Cieśliński

Matrix square roots and their inverses arise frequently in machine learning, e.g., when sampling from high-dimensional Gaussians $\mathcal{N}(\mathbf 0, \mathbf K)$ or whitening a vector $\mathbf b$ against covariance matrix $\mathbf K$.…

Machine Learning · Computer Science 2020-12-02 Geoff Pleiss , Martin Jankowiak , David Eriksson , Anil Damle , Jacob R. Gardner

We prove an a priori lower bound for the pressure, or $p$-norm joint spectral radius, of a measure on the set of $d \times d$ real matrices which parallels a result of J. Bochi for the joint spectral radius. We apply this lower bound to…

Dynamical Systems · Mathematics 2016-07-29 Ian D. Morris

In this paper, we examine an analogue of the recently solved spectrum conjecture by Fujita in the setting of Fine polyhedral adjunction theory. We present computational results for lower-dimensional polytopes, which lead to a complete…

Combinatorics · Mathematics 2026-01-07 Sofía Garzón Mora , Christian Haase

This paper proposes a fast multi-band image fusion algorithm, which combines a high-spatial low-spectral resolution image and a low-spatial high-spectral resolution image. The well admitted forward model is explored to form the likelihoods…

Computer Vision and Pattern Recognition · Computer Science 2015-10-28 Qi Wei , Nicolas Dobigeon , Jean-Yves Tourneret

We give the first polynomial time and sample $(\epsilon, \delta)$-differentially private (DP) algorithm to estimate the mean, covariance and higher moments in the presence of a constant fraction of adversarial outliers. Our algorithm…

Machine Learning · Statistics 2021-12-08 Pravesh K. Kothari , Pasin Manurangsi , Ameya Velingker

Detecting elliptical objects from an image is a central task in robot navigation and industrial diagnosis where the detection time is always a critical issue. Existing methods are hardly applicable to these real-time scenarios of limited…

Computer Vision and Pattern Recognition · Computer Science 2017-08-02 Qi Jia , Xin Fan , Zhongxuan Luo , Lianbo Song , Tie Qiu

We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…

Optimization and Control · Mathematics 2009-01-24 Shmuel Onn