Related papers: The Proximal Map of the Weighted Mean Absolute Err…

This paper addresses the problem of finding a B-term wavelet representation of a given discrete function $f \in \real^n$ whose distance from f is minimized. The problem is well understood when we seek to minimize the Euclidean distance…

This paper addresses the problem of approximate MAP-MRF inference in general graphical models. Following [36], we consider a family of linear programming relaxations of the problem where each relaxation is specified by a set of nested pairs…

Machine learning algorithms have grown in sophistication over the years and are increasingly deployed for real-life applications. However, when using machine learning techniques in practical settings, particularly in high-risk applications…

In this paper, we consider matrix completion with absolute deviation loss and obtain an estimator of the median matrix. Despite several appealing properties of median, the non-smooth absolute deviation loss leads to computational challenge…

We present a method that takes as input a single dual-pixel image, and simultaneously estimates the image's defocus map -- the amount of defocus blur at each pixel -- and recovers an all-in-focus image. Our method is inspired from recent…

One of the most important problems in regression-based error model is modeling the complex representation error caused by various corruptions and environment changes in images. For example, in robust face recognition, images are often…

We propose a proximal point algorithm to solve LAROS problem, that is the problem of finding a "large approximately rank-one submatrix". This LAROS problem is used to sequentially extract features in data. We also develop a new stopping…

We present an edge preserving and denoising filter for enhancing the features in images, which contain an ROI having a narrow spatial extent. Typical examples include angiograms, or ROI spatially distributed in multiple locations and…

Most of the existing denoising algorithms are developed for grayscale images, while it is not a trivial work to extend them for color image denoising because the noise statistics in R, G, B channels can be very different for real noisy…

Rational approximation appears in many contexts throughout science and engineering, playing a central role in linear systems theory, special function approximation, and many others. There are many existing methods for solving the rational…

We studied linear weighted sampling algorithms and their optimality for approximate recovery of functions with mixed smoothness on $\mathbb{R}^d$ from a set of $n$ their sampled values. Functions to be recovered are in weighted Sobolev…

The problem of estimating a random vector x from noisy linear measurements y = A x + w with unknown parameters on the distributions of x and w, which must also be learned, arises in a wide range of statistical learning and linear inverse…

In this paper, we consider a broad class of nonconvex and nonsmooth optimization problems, where one objective component is a nonsmooth weakly convex function composed with a linear operator. By integrating variable smoothing techniques…

We study the problem of constructing approximations to a weighted automaton. Weighted finite automata (WFA) are closely related to the theory of rational series. A rational series is a function from strings to real numbers that can be…

The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…

Automatic Mean Opinion Score (MOS) prediction is crucial to evaluate the perceptual quality of the synthetic speech. While recent approaches using pre-trained self-supervised learning (SSL) models have shown promising results, they only…

We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…

This paper introduces a novel error estimator for the Proper Generalized Decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: It builds on concentration inequalities of Gaussian maps and an…

In this paper, we obtain error bound for binomial and negative binomial approximations to weighted sums of locally dependent random variables, using Stein's method. We also discuss approximation results for weighted sums of independent…

Parameter estimation in robotics and computer vision faces formidable challenges from both outlier contamination and nonconvex optimization landscapes. While M-estimation addresses the problem of outliers through robust loss functions, it…