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In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model $y$ with a surrogate model $y_s$ that can be evaluated quickly leads to a significant speedup. The…
We analyse and explain the increased generalisation performance of iterate averaging using a Gaussian process perturbation model between the true and batch risk surface on the high dimensional quadratic. We derive three phenomena…
This paper introduces a general framework for iterative optimization algorithms and establishes under general assumptions that their convergence is asymptotically geometric. We also prove that under appropriate assumptions, the rate of…
The problem of low-tubal-rank tensor estimation is a fundamental task with wide applications across high-dimensional signal processing, machine learning, and image science. Traditional approaches tackle such a problem by performing tensor…
Oversampled adaptive sensing (OAS) is a recently proposed Bayesian framework which sequentially adapts the sensing basis. In OAS, estimation quality is, in each step, measured by conditional mean squared errors (MSEs), and the basis for the…
In the first part of the paper we consider accelerated first order optimization method for convex functions with $L$-Lipschitz-continuous gradient, that is able to automatically adapts to problems which satisfies Polyak-{\L}ojasiewicz…
Recent work by Rauhut and Ward developed a notion of weighted sparsity and a corresponding notion of Restricted Isometry Property for the space of weighted sparse signals. Using these notions, we pose a best weighted sparse approximation…
The Recently proposed Vector Approximate Message Passing (VAMP) algorithm demonstrates a great reconstruction potential at solving compressed sensing related linear inverse problems. VAMP provides high per-iteration improvement, can utilize…
Object detection is a fundamental vision task. It has been highly researched in academia and has been widely adopted in industry. Average Precision (AP) is the standard score for evaluating object detectors. Our understanding of the…
The inverse Ising problem consists in inferring the coupling constants of an Ising model given the correlation matrix. The fastest methods for solving this problem are based on mean-field approximations, but which one performs better in the…
Gaussian processes (GPs) play an essential role in biostatistics, scientific machine learning, and Bayesian optimization for their ability to provide probabilistic predictions and model uncertainty. However, GP inference struggles to scale…
We consider convergence of alternating projections between non-convex sets and obtain applications to convergence of the Gerchberg-Saxton error reduction method, of the Gaussian expectation-maximization algorithm, and of Cadzow's algorithm.
This article aims to present the $AT$ algorithm, a novel two-step iterative approach for approximating fixed points of weak contractions within complete normed linear spaces. The article demonstrates the convergence of $AT$ algorithm…
We consider a distributed compressed sensing scenario where many sensors measure correlated sparse signals and the sensors are connected through a network. Correlation between sparse signals is modeled by a partial common support-set. For…
Additive-interactive regression has recently been shown to offer attractive minimax error rates over traditional nonparametric multivariate regression in a wide variety of settings, including cases where the predictor count is much larger…
Compressive Sensing, which offers exact reconstruction of sparse signal from a small number of measurements, has tremendous potential for trajectory compression. In order to optimize the compression, trajectory compression algorithms need…
The restricted isometry property (RIP) is an integral tool in the analysis of various inverse problems with sparsity models. Motivated by the applications of compressed sensing and dimensionality reduction of low-rank tensors, we propose…
In many real-world problems, recovering sparse signals from underdetermined linear systems remains a fundamental challenge. Although $\ell_1$ norm minimization is widely used, it suffers from estimation bias that prevents it from reaching…
We study the convergence issue for the gradient algorithm (employing general step sizes) for optimization problems on general Riemannian manifolds (without curvature constraints). Under the assumption of the local convexity/quasi-convexity…
We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix…