Related papers: Constrained and Composite Sampling via Proximal Sa…

The split feasibility problem is to find an element in the intersection of a closed set $C$ and the linear preimage of another closed set $D$, assuming the projections onto $C$ and $D$ are easy to compute. This class of problems arises…

Reachability analysis is at the core of many applications, from neural network verification, to safe trajectory planning of uncertain systems. However, this problem is notoriously challenging, and current approaches tend to be either too…

Sparse high dimensional graphical model selection is a popular topic in contemporary machine learning. To this end, various useful approaches have been proposed in the context of $\ell_1$-penalized estimation in the Gaussian framework.…

This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…

We propose an adaptive proximal gradient method for minimizing the sum of two functions, where one is a simple convex function, and the other belongs to one of the three classes: nonconvex smooth, convex nonsmooth, or convex smooth. The key…

We study the complexity of heavy-tailed sampling and present a separation result in terms of obtaining high-accuracy versus low-accuracy guarantees i.e., samplers that require only $O(\log(1/\varepsilon))$ versus…

This paper considers stochastic convex optimization problems with smooth functional constraints arising in constrained estimation and robust signal recovery. We operate in the high-dimensional and highly-constrained setting, where oracle…

The nonlinear conjugate gradient methods are known to be an effective approach for standard unconstrained optimization problems especially for large-scale problems. This paper proposes a proximal nonlinear conjugate gradient method, which…

Bayesian inference with Markov Chain Monte Carlo (MCMC) is challenging when the likelihood function is irregular and expensive to compute. We explore several sampling algorithms that make use of subset evaluations to reduce computational…

Reducing acquisition time is of fundamental importance in various imaging modalities. The concept of variable density sampling provides a nice framework to achieve this. It was justified recently from a theoretical point of view in the…

Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance…

Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…

In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…

Constraints are a natural choice for prior information in Bayesian inference. In various applications, the parameters of interest lie on the boundary of the constraint set. In this paper, we use a method that implicitly defines a…

Compressive sampling has become a widely used approach to construct polynomial chaos surrogates when the number of available simulation samples is limited. Originally, these expensive simulation samples would be obtained at random locations…

Uniform sampling of training data has been commonly used in traditional stochastic optimization algorithms such as Proximal Stochastic Gradient Descent (prox-SGD) and Proximal Stochastic Dual Coordinate Ascent (prox-SDCA). Although uniform…

Equality-constrained models naturally arise in problems in which measurements are taken at different levels of resolution. The challenge in this setting is that the models usually induce a joint distribution which is intractable. Resorting…

In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of…

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…

Score based approaches to sampling have shown much success as a generative algorithm to produce new samples from a target density given a pool of initial samples. In this work, we consider if we have no initial samples from the target…