Related papers: Adaptive Sketch-and-Project Methods for Solving Li…
In this work, we introduce a novel class of adaptive Monte Carlo methods, called adaptive independent sticky MCMC algorithms, for efficient sampling from a generic target probability density function (pdf). The new class of algorithms…
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…
Maximum consensus estimation plays a critically important role in robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify…
In this article we consider the problem of choosing an optimal sampling scheme for the regression problem simultaneously with that of model selection. We consider a batch type approach and an on-line approach following algorithms recently…
The Kaczmarz method is a popular iterative scheme for solving large-scale linear systems. The randomized Kaczmarz method (RK) greatly improves the convergence rate of the Kaczmarz method, by using the rows of the coefficient matrix in…
Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…
We propose a new randomized algorithm for solving L2-regularized least-squares problems based on sketching. We consider two of the most popular random embeddings, namely, Gaussian embeddings and the Subsampled Randomized Hadamard Transform…
This paper studies iterative schemes for measure transfer and approximation problems, which are defined through a slicing-and-matching procedure. Similar to the sliced Wasserstein distance, these schemes benefit from the availability of…
We propose a trust-region method for finite-sum minimization with an adaptive sample size adjustment technique, which is practical in the sense that it leads to a globally convergent method that shows strong performance empirically without…
We propose a distributed algorithm based on Alternating Direction Method of Multipliers (ADMM) to minimize the sum of locally known convex functions using communication over a network. This optimization problem emerges in many applications…
In this paper, we study the application of quasi-Newton methods for solving empirical risk minimization (ERM) problems defined over a large dataset. Traditional deterministic and stochastic quasi-Newton methods can be executed to solve such…
Compressive Sensing (CS) stipulates that a sparse signal can be recovered from a small number of linear measurements, and that this recovery can be performed efficiently in polynomial time. The framework of model-based compressive sensing…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
This paper improves the performance of RRT$^*$-like sampling-based path planners by combining admissible informed sampling and local sampling (i.e., sampling the neighborhood of the current solution). An adaptive strategy regulates the…
We propose a stochastic optimization method for minimizing loss functions, expressed as an expected value, that adaptively controls the batch size used in the computation of gradient approximations and the step size used to move along such…
In the context of the graph matching problem we propose a novel method for projecting a matrix $Q$, which may be a doubly stochastic matrix, to a permutation matrix $P.$ We observe that there is an intuitve mapping, depending on a given…
In this work we investigate stochastic non-convex optimization problems where the objective is an expectation over smooth loss functions, and the goal is to find an approximate stationary point. The most popular approach to handling such…
The randomized Kaczmarz (RK) method is an iterative method for approximating the least-squares solution of large linear systems of equations. The standard RK method uses sequential updates, making parallel computation difficult. Here, we…
We study the optimal design problems where the goal is to choose a set of linear measurements to obtain the most accurate estimate of an unknown vector in $d$ dimensions. We study the $A$-optimal design variant where the objective is to…
We consider constrained sampling problems in paid research studies or clinical trials. When qualified volunteers are more than the budget allowed, we recommend a D-optimal sampling strategy based on the optimal design theory and develop a…