Related papers: Volesti: Volume Approximation and Sampling for Con…
Suppose an $n \times d$ design matrix in a linear regression problem is given, but the response for each point is hidden unless explicitly requested. The goal is to sample only a small number $k \ll n$ of the responses, and then produce a…
The volume function V(t) of a compact set S\in R^d is just the Lebesgue measure of the set of points within a distance to S not larger than t. According to some classical results in geometric measure theory, the volume function turns out to…
In computed tomography, the approximation quality of a scan of a physical object is typically limited by the acquisition modalities, especially the hardware including X-ray detectors. To improve upon this, we experiment with a…
We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…
Let ${\bf K} = (K_1, ..., K_n)$ be an $n$-tuple of convex compact subsets in the Euclidean space $\R^n$, and let $V(\cdot)$ be the Euclidean volume in $\R^n$. The Minkowski polynomial $V_{{\bf K}}$ is defined as $V_{{\bf K}}(\lambda_1, ...…
Variational autoencoders are among the most popular methods for distilling low-dimensional structure from high-dimensional data, making them increasingly valuable as tools for data exploration and scientific discovery. However, unlike…
The convex hull of N independent random points chosen on the boundary of a simple polytope in R^n is investigated. Asymptotic formulas for the expected number of vertices and facets, and for the expectation of the volume difference are…
In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the…
Biclustering is widely used in different kinds of fields including gene information analysis, text mining, and recommendation system by effectively discovering the local correlation between samples and features. However, many biclustering…
We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an…
We present complexity and numerical results for a new asynchronous parallel algorithmic method for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex…
Accurate body weight estimation is critical in emergency medicine for proper dosing of weight-based medications, yet direct measurement is often impractical in urgent situations. This paper presents a non-invasive method for estimating body…
A simple sample-based planning method is presented which approximates connected regions of free space with volumes in Configuration space instead of points. The algorithm produces very sparse trees compared to point-based planning…
In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…
Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…
Suppose we choose $N$ points uniformly randomly from a convex body in $d$ dimensions. How large must $N$ be, asymptotically with respect to $d$, so that the convex hull of the points is nearly as large as the convex body itself? It was…
This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…
The extraction of inhomogeneous 3-dimensional densities around tagged solutes from molecular simulations is known to have a very high computational cost because this is traditionally performed by collecting histograms, with each discrete…
An efficient algorithm to enumerate the vertices of a two-dimensional (2D) projection of a polytope, is presented in this paper. The proposed algorithm uses the support function of the polytope to be projected and enumerated for vertices.…