Related papers: An iterated $I$-projection procedure for solving t…
A foundational challenge in uncertainty quantification involves estimating a probability measure on the space of uncertain parameters such that its push-forward through a computational model matches an observed probability measure on the…
Many real-world applications involve black-box optimization of multiple objectives using continuous function approximations that trade-off accuracy and resource cost of evaluation. For example, in rocket launching research, we need to find…
In equality-constrained optimization, a standard regularity assumption is often associated with feasible point methods, namely the gradients of constraints are linearly independent. In practice, the regularity assumption may be violated. To…
The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…
Quantum relative entropy optimization refers to a class of convex problems in which a linear functional is minimized over an affine section of the epigraph of the quantum relative entropy function. Recently, the self-concordance of a…
We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…
Iterative magnitude pruning methods (IMPs), proven to be successful in reducing the number of insignificant nodes in over-parameterized deep neural networks (DNNs), have been getting an enormous amount of attention with the rapid deployment…
The problem of reconstruction of digital images from their degraded measurements is regarded as a problem of central importance in various fields of engineering and imaging sciences. In such cases, the degradation is typically caused by the…
Information theory is a mathematical theory of learning with deep connections with topics as diverse as artificial intelligence, statistical physics, and biological evolution. Many primers on information theory paint a broad picture with…
We consider copulas with a given diagonal section and compute the explicit density of the unique optimal copula which maximizes the entropy. In this sense, this copula is the least informative among the copulas with a given diagonal…
In this paper we develop a randomized block-coordinate descent method for minimizing the sum of a smooth and a simple nonsmooth block-separable convex function and prove that it obtains an $\epsilon$-accurate solution with probability at…
Physics concepts have often been borrowed and independently developed by other fields of science. In this perspective a significant example is that of entropy in Information Theory. The aim of this paper is to provide a short and…
Approximate solutions of linear and nonlinear integral equations using methods related to an interpolatory projection involve many integrals which need to be evaluated using a numerical quadrature formula. In this paper, we consider…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
As a judicious correspondence to the classical maxcut, the anti-Cheeger cut has more balanced structure, but few numerical results on it have been reported so far. In this paper, we propose a continuous iterative algorithm (CIA) for the…
Despite the empirical success of knowledge distillation, current state-of-the-art methods are computationally expensive to train, which makes them difficult to adopt in practice. To address this problem, we introduce two distinct…
We study the problem of distributed cooperative learning, where a group of agents seeks to agree on a set of hypotheses that best describes a sequence of private observations. In the scenario where the set of hypotheses is large, we propose…
In mixture models, anisotropic noise within each cluster is widely present in real-world data. This work investigates both computationally efficient procedures and fundamental statistical limits for clustering in high-dimensional…
We consider information retrieval when the data, for instance multimedia, is coputationally expensive to fetch. Our approach uses "information filters" to considerably narrow the universe of possiblities before retrieval. We are especially…
We observe an infinite sequence of independent identically distributed random variables $X_1,X_2,\ldots$ drawn from an unknown distribution $p$ over $[n]$, and our goal is to estimate the entropy $H(p)=-\mathbb{E}[\log p(X)]$ within an…