Related papers: Maximum information divergence from linear and tor…
A lexicographic maximum of a set $X \subseteq \mathbb{R}^n$ is a vector in $X$ whose smallest component is as large as possible, and subject to that requirement, whose second smallest component is as large as possible, and so on for the…
We consider optimal decision-making problems in an uncertain environment. In particular, we consider the case in which the distribution of the input is unknown, yet there is abundant historical data drawn from the distribution. In this…
We study the computational complexity of determining the Hausdorff distance of two polytopes given in halfspace- or vertex-presentation in arbitrary dimension. Subsequently, a matching problem is investigated where a convex body is allowed…
The maximum likelihood estimation of the left-truncated log-logistic distribution with a given truncation point is analyzed in detail from both mathematical and numerical perspectives. These maximum likelihood equations often do not possess…
This paper studies best finitely supported approximations of one-dimensional probability measures with respect to the $L^r$-Kantorovich (or transport) distance, where either the locations or the weights of the approximations' atoms are…
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…
In this paper, we propose a new max-margin based discriminative feature learning method. Specifically, we aim at learning a low-dimensional feature representation, so as to maximize the global margin of the data and make the samples from…
Extraction of structure, in particular of group symmetries, is increasingly crucial to understanding and building intelligent models. In particular, some information-theoretic models of parsimonious learning have been argued to induce…
When additional information sources are available in decision making problems that allow stochastic optimization formulations, an important question is how to optimally use the information the sources are capable of providing. A framework…
We derive the closed-form expression of the maximum mutual information - the maximum value of $I(X;Z)$ obtainable via training - for a broad family of neural network architectures. The quantity is essential to several branches of machine…
We introduce machine learning methodology to the study of lattice polytopes. With supervised learning techniques, we predict standard properties such as volume, dual volume, reflexivity, etc, with accuracies up to 100%. We focus on 2d…
We consider the problem of clustering data that reside on discrete, low dimensional lattices. Canonical examples for this setting are found in image segmentation and key point extraction. Our solution is based on a recent approach to…
We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…
In this paper we study the problem of maximizing the distance to a given point $C_0$ over a polytope $\mathcal{P}$. Assuming that the polytope is circumscribed by a known ball we construct an intersection of balls which preserves the…
Bayesian Inference and Information Bottleneck are the two most popular objectives for neural networks, but they can be optimised only via a variational lower bound: the Variational Information Bottleneck (VIB). In this manuscript we show…
The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a…
The problem of distributed representation learning is one in which multiple sources of information $X_1,\ldots,X_K$ are processed separately so as to learn as much information as possible about some ground truth $Y$. We investigate this…
We develop quantitative algorithmic information bounds for orthogonal projections and distances in the plane. Under mild independence conditions, the distance $|x-y|$ and a projection coordinate $p_e x$ each retain at least half the…
Given a compact parameter set $Y\subset R^p$, we consider polynomial optimization problems $(P_y$) on $R^n$ whose description depends on the parameter $y\inY$. We assume that one can compute all moments of some probability measure $\phi$ on…
The study of the fundamental limits of information systems is a central theme in information theory. Both the traditional analytical approach and the recently proposed computational approach have significant limitations, where the former is…