Related papers: A Constructive Method to Maximize Entropy under Ma…
The estimation of categorical distributions under marginal constraints summarizing some sample from a population in the most-generalizable way is key for many machine-learning and data-driven approaches. We provide a parameter-agnostic…
We study the small-regularisation limit of the entropic optimal transport problem on the line with distance cost. While convergence of entropic minimizers is well understood in the discrete setting and in the case where the cost is…
This paper focuses on stochastic optimal control problems with constraints in law, which are rewritten as optimization (minimization) of probability measures problem on the canonical space. We introduce a penalized version of this type of…
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…
We study the finite element approximation of the solid isotropic material with penalization method (SIMP) for the topology optimization problem of minimizing the compliance of a linearly elastic structure. To ensure the existence of a local…
Moment-closure methods are popular tools to simplify the mathematical analysis of stochastic models defined on networks, in which high dimensional joint distributions are approximated (often by some heuristic argument) as functions of lower…
A formalism capable of handling the first step of hierarchical replica symmetry breaking in finite-connectivity models is introduced. The emerging order parameter is claimed to be a probability distribution over the space of field…
Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…
We study the problem of identifying the causal relationship between two discrete random variables from observational data. We recently proposed a novel framework called entropic causality that works in a very general functional model but…
A well-known result across information theory, machine learning, and statistical physics shows that the maximum entropy distribution under a mean constraint has an exponential form called the Gibbs-Boltzmann distribution. This is used for…
If moments of singular measures are passed as inputs to the entropy maximization procedure, the optimization algorithm might not terminate. The framework developed in our previous paper demonstrated how input moments of measures, on a broad…
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 compute the tightest possible bounds on the probability that the optimal value of a combinatorial optimization problem in maximization form with a random objective exceeds a given number, assuming only knowledge of the…
This paper investigates the optimality conditions for characterizing the local minimizers of the constrained optimization problems involving an $\ell_p$ norm ($0<p<1$) of the variables, which may appear in either the objective or the…
We consider a general class of two-stage distributionally robust optimization (DRO) problems where the ambiguity set is constrained by fixed marginal probability laws that are not necessarily discrete. We derive primal and dual formulations…
Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…
The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance…
The paper search for the minimum of the entropy of a two- dimensional distribution in the Fr\'echet class, the class of distributions with given marginals. The main result for discrete distributions is an algorithm for building the…
Optimisation problems in science and engineering typically involve finding the ground state (i.e. the minimum energy configuration) of a cost function with respect to many variables. If the variables are corrupted by noise then this…
This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…