Related papers: A New Class of Upper Bounds on the Log Partition F…

Optimal Transport (OT) is a fundamental tool for comparing probability distributions, but its exact computation remains prohibitive for large datasets. In this work, we introduce novel families of upper and lower bounds for the OT problem…

This paper presents a new probabilistic generative model for image segmentation, i.e. the task of partitioning an image into homogeneous regions. Our model is grounded on a mid-level image representation, called a region tree, in which…

This paper considers global optimization with a black-box unknown objective function that can be non-convex and non-differentiable. Such a difficult optimization problem arises in many real-world applications, such as parameter tuning in…

In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…

We derive two related novel bounds on single-variable marginal probability distributions in factor graphs with discrete variables. The first method propagates bounds over a subtree of the factor graph rooted in the variable, and the second…

Since its original formulation, Jensen's inequality has played a fundamental role across mathematics, statistics, and machine learning, with its probabilistic version highlighting the nonnegativity of the so-called Jensen's gap, i.e., the…

Statistical inference from high-dimensional data with low-dimensional structures has recently attracted lots of attention. In machine learning, deep generative modeling approaches implicitly estimate distributions of complex objects by…

The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…

We consider the problem of stochastic convex optimization with exp-concave losses using Empirical Risk Minimization in a convex class. Answering a question raised in several prior works, we provide a $O( d / n + \log( 1 / \delta) / n )$…

We study the problem of bounding the posterior distribution of discrete probabilistic programs with unbounded support, loops, and conditioning. Loops pose the main difficulty in this setting: even if exact Bayesian inference is possible,…

We establish concentration inequalities in the class of ultra log-concave distributions. In particular, we show that ultra log-concave distributions satisfy Poisson concentration bounds. As an application, we derive concentration bounds for…

Sampling from Gibbs distributions and computing their log-partition function are fundamental tasks in statistics, machine learning, and statistical physics. While efficient algorithms are known for log-concave densities, the worst-case…

Recently a majorization method for optimizing partition functions of log-linear models was proposed alongside a novel quadratic variational upper-bound. In the batch setting, it outperformed state-of-the-art first- and second-order…

The study of convex functions - in particular, of their optimization (really minimization) is one of the most important fields of applied mathematics. Convexity seems to be one of those incredibly well-chosen hypotheses which is just…

In this article we show the rough outline of a computer algorithm to generate lower bounds on the exponential function of (in principle) arbitrary precision. We implemented this to generate all necessary analytic terms for the Boltzmann…

This paper investigates the a-posteriori analysis of Branch-and-Bound~(BB) trees to extract structural information about the feasible region of mixed-binary linear programs. We introduce three novel outer approximations of the feasible…

We derive lower bounds on the black-box oracle complexity of large-scale smooth convex minimization problems, with emphasis on minimizing smooth (with Holder continuous, with a given exponent and constant, gradient) convex functions over…

We establish new hardness results for decision tree optimization problems, adding to a line of work that dates back to Hyafil and Rivest in 1976. We prove, under randomized ETH, superpolynomial lower bounds for two basic problems: given an…

We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labeled by integers representing their position in the target space, with the SOS constraint that…

Consider a convex function that is invariant under an group of transformations. If it has a minimizer, does it also have an invariant minimizer? Variants of this problem appear in nonparametric statistics and in a number of adjacent fields.…