Related papers: Path Planning with Divergence-Based Distance Funct…
In this paper, we revisit the old problem of compact finite difference approximations of the homogeneous Dirichlet problem in dimension 1. We design a large and natural set of schemes of arbitrary high order, and we equip this set with an…
Divergences are quantities that measure discrepancy between two probability distributions and play an important role in various fields such as statistics and machine learning. Divergences are non-negative and are equal to zero if and only…
We propose a family of recursive cutting-plane algorithms to solve feasibility problems with constrained memory, which can also be used for first-order convex optimization. Precisely, in order to find a point within a ball of radius…
Density-based directed distances -- particularly known as divergences -- between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine…
The recent years have witnessed advances in parallel algorithms for large scale optimization problems. Notwithstanding demonstrated success, existing algorithms that parallelize over features are usually limited by divergence issues under…
In this work, we propose efficient and accurate numerical algorithms based on Difference Potentials Method for numerical solution of chemotaxis systems and related models in 3D. The developed algorithms handle 3D irregular geometry with the…
This paper provides a block coordinate descent algorithm to solve unconstrained optimization problems. In our algorithm, computation of function values or gradients is not required. Instead, pairwise comparison of function values is used.…
Computing the reachability probability in infinite state probabilistic models has been the topic of numerous works. Here we introduce a new property called \emph{divergence} that when satisfied allows to compute reachability probabilities…
While much progress has been achieved over the last decades in neuro-inspired machine learning, there are still fundamental theoretical problems in gradient-based learning using combinations of neurons. These problems, such as saddle points…
A function approximation method is developed that aims to approximate a function in a small neighborhood of a state that travels within a compact set. The development is based on the theory of universal reproducing kernel Hilbert spaces…
We present a unified technique for sequential estimation of convex divergences between distributions, including integral probability metrics like the kernel maximum mean discrepancy, $\varphi$-divergences like the Kullback-Leibler…
The convergence theory for the gradient sampling algorithm is extended to directionally Lipschitz functions. Although directionally Lipschitz functions are not necessarily locally Lipschitz, they are almost everywhere differentiable and…
We design a Quasi-Polynomial time deterministic approximation algorithm for computing the integral of a multi-dimensional separable function, supported by some underlying hyper-graph structure, appropriately defined. Equivalently, our…
Given a bounded domain, we deal with the problem of estimating the distance function from the internal points of the domain to the boundary of the domain. Convolutional and differential distance estimation schemes are considered and, for…
When planning motions in a configuration space that has underlying symmetries (e.g. when manipulating one or multiple symmetric objects), the ideal planning algorithm should take advantage of those symmetries to produce shorter…
This paper presents a method for the approximation of harmonic potentials that combines downward continuation of globally available data on a sphere $\Omega_R$ of radius $R$ (e.g., a satellite's orbit) with locally available data on a…
The Distance Geometry Problem (DGP) seeks to find positions for a set of points in geometric space when some distances between pairs of these points are known. The so-called discretization assumptions allow to discretize the search space of…
This paper proposes the divergence triangle as a framework for joint training of generator model, energy-based model and inference model. The divergence triangle is a compact and symmetric (anti-symmetric) objective function that seamlessly…
This book deals with functions allowing to express the dissimilarity (discrepancy) between two data fields or ''divergence functions'' with the aim of applications to linear inverse problems. Most of the divergences found in the litterature…
We present a novel approach to differential cost analysis that, given a program revision, attempts to statically bound the difference in resource usage, or cost, between the two program versions. Differential cost analysis is particularly…