Related papers: Score Operator Newton transport
In machine learning and computer graphics, a fundamental task is the approximation of a probability density function through a well-dispersed collection of samples. Providing a formal metric for measuring the distance between probability…
Newton's method is a fundamental technique in optimization with quadratic convergence within a neighborhood around the optimum. However reaching this neighborhood is often slow and dominates the computational costs. We exploit two…
In the field of inverse estimation for systems modeled by partial differential equations (PDEs), challenges arise when estimating high- (or even infinite-) dimensional parameters. Typically, the ill-posed nature of such problems…
We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods…
This paper proposes a novel diffusion-based posterior sampling method within a plug-and-play (PnP) framework. Our approach constructs a probability transport from an easy-to-sample terminal distribution to the target posterior, using a…
We propose a deterministic sampling framework using Score-Based Transport Modeling for sampling an unnormalized target density $\pi$ given only its score $\nabla \log \pi$. Our method approximates the Wasserstein gradient flow on…
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…
With the widespread application of optimal transport (OT), its calculation becomes essential, and various algorithms have emerged. However, the existing methods either have low efficiency or cannot represent discontinuous maps. A novel…
In this work, we propose a novel implementation of Newton's method for solving semi-discrete optimal transport (OT) problems for cost functions which are a positive combination of $p$-norms, $1<p<\infty$. It is well understood that the…
We propose an efficient transfer Bayesian optimization method, which finds the maximum of an expensive-to-evaluate black-box function by using data on related optimization tasks. Our method uses auxiliary information that represents the…
Score based approaches to sampling have shown much success as a generative algorithm to produce new samples from a target density given a pool of initial samples. In this work, we consider if we have no initial samples from the target…
We propose a Bayesian inference approach for static Origin-Destination (OD)-estimation in large-scale networked transit systems. The approach finds posterior distribution estimates of the OD-coefficients, which describe the relative…
We provide a method to solve optimization problem when objective function is a complex stochastic simulator of an urban transportation system. To reach this goal, a Bayesian optimization framework is introduced. We show how the choice of…
Self consistent transfer operators arise naturally in the study of mean-field coupled dynamical systems and are closely related to kinetic PDEs such as the Vlasov equation. Despite substantial progress on existence and uniqueness of fixed…
An adaptive, adversarial methodology is developed for the optimal transport problem between two distributions $\mu$ and $\nu$, known only through a finite set of independent samples $(x_i)_{i=1..N}$ and $(y_j)_{j=1..M}$. The methodology…
We develop an iterative framework for Bayesian inference problems where the posterior distribution may involve computationally intensive models, intractable gradients, significant posterior concentration, and pronounced non-Gaussianity. Our…
This paper investigates how an autonomous agent can transmit information through its motion in an adversarial setting. We consider scenarios where an agent must reach its goal while deceiving an intelligent observer about its destination.…
Motivated by economic dispatch and linearly-constrained resource allocation problems, this paper proposes a class of novel Distributed-Approx Newton algorithms that approximate the standard Newton optimization method. We first develop the…
We introduce and prove convergence of a damped Newton algorithm to approximate solutions of the semi-discrete optimal transport problem with storage fees, corresponding to a problem with hard capacity constraints. This is a variant of the…
This paper presents a novel distributed algorithm for tracking a maneuvering target using bearing or direction of arrival measurements collected by a networked sensor array. The proposed approach is built on the dynamic average-consensus…