相关论文: Vector quantile regression and optimal transport, …

The phenomenon of entropy concentration provides strong support for the maximum entropy method, MaxEnt, for inferring a probability vector from information in the form of constraints. Here we extend this phenomenon, in a discrete setting,…

Quantile regression is studied in combination with a penalty which promotes structured (or group) sparsity. A mixed $\ell_{1,\infty}$-norm on the parameter vector is used to impose structured sparsity on the traditional quantile regression…

Disentangled representations, where the higher level data generative factors are reflected in disjoint latent dimensions, offer several benefits such as ease of deriving invariant representations, transferability to other tasks,…

Shared mobility services require accurate demand models for effective service planning. On the one hand, modeling the full probability distribution of demand is advantageous because the entire uncertainty structure preserves valuable…

Optimal transport has emerged as a fundamental methodology with applications spanning multiple research areas in recent years. However, the convergence rate of the empirical estimator to its population counterpart suffers from the curse of…

In this paper we consider an optimization problem for Ces\`aro means of bivariate functions. We apply methods from uniform distribution theory, calculus of variations and ideas from the theory of optimal transport.

We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…

We build a sharp approximation of the whole distribution of the sum of iid heavy-tailed random vectors, combining mean and extreme behaviors. It extends the so-called 'normex' approach from a univariate to a multivariate framework. We…

Randomized experiments have become important tools in empirical research. In a completely randomized treatment-control experiment, the simple difference in means of the outcome is unbiased for the average treatment effect, and covariate…

In this paper, we present a unified analysis of methods for such a wide class of problems as variational inequalities, which includes minimization problems and saddle point problems. We develop our analysis on the modified Extra-Gradient…

Variational inference is increasingly being addressed with stochastic optimization. In this setting, the gradient's variance plays a crucial role in the optimization procedure, since high variance gradients lead to poor convergence. A…

We show that the estimating equations for quantile regression can be solved using a simple EM algorithm in which the M-step is computed via weighted least squares, with weights computed at the E-step as the expectation of independent…

Flexibly modeling how an entire density changes with covariates is an important but challenging generalization of mean and quantile regression. While existing methods for density regression primarily consist of covariate-dependent discrete…

In this article, we consider a non-parametric Bayesian approach to multivariate quantile regression. The collection of related conditional distributions of a response vector Y given a univariate covariate X is modeled using a Dependent…

The Vehicle Routing Problem (VRP) is an example of a combinatorial optimization problem that has attracted academic attention due to its potential use in various contexts. VRP aims to arrange vehicle deliveries to several sites in the most…

We present and analyze an algorithm designed for addressing vector-valued regression problems involving possibly infinite-dimensional input and output spaces. The algorithm is a randomized adaptation of reduced rank regression, a technique…

In this article we study a variational problem providing a way to extend for all times minimizing geodesics connecting two given probability measures, in the Wasserstein space. This is simply obtained by allowing for negative coefficients…

We propose a novel method for reducing the number of variables in quadratic unconstrained binary optimization problems, using a quantum annealer (or any sampler) to fix the value of a large portion of the variables to values that have a…

We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…

We consider vector-quantized (VQ) transmission of compressed sensing (CS) measurements over noisy channels. Adopting mean-square error (MSE) criterion to measure the distortion between a sparse vector and its reconstruction, we derive…