Related papers: Estimating divergence functionals and the likeliho…
We study the minimax estimation of $\alpha$-divergences between discrete distributions for integer $\alpha\ge 1$, which include the Kullback--Leibler divergence and the $\chi^2$-divergences as special examples. Dropping the usual…
In information theory, some optimization problems result in convex optimization problems on strictly convex functionals of probability densities. In this note, we study these problems and show conditions of minimizers and the uniqueness of…
Estimating location is a central problem in functional data analysis, yet most current estimation procedures either unrealistically assume completely observed trajectories or lack robustness with respect to the many kinds of anomalies one…
We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that…
The estimation of an f-divergence between two probability distributions based on samples is a fundamental problem in statistics and machine learning. Most works study this problem under very weak assumptions, in which case it is provably…
We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set $\mathcal{G}$ up to the smallest possible additive term, called the convergence rate. When the…
We study estimation of a multivariate function $f:{\bf R}^d \to {\bf R}$ when the observations are available from function $Af$, where $A$ is a known linear operator. Both the Gaussian white noise model and density estimation are studied.…
We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable confidence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation…
We consider the problem of designing minimax estimators for estimating the parameters of a probability distribution. Unlike classical approaches such as the MLE and minimum distance estimators, we consider an algorithmic approach for…
M-estimation, aka empirical risk minimization, is at the heart of statistics and machine learning: Classification, regression, location estimation, etc. Asymptotic theory is well understood when the loss satisfies some smoothness…
We consider a class of hypothesis testing problems where the null hypothesis postulates $M$ distributions for the observed data, and there is only one possible distribution under the alternative. We show that one can use a stochastic mirror…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…
We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator…
Most high-dimensional estimation and prediction methods propose to minimize a cost function (empirical risk) that is written as a sum of losses associated to each data point. In this paper we focus on the case of non-convex losses, which is…
We develop improved rearrangement algorithms to find the dependence structure that minimizes a convex function of the sum of dependent variables with given margins. We propose a new multivariate dependence measure, which can assess the…
For nonparametric regression with one-sided errors and a boundary curve model for Poisson point processes we consider the problem of efficient estimation for linear functionals. The minimax optimal rate is obtained by an unbiased estimation…
In this paper we investigate the performance of a variety of estimation techniques for the scale and shape parameter of the Lomax distribution. These methods include traditional methods such as the maximum likelihood estimator and the…
We present a minimax optimal solution to the problem of estimating a compact, convex set from finitely many noisy measurements of its support function. The solution is based on appropriate regularizations of the least squares estimator.…