Related papers: Learning discrete distributions with infinite supp…
The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…
We present a distribution optimization framework that significantly improves confidence bounds for various risk measures compared to previous methods. Our framework encompasses popular risk measures such as the entropic risk measure,…
Established approaches to obtain generalization bounds in data-driven optimization and machine learning mostly build on solutions from empirical risk minimization (ERM), which depend crucially on the functional complexity of the hypothesis…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a {\em stochastic maximal inequality} derived by using the formula for…
Causal inference from observational data provides strong evidence for the best action in decision-making without performing expensive randomized trials. The effect of an action is usually not identifiable under unobserved confounding, even…
The basic question of delineating those statistical problems that are solvable without making any assumptions on the underlying data distribution has long animated statistics and learning theory. This paper characterizes when a convex…
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 control of constrained linear systems with only partial statistical information about the uncertainty affecting the system dynamics and the sensor measurements. Specifically, given a finite collection of disturbance realizations…
We study the risk performance of distributed learning for the regularization empirical risk minimization with fast convergence rate, substantially improving the error analysis of the existing divide-and-conquer based distributed learning.…
Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…
We provide sample complexity upper bounds for agnostically learning multivariate Gaussians under the constraint of approximate differential privacy. These are the first finite sample upper bounds for general Gaussians which do not impose…
The paper deals with the problem of nonparametric estimating the $L_p$--norm, $p\in (1,\infty)$, of a probability density on $R^d$, $d\geq 1$ from independent observations. The unknown density %to be estimated is assumed to belong to a ball…
This paper formalizes a latent variable inference problem we call {\em supervised pattern discovery}, the goal of which is to find sets of observations that belong to a single ``pattern.'' We discuss two versions of the problem and prove…
The generalization ability of minimizers of the empirical risk in the context of binary classification has been investigated under a wide variety of complexity assumptions for the collection of classifiers over which optimization is…
This work studies the learning ability of consensus and diffusion distributed learners from continuous streams of data arising from different but related statistical distributions. Four distinctive features for diffusion learners are…
We consider the problem of distribution-free predictive inference, with the goal of producing predictive coverage guarantees that hold conditionally rather than marginally. Existing methods such as conformal prediction offer marginal…
We consider the general branching random walk under minimal assumptions, which in particular guarantee that the empirical particle distribution admits an almost sure central limit theorem. For such a process, we study the large time decay…
Non-parametric estimation of a convex discrete distribution may be of interest in several applications, such as the estimation of species abundance distribution in ecology. In this paper we study the least squares estimator of a discrete…
In this work, we develop a numerical method to study the error estimates of the $\alpha$-stable central limit theorem under sublinear expectation with $\alpha \in(0,2)$, whose limit distribution can be characterized by a fully nonlinear…
The continuous extension of a discrete random variable is amongst the computational methods used for estimation of multivariate normal copula-based models with discrete margins. Its advantage is that the likelihood can be derived…