Related papers: Competitive Distribution Estimation
This paper considers the estimation of Shannon entropy for discrete distributions with countably infinite support. While minimax rates for finite-support distributions are established, infinite-support distributions present distinct…
We consider the classical problem of learning, with arbitrary accuracy, the natural parameters of a $k$-parameter truncated \textit{minimal} exponential family from i.i.d. samples in a computationally and statistically efficient manner. We…
We consider statistical methods which invoke a min-max distributionally robust formulation to extract good out-of-sample performance in data-driven optimization and learning problems. Acknowledging the distributional uncertainty in learning…
The quantification of uncertainty is important for the adoption of machine learning, especially to reject out-of-distribution (OOD) data back to human experts for review. Yet progress has been slow, as a balance must be struck between…
We study the problem of online learning with a notion of regret defined with respect to a set of strategies. We develop tools for analyzing the minimax rates and for deriving regret-minimization algorithms in this scenario. While the…
We consider online prediction of a binary sequence with expert advice. For this setting, we devise label-efficient forecasting algorithms, which use a selective sampling scheme that enables collecting much fewer labels than standard…
We consider a setting where a system learns to rank a fixed set of $m$ items. The goal is produce good item rankings for users with diverse interests who interact online with the system for $T$ rounds. We consider a novel top-$1$ feedback…
In a wide range of statistical learning problems such as ranking, clustering or metric learning among others, the risk is accurately estimated by $U$-statistics of degree $d\geq 1$, i.e. functionals of the training data with low variance…
Traditional online algorithms encapsulate decision making under uncertainty, and give ways to hedge against all possible future events, while guaranteeing a nearly optimal solution as compared to an offline optimum. On the other hand,…
We study reinforcement learning with linear function approximation and adversarially changing cost functions, a setup that has mostly been considered under simplifying assumptions such as full information feedback or exploratory…
The $k$-of-$n$ testing problem involves performing $n$ independent tests sequentially, in order to determine whether/not at least $k$ tests pass. The objective is to minimize the expected cost of testing. This is a fundamental and…
We study the stochastic shortest path (SSP) problem in reinforcement learning with linear function approximation, where the transition kernel is represented as a linear mixture of unknown models. We call this class of SSP problems as linear…
The framework of distribution testing is currently ubiquitous in the field of property testing. In this model, the input is a probability distribution accessible via independently drawn samples from an oracle. The testing task is to…
Inspired by real-time ad exchanges for online display advertising, we consider the problem of inferring a buyer's value distribution for a good when the buyer is repeatedly interacting with a seller through a posted-price mechanism. We…
This paper studies the problem of inferring a global preference based on the partial rankings provided by many users over different subsets of items according to the Plackett-Luce model. A question of particular interest is how to optimally…
This letter studies the problem of online multi-step-ahead prediction for unknown linear stochastic systems. Using conditional distribution theory, we derive an optimal parameterization of the prediction policy as a linear function of…
We consider the estimation of two-sample integral functionals, of the type that occur naturally, for example, when the object of interest is a divergence between unknown probability densities. Our first main result is that, in wide…
We study the effectiveness of stochastic side information in deterministic online learning scenarios. We propose a forecaster to predict a deterministic sequence where its performance is evaluated against an expert class. We assume that…
We study the asymptotic error of score-based diffusion model sampling in large-sample scenarios from a non-parametric statistics perspective. We show that a kernel-based score estimator achieves an optimal mean square error of…
We study the problems of offline and online contextual optimization with feedback information, where instead of observing the loss, we observe, after-the-fact, the optimal action an oracle with full knowledge of the objective function would…