Related papers: Bernstein-type dimension-free concentration for se…
We study the distribution of regret in stochastic multi-armed bandits and episodic reinforcement learning through a unified framework. We formalize a distributional regret bound as a probabilistic guarantee that holds uniformly over all…
We present dimension-free convergence and discretization error bounds for the unadjusted Hamiltonian Monte Carlo algorithm applied to high-dimensional probability distributions of mean-field type. These bounds require the discretization…
This paper develops techniques to study the number of descents in random permutations via martingales. We relax an assumption in the Berry-Esseen theorem of Bolthausen (1982) to extend the theorem's scope to martingale differences of…
The probability and structure of co-occurrences of extreme values in multivariate data may critically depend on auxiliary information provided by covariates. In this contribution, we develop a flexible generalized additive modeling…
We develop a new tool for data-dependent analysis of the exploration-exploitation trade-off in learning under limited feedback. Our tool is based on two main ingredients. The first ingredient is a new concentration inequality that makes it…
We study the linear stochastic bandit problem, relaxing the standard i.i.d. assumption on the observation noise. As an alternative to this restrictive assumption, we allow the noise terms across rounds to be sub-Gaussian but interdependent,…
We obtain rates of convergence to stationarity in L^1-Wasserstein distance for a d-dimensional reflected Brownian motion (RBM) in the nonnegative orthant that are explicit in the dimension and the system parameters. The results are then…
In this paper, we introduce reduced-bias estimators for the estimation of the tail index of a Pareto-type distribution. This is achieved through the use of a regularised weighted least squares with an exponential regression model for…
Clustered observations are ubiquitous in controlled and observational studies and arise naturally in multi-centre trials or longitudinal surveys. We present a novel model for the analysis of clustered observations where the marginal…
We give improved constants for data dependent and variance sensitive confidence bounds, called empirical Bernstein bounds, and extend these inequalities to hold uniformly over classes of functionswhose growth function is polynomial in the…
We provide optimal lower bounds for two well-known parameter estimation (also known as statistical estimation) tasks in high dimensions with approximate differential privacy. First, we prove that for any $\alpha \le O(1)$, estimating the…
This paper is focused on dimension-free PAC-Bayesian bounds, under weak polynomial moment assumptions, allowing for heavy tailed sample distributions. It covers the estimation of the mean of a vector or a matrix, with applications to least…
This paper investigates the problem of non-stationary linear bandits, where the unknown regression parameter is evolving over time. Existing studies develop various algorithms and show that they enjoy an…
We study contextual bandits with finitely many actions in which the reward of each arm follows a single-index model with an arm-specific index parameter and an unknown nonparametric link function. We consider a regime in which arms…
We consider the eigenvalues of a fixed, non-normal matrix subject to a small additive perturbation. In particular, we consider the case when the fixed matrix is a banded Toeplitz matrix, where the bandwidth is allowed to grow slowly with…
In this paper, we establish novel concentration inequalities for additive functionals of geometrically ergodic Markov chains similar to Rosenthal inequalities for sums of independent random variables. We pay special attention to the…
For highly skewed or fat-tailed distributions, mean or median-based methods often fail to capture the central tendencies in the data. Despite being a viable alternative, estimating the conditional mode given certain covariates (or mode…
Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of…
This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of…
This paper presents new \emph{variance-aware} confidence sets for linear bandits and linear mixture Markov Decision Processes (MDPs). With the new confidence sets, we obtain the follow regret bounds: For linear bandits, we obtain an…