Related papers: Sharp Deviations Bounds for Dirichlet Weighted Sum…

We study the multi-armed bandit problem where the rewards are realizations of general non-stationary stochastic processes, a setting that generalizes many existing lines of work and analyses. In particular, we present a theoretical analysis…

We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.'s sequence, we provide approximations and error bounds for the probability distribution of the three dimensional scan…

In the Bayes paradigm and for a given loss function, we propose the construction of a new type of posterior distributions, that extends the classical Bayes one, for estimating the law of an $n$-sample. The loss functions we have in mind are…

The martingale posterior framework is a generalization of Bayesian inference where one elicits a sequence of one-step ahead predictive densities instead of the likelihood and prior. Posterior sampling then involves the imputation of unseen…

We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution.…

We use the lens of weak signal asymptotics to study a class of sequentially randomized experiments, including those that arise in solving multi-armed bandit problems. In an experiment with $n$ time steps, we let the mean reward gaps between…

This paper studies the asymptotic behavior of several central objects in Dunkl theory as the dimension of the underlying space grows large. Our starting point is the observation that a recent result from the random matrix theory literature…

This paper investigates the asymptotic behavior of the soft-margin and hard-margin support vector machine (SVM) classifiers for simultaneously high-dimensional and numerous data (large $n$ and large $p$ with $n/p\to\delta$) drawn from a…

Bayesian neural networks (BNNs) can account for both aleatoric and epistemic uncertainty. However, in BNNs the priors are often specified over the weights which rarely reflects true prior knowledge in large and complex neural network…

We investigate the asymptotic normality of the posterior distribution in the discrete setting, when model dimension increases with sample size. We consider a probability mass function $\theta_0$ on $\mathbbm{N}\setminus \{0\}$ and a…

We develop stochastic variational inference, a scalable algorithm for approximating posterior distributions. We develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models,…

Many enumeration problems in combinatorics, including such fundamental questions as the number of regular graphs, can be expressed as high-dimensional complex integrals. Motivated by the need for a systematic study of the asymptotic…

Restless bandit problems assume time-varying reward distributions of the arms, which adds flexibility to the model but makes the analysis more challenging. We study learning algorithms over the unknown reward distributions and prove a…

We present new and improved non-asymptotic deviation bounds for Dirichlet processes (DPs), formulated using the Kullback-Leibler (KL) divergence, which is known for its optimal characterization of the asymptotic behavior of DPs. Our method…

We propose a consistent estimator of sharp bounds on the variance of the difference-in-means estimator in completely randomized experiments. Generalizing Robins [Stat. Med. 7 (1988) 773-785], our results resolve a well-known identification…

In this paper, we address the issue on non-asymptotic convergence bounds of Euler-type schemes associated with non-dissipative SDEs. On the one hand, for non-degenerate SDEs with super-linear drifts, we propose a novel modified Euler scheme…

Distribution shift between the training domain and the test domain poses a key challenge for modern machine learning. An extensively studied instance is the \emph{covariate shift}, where the marginal distribution of covariates differs…

Ratios of integrals can be bounded in terms of ratios of integrands under certain monotonicity conditions. This result, related with L'H\^{o}pital's monotone rule, can be used to obtain sharp bounds for cumulative distribution functions. We…

Modern regression analyses are often undermined by covariate measurement error, misspecification of the regression model, and misspecification of the measurement error distribution. We present, to the best of our knowledge, the first…

A method is developed for calculating effective sums of divergent series. This approach is a variant of the self-similar approximation theory. The novelty here is in using an algebraic transformation with a power providing the maximal…