Related papers: Bayesian Multiple Testing Under Sparsity for Polyn…
Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…
In this work we consider a problem of multi-label classification, where each instance is associated with some binary vector. Our focus is to find a classifier which minimizes false negative discoveries under constraints. Depending on the…
We consider exact asymptotics of the minimax risk for global testing against sparse alternatives in the context of high dimensional linear regression. Our results characterize the leading order behavior of this minimax risk in several…
It is frequently of interest to jointly analyze multiple sequences of multiple tests in order to identify simultaneous signals, defined as features tested in multiple studies whose test statistics are non-null in each. In many problems,…
In stochastic bandit problems, a Bayesian policy called Thompson sampling (TS) has recently attracted much attention for its excellent empirical performance. However, the theoretical analysis of this policy is difficult and its asymptotic…
Multiple hypothesis testing is a central topic in statistics, but despite abundant work on the false discovery rate (FDR) and the corresponding Type-II error concept known as the false non-discovery rate (FNR), a fine-grained understanding…
Frequentist-style large-sample properties of Bayesian posterior distributions, such as consistency and convergence rates, are important considerations in nonparametric problems. In this paper we give an analysis of Bayesian asymptotics…
In a multiple testing framework, we propose a method that identifies the interval with the highest estimated false discovery rate of P-values and rejects the corresponding null hypotheses. Unlike the Benjamini-Hochberg method, which does…
An important limitation of standard multiple testing procedures is that the null distribution should be known. Here, we consider a null distribution-free approach for multiple testing in the following semi-supervised setting: the user does…
In this paper, we study the learning rate of generalized Bayes estimators in a general setting where the hypothesis class can be uncountable and have an irregular shape, the loss function can have heavy tails, and the optimal hypothesis may…
This work investigates multiple testing by considering minimax separation rates in the sparse sequence model, when the testing risk is measured as the sum FDR+FNR (False Discovery Rate plus False Negative Rate). First using the popular…
The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds on tail…
In high dimensional variable selection problems, statisticians often seek to design multiple testing procedures that control the False Discovery Rate (FDR), while concurrently identifying a greater number of relevant variables. Model-X…
A variety of estimators for the parameters of the Generalized Pareto distribution, the approximating distribution for excesses over a high threshold, have been proposed, always assuming the underlying data to be independent. We recently…
This paper explores a connection between empirical Bayes posterior distributions and false discovery rate (FDR) control. In the Gaussian sequence model, this work shows that empirical Bayes-calibrated spike and slab posterior distributions…
Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…
The theory of Bayesian learning incorporates the use of Student-t Processes to model heavy-tailed distributions and datasets with outliers. However, despite Student-t Processes having a similar computational complexity as Gaussian…
We consider the nonparametric regression problem with multiple predictors and an additive error, where the regression function is assumed to be coordinatewise nondecreasing. We propose a Bayesian approach to make an inference on the…
A topological multiple testing scheme for one-dimensional domains is proposed where, rather than testing every spatial or temporal location for the presence of a signal, tests are performed only at the local maxima of the smoothed observed…
Many methods have been developed to estimate the set of relevant variables in a sparse linear model Y= XB+e where the dimension p of B can be much higher than the length n of Y. Here we propose two new methods based on multiple hypotheses…