Related papers: Sharp Asymptotic Minimaxity for Multiple Testing U…

Statistical dependence between hypotheses poses a significant challenge to the stability of large scale multiple hypotheses testing. Ignoring it often results in an unacceptably large spread in the false positive proportion even though the…

In the spirit of modeling inference for microarrays as multiple testing for sparse mixtures, we present a similar approach to a simplified version of quantitative trait loci (QTL) mapping. Unlike in case of microarrays, where the number of…

In this paper, we consider simultaneous estimation of Poisson parameters in situations where we can use side information in aggregated data. We use standardized squared error and entropy loss functions. Bayesian shrinkage estimators are…

From the sampling of data to the initialisation of parameters, randomness is ubiquitous in modern Machine Learning practice. Understanding the statistical fluctuations engendered by the different sources of randomness in prediction is…

A family of variable stage size multistage tests of simple hypotheses is described, based on efficient multistage sampling procedures. Using a loss function that is a linear combination of sampling costs and error probabilities, these tests…

We study a seemingly unexpected and relatively less understood overfitting aspect of a fundamental tool in sparse linear modeling - best subset selection, which minimizes the residual sum of squares subject to a constraint on the number of…

We study frequentist asymptotic properties of Bayesian procedures for high-dimensional Gaussian sparse regression when unknown nuisance parameters are involved. Nuisance parameters can be finite-, high-, or infinite-dimensional. A mixture…

We provide a means of computing and estimating the asymptotic distributions of statistics based on an outer minimization of an inner maximization. Such test statistics, which arise frequently in moment models, are of special interest in…

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 study the problems of data compression, gambling and prediction of a sequence $x^n=x_1x_2...x_n$ from an alphabet ${\cal X}$, in terms of regret and expected regret (redundancy) with respect to various smooth families of probability…

Given an observation $\mathbf Y \in \mathbb{R}^{d_1\times d_2}$ from the model $\mathbf Y = \mathbf X + \mathbf E$ where $\mathbf X$ is constant and $\mathbf E$ has i.i.d. $N(0,1)$ entries, we consider the problem of detecting a planted…

Traditional machine learning methods usually minimize a simple loss function to learn a predictive model, and then use a complex performance measure to measure the prediction performance. However, minimizing a simple loss function cannot…

Variable selection has received widespread attention over the last decade as we routinely encounter high-throughput datasets in complex biological and environment research. Most Bayesian variable selection methods are restricted to mixture…

This paper proposes a flexible Bayesian approach to multiple imputation using conditional Gaussian mixtures. We introduce novel shrinkage priors for covariate-dependent mixing proportions in the mixture models to automatically select the…

The design of asymptotically minimax robust hypothesis testing is formalized for the Bayesian and Neyman-Pearson tests of Type-I and Type-II. The uncertainty classes based on the KL-divergence, $\alpha$-divergence, symmetrized…

We observe a $N\times M$ matrix $Y_{ij}=s_{ij}+\xi_{ij}$ with $\xi_{ij}\sim {\mathcal {N}}(0,1)$ i.i.d. in $i,j$, and $s_{ij}\in \mathbb {R}$. We test the null hypothesis $s_{ij}=0$ for all $i,j$ against the alternative that there exists…

The effect of measurement errors in discriminant analysis is investigated. Given observations $Z=X+\epsilon$, where $\epsilon$ denotes a random noise, the goal is to predict the density of $X$ among two possible candidates $f$ and $g$. We…

A signal recovery problem is considered, where the same binary testing problem is posed over multiple, independent data streams. The goal is to identify all signals, i.e., streams where the alternative hypothesis is correct, and noises,…

Sparse Bayesian Learning (SBL) is a powerful framework for attaining sparsity in probabilistic models. Herein, we propose a coordinate ascent algorithm for SBL termed Relevance Matching Pursuit (RMP) and show that, as its noise variance…

We construct a classifier which attains the rate of convergence $\log n/n$ under sparsity and margin assumptions. An approach close to the one met in approximation theory for the estimation of function is used to obtain this result. The…