Related papers: Variable selection, monotone likelihood ratio and …
We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. Focusing on a stochastic query model that provides noisy evaluations of the operator, we analyze a variance-reduced stochastic…
We investigate the performance of the scan (maximum likelihood ratio statistic) and of the average likelihood ratio statistic in the problem of detecting a deterministic signal with unknown spatial extent in the prototypical univariate…
We consider the problem of recovery of an unknown multivariate signal $f$ observed in a $d$-dimensional Gaussian white noise model of intensity $\varepsilon$. We assume that $f$ belongs to a class of smooth functions ${\cal F}^d\subset…
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…
Estimating the matrix of connections probabilities is one of the key questions when studying sparse networks. In this work, we consider networks generated under the sparse graphon model and the in-homogeneous random graph model with missing…
In this note, we introduce a general version of the well-known elliptical potential lemma that is a widely used technique in the analysis of algorithms in sequential learning and decision-making problems. We consider a stochastic linear…
We consider a variable selection problem for the prediction of binary outcomes. We study the best subset selection procedure by which the covariates are chosen by maximizing Manski (1975, 1985)'s maximum score objective function subject to…
In this article we study the asymptotic predictive optimality of a model selection criterion based on the cross-validatory predictive density, already available in the literature. For a dependent variable and associated explanatory…
Consider the Gaussian vector model with mean value {\theta}. We study the twin problems of estimating the number |{\theta}|_0 of non-zero components of {\theta} and testing whether |{\theta}|_0 is smaller than some value. For testing, we…
Many practical applications such as gene expression analysis, multi-task learning, image recognition, signal processing, and medical data analysis pursue a sparse solution for the feature selection purpose and particularly favor the…
For the important classical problem of inference on a sparse high-dimensional normal mean vector, we propose a novel empirical Bayes model that admits a posterior distribution with desirable properties under mild conditions. In particular,…
We consider the problem of estimating the predictive density of future observations from a non-parametric regression model. The density estimators are evaluated under Kullback--Leibler divergence and our focus is on establishing the exact…
We consider the high-dimensional discriminant analysis problem. For this problem, different methods have been proposed and justified by establishing exact convergence rates for the classification risk, as well as the l2 convergence results…
We derive asymptotically optimal statistical decision rules for discrete choice problems when payoffs depend on a partially-identified parameter $\theta$ and the decision maker can use a point-identified parameter $\mu$ to deduce…
Let $(Y,X_1,...,X_m)$ be a random vector. It is desired to predict $Y$ based on $(X_1,...,X_m)$. Examples of prediction methods are regression, classification using logistic regression or separating hyperplanes, and so on. We consider the…
There has been an intense development on the estimation of a sparse regression coefficient vector in statistics, machine learning and related fields. In this paper, we focus on the Bayesian approach to this problem, where sparsity is…
Modern biomedical studies frequently collect complex, high-dimensional physiological signals using wearables and sensors along with time-to-event outcomes, making efficient variable selection methods crucial for interpretation and improving…
We introduce a very general method for sparse and large-scale variable selection. The large-scale regression settings is such that both the number of parameters and the number of samples are extremely large. The proposed method is based on…
We consider a Bayesian approach to model selection in Gaussian linear regression, where the number of predictors might be much larger than the number of observations. From a frequentist view, the proposed procedure results in the penalized…
Knot-based, sparse Gaussian processes have enjoyed considerable success as scalable approximations to full Gaussian processes. Problems can occur, however, when knot selection is done by optimizing the marginal likelihood. For example, the…