Related papers: Asymptotic Bayes-optimality under sparsity of some…
In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does…
Stepwise multiple testing procedures have attracted several statisticians for decades and are also quite popular with statistics users because of their technical simplicity. The Bonferroni procedure has been one of the earliest and most…
Selective classification is a powerful tool for automated decision-making in high-risk scenarios, allowing classifiers to act only when confident and abstain when uncertainty is high. Given a target accuracy, our goal is to minimize…
We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often…
We introduce a model for neural scaling laws under sparse activations. In the model, test loss is often dominated by rare coordinates that are never observed in the training input. This mechanism induces a novel bottleneck absent from dense…
Higher criticism is a large-scale testing procedure that can attain the optimal detection boundary for sparse and faint signals. However, there has been a lack of knowledge in most existing works about its asymptotic distribution for more…
Recently, it has been shown that incoherence is an unrealistic assumption for compressed sensing when applied to many inverse problems. Instead, the key property that permits efficient recovery in such problems is so-called local…
Bayesian optimization (BO) is a powerful paradigm for efficient optimization of black-box objective functions. High-dimensional BO presents a particular challenge, in part because the curse of dimensionality makes it difficult to define --…
Optimizing objectives under constraints, where both the objectives and constraints are black box functions, is a common scenario in real-world applications such as scientific experimental design, design of medical therapies, and industrial…
The aim of this paper is to discuss both higher-order asymptotic expansions and skewed approximations for the Bayesian Discrepancy Measure for testing precise statistical hypotheses. In particular, we derive results on third-order…
A Bayesian non-parametric framework for studying time-to-event data is proposed, where the prior distribution is allowed to depend on an additional random source, and may update with the sample size. Such scenarios are natural, for…
We consider the problem of binary classification with abstention in the relatively less studied \emph{bounded-rate} setting. We begin by obtaining a characterization of the Bayes optimal classifier for an arbitrary input-label distribution…
We revisit the asymptotic bias analysis of the distributed Pareto optimization algorithm developed based on the diffusion strategies. We propose an alternative way to analyze the asymptotic bias of this algorithm at small step-sizes and…
Consider the problem on sequential change-point detection on multiple data streams. We provide the asymptotic lower bounds of the detection delays at all levels of change-point sparsity and we derive a smaller asymptotic lower bound of the…
Bayesian model selection provides a formal method of determining the level of support for new parameters in a model. However, if there is not a specific enough underlying physical motivation for the new parameters it can be hard to assign…
This paper presents a Bayesian framework for assessing the adequacy of a model without the necessity of explicitly enumerating a specific alternate model. A test statistic is developed for tracking the performance of the model across…
Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…
We consider the problem of estimating the proportion $\theta$ of true null hypotheses in a multiple testing context. The setup is classically modeled through a semiparametric mixture with two components: a uniform distribution on interval…
In this paper we construct optimal designs for frequentist model averaging estimation. We derive the asymptotic distribution of the model averaging estimate with fixed weights in the case where the competing models are non-nested and none…
A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from…