Related papers: Nearly Minimax One-Sided Mixture-Based Sequential …
In this article, we propose a novel Bayesian multiple testing formulation for model and variable selection in inverse setups, judiciously embedding the idea of inverse reference distributions proposed by Bhattacharya (2013) in a mixture…
We consider composite-composite testing problems for the expectation in the Gaussian sequence model where the null hypothesis corresponds to a convex subset $\mathcal{C}$ of $\mathbb{R}^d$. We adopt a minimax point of view and our primary…
The first- and second-order optimum achievable exponents in the simple hypothesis testing problem are investigated. The optimum achievable exponent for type II error probability, under the constraint that the type I error probability is…
In many applications one is interested to detect certain (known) patterns in the mean of a process with smallest delay. Using an asymptotic framework which allows to capture that feature, we study a class of appropriate sequential…
In the binary hypothesis testing problem, it is well known that sequentiality in taking samples eradicates the trade-off between two error exponents, yet implementing the optimal test requires the knowledge of the underlying distributions,…
This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly…
In this paper, both non-mixing and mixing local minima of the entropy are analyzed from the viewpoint of blind source separation (BSS); they correspond respectively to acceptable and spurious solutions of the BSS problem. The contribution…
We consider the minimal distance between orbits of measure preserving dynamical systems. In the spirit of dynamical shrinking target problems we identify distance rates for which almost sure asymptotic closeness properties can be ensured.…
Consider the multiple testing problem of testing k null hypotheses, where the unknown family of distributions is assumed to satisfy a certain monotonicity assumption. Attention is restricted to procedures that control the familywise error…
This paper addresses the qualitative theory of mixed-order positive linear coupled systems with bounded or unbounded delays. First, we introduce a general result on the existence and uniqueness of solutions to mixed-order linear coupled…
We study the minimax estimation of $\alpha$-divergences between discrete distributions for integer $\alpha\ge 1$, which include the Kullback--Leibler divergence and the $\chi^2$-divergences as special examples. Dropping the usual…
We study one-way matching of a pair of datasets with low rank signals. Under a stylized model, we first derive information-theoretic limits of matching under a mismatch proportion loss. We then show that linear assignment with projected…
While the Bayesian decision-theoretic framework offers an elegant solution to the problem of decision making under uncertainty, one question is how to appropriately select the prior distribution. One idea is to employ a worst-case prior.…
In this paper we study the asymptotic properties of Bayesian multiple testing procedures for a large class of Gaussian scale mixture pri- ors. We study two types of multiple testing risks: a Bayesian risk proposed in Bogdan et al. (2011)…
We derive a new asymptotic expansion for the global excess risk of a local-$k$-nearest neighbour classifier, where the choice of $k$ may depend upon the test point. This expansion elucidates conditions under which the dominant contribution…
The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For…
Online evaluation of machine learning models is typically conducted through A/B experiments. Sequential statistical tests are valuable tools for analysing these experiments, as they enable researchers to stop data collection early without…
We consider the problem of simultaneous detection and estimation under a sequential framework. In particular we are interested in sequential tests that distinguish between the null and the alternative hypothesis and every time the decision…
In hypothesis testing, the phenomenon of label noise, in which hypothesis labels are switched at random, contaminates the likelihood functions. In this paper, we develop a new method to determine the decision rule when we do not have…
Most clinical prediction studies are developed from retrospective cohorts and reported as if all patient information were observed at once. In practice, clinicians face a more consequential question: \emph{when is there already enough…