相关论文: Discussion on the paper: Hypotheses testing by con…
We discuss an "operational" approach to testing convex composite hypotheses when the underlying distributions are heavy-tailed. It relies upon Euclidean separation of convex sets and can be seen as an extension of the approach to testing by…
We propose a new approach to sequential testing which is an adaptive (on-line) extension of the (off-line) framework developed in [10]. It relies upon testing of pairs of hypotheses in the case where each hypothesis states that the vector…
We discuss a general approach to handling "multiple hypotheses" testing in the case when a particular hypothesis states that the vector of parameters identifying the distribution of observations belongs to a convex compact set associated…
Discussion of "Latent variable graphical model selection via convex optimization" by Venkat Chandrasekaran, Pablo A. Parrilo and Alan S. Willsky [arXiv:1008.1290].
Discussion of "Latent variable graphical model selection via convex optimization" by Venkat Chandrasekaran, Pablo A. Parrilo and Alan S. Willsky [arXiv:1008.1290].
Discussion of "Latent variable graphical model selection via convex optimization" by Venkat Chandrasekaran, Pablo A. Parrilo and Alan S. Willsky [arXiv:1008.1290].
Discussion of "Latent variable graphical model selection via convex optimization" by Venkat Chandrasekaran, Pablo A. Parrilo and Alan S. Willsky [arXiv:1008.1290].
Discussion of "Latent variable graphical model selection via convex optimization" by Venkat Chandrasekaran, Pablo A. Parrilo and Alan S. Willsky [arXiv:1008.1290].
Discussion of "Latent variable graphical model selection via convex optimization" by Venkat Chandrasekaran, Pablo A. Parrilo and Alan S. Willsky [arXiv:1008.1290].
In this paper, we further develop the approach, originating in [GJN], to "computation-friendly" hypothesis testing via Convex Programming. Most of the existing results on hypothesis testing aim to quantify in a closed analytic form…
We study the problem of testing composite hypotheses versus composite alternatives, using a convex duality approach. In contrast to classical results obtained by Krafft and Witting (Z. Wahrsch. Verw. Gebiete 7 (1967) 289--302), where…
In the recent review published in 2019, Malinovsky and Albert conjectured analytical formulae of the optimal sample sizes for the modified Dorfman and Sterret group testing schemes and verified the validity of the formulae numerically…
This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. Starting from the fundamental theory of black-box optimization, the material progresses towards recent advances in structural…
We present a new framework to address the non-convex robust hypothesis testing problem, wherein the goal is to seek the optimal detector that minimizes the maximum of worst-case type-I and type-II risk functions. The distributional…
This paper builds upon our prior formalisation of R^n in ACL2(r) by presenting a set of theorems for reasoning about convex functions. This is a demonstration of the higher-dimensional analytical reasoning possible in our metric space…
In information theory, some optimization problems result in convex optimization problems on strictly convex functionals of probability densities. In this note, we study these problems and show conditions of minimizers and the uniqueness of…
Under study are some vector optimization problems over the space of Minkowski balls, i.e., symmetric convex compact subsets in Euclidean space. A typical problem requires to achieve the best result in the presence of conflicting goals;…
Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…
This paper describes the theory of Minkowski problems for geometric measures in convex geometric analysis. The theory goes back to Minkowski and Aleksandrov and has been developed extensively in recent years. The paper surveys classical and…
Generalized polyhedral convex optimization problems in locally convex Hausdorff topological vector spaces are studied systematically in this paper. We establish solution existence theorems, necessary and sufficient optimality conditions,…