Related papers: The Neyman-Pearson lemma for convex expectations
We propose a universal classifier for binary Neyman-Pearson classification where null distribution is known while only a training sequence is available for the alternative distribution. The proposed classifier interpolates between…
Testing of hypotheses is a well studied topic in mathematical statistics. Recently, this issue has also been addressed in the context of Inverse Problems, where the quantity of interest is not directly accessible but only after the…
Myerson derived a simple and elegant solution to the single-parameter revenue-maximization problem in his seminal work on optimal auction design assuming the usual model of quasi-linear utilities. In this paper, we consider a slight…
Consider the regularized sparse minimization problem, which involves empirical sums of loss functions for $n$ data points (each of dimension $d$) and a nonconvex sparsity penalty. We prove that finding an…
We show that in any complete metric space the probability measures $\mu$ with compact and connected support are the ones having the property that the optimal tranportation distance to any other probability measure $\nu$ living on the…
We propose and study a general method for construction of consistent statistical tests on the basis of possibly indirect, corrupted, or partially available observations. The class of tests devised in the paper contains Neyman's smooth…
The problem of robust hypothesis testing is studied, where under the null and the alternative hypotheses, the data-generating distributions are assumed to be in some uncertainty sets, and the goal is to design a test that performs well…
We consider a critically-loaded multiclass queueing control problem with model uncertainty. The model consists of $I$ types of customers and a single server. At any time instant, a decision-maker (DM) allocates the server's effort to the…
Everybody writes that ROC curves, a very common tool in binary classification problems, should be optimal, and in particular concave, non-decreasing and above the 45-degree line. Everybody uses ROC curves, theoretical and especially…
Detecting hidden convexity is one of the tools to address nonconvex minimization problems. After giving a formal definition of hidden convexity, we introduce the notion of conditional infimum, as it will prove instrumental in detecting…
The Neyman-Pearson strategy for hypothesis testing can be employed for goodness of fit if the alternative hypothesis is selected from data by exploring a rich parametrised family of models, while controlling the impact of statistical…
This work addresses the issue of large covariance matrix estimation in high-dimensional statistical analysis. Recently, improved iterative algorithms with positive-definite guarantee have been developed. However, these algorithms cannot be…
In this paper, we study the minimax rates and provide an implementable convex algorithm for Poisson inverse problems under weak sparsity and physical constraints. In particular we assume the model $y_i \sim \mbox{Poisson}(Ta_i^{\top}f^*)$…
We consider nonconvex constrained optimization problems and propose a new approach to the convergence analysis based on penalty functions. We make use of classical penalty functions in an unconventional way, in that penalty functions only…
We prove the following theorem. Let $\mu$ be a measure on $R^n$ with even continuous density, and let $K,L$ be origin-symmetric convex bodies in $R^n$ so that $\mu(K\cap H)\le \mu(L\cap H)$ for any central hyperplane H. Then $\mu(K)\le…
The Edelman-Jamison problem is to characterize those abstract convex geometries that are representable by a set of points in the plane. We show that some natural modification of the Edelman-Jamison problem is equivalent to the well known…
In the area of sparse recovery, numerous researches hint that non-convex penalties might induce better sparsity than convex ones, but up until now those corresponding non-convex algorithms lack convergence guarantees from the initial…
Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a…
This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…
An emerging line of work has shown that machine-learned predictions are useful to warm-start algorithms for discrete optimization problems, such as bipartite matching. Previous studies have shown time complexity bounds proportional to some…