Related papers: The Neyman-Pearson lemma for convex expectations
The deployment of safe and trustworthy machine learning systems, and particularly complex black box neural networks, in real-world applications requires reliable and certified guarantees on their performance. The conformal prediction…
We consider the problem of Neyman-Pearson classification which models unbalanced classification settings where error w.r.t. a distribution $\mu_1$ is to be minimized subject to low error w.r.t. a different distribution $\mu_0$. Given a…
We propose a new PAC-Bayesian bound and a way of constructing a hypothesis space, so that the bound is convex in the posterior distribution and also convex in a trade-off parameter between empirical performance of the posterior distribution…
We consider best approximation problems in a nonlinear subset $\mathcal{M}$ of a Banach space of functions $(\mathcal{V},\|\bullet\|)$. The norm is assumed to be a generalization of the $L^2$-norm for which only a weighted Monte Carlo…
We study the regret of optimal strategies for online convex optimization games. Using von Neumann's minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical…
In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm…
This paper considers the design of a minimax test for two hypotheses where the actual probability densities of the observations are located in neighborhoods obtained by placing a bound on the relative entropy between actual and nominal…
We try to find an optimal quantum measurement for generalized quantum state discrimination problems, which include the problem of finding an optimal measurement maximizing the average correct probability with and without a fixed rate of…
In this paper, we consider a functional linear regression model, where both the covariate and the response variable are functional random variables. We address the problem of optimal nonparametric estimation of the conditional expectation…
We consider the problem of choosing a portfolio that maximizes the cumulative prospect theory (CPT) utility on an empirical distribution of asset returns. We show that while CPT utility is not a concave function of the portfolio weights, it…
Given observations from a circular random variable contaminated by an additive measurement error, we consider the problem of minimax optimal goodness-of-fit testing in a non-asymptotic framework. We propose direct and indirect testing…
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…
The Wallace--Freeman estimator is a classical invariant point estimator whose large-sample properties have not been fully developed in a modern asymptotic framework. We show that the estimator can be formulated as a penalised M-estimator…
The aim of this paper is to present an original approach that takes advantage from the geometric features of strictly convex functions to tackle the problem of finding the minimum from another perspective. The general idea is that near the…
Recently, based on the idea of randomizing space theory, random convex analysis has been being developed in order to deal with the corresponding problems in random environments such as analysis of conditional convex risk measures and the…
Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…
We study local complexity measures for stochastic convex optimization problems, providing a local minimax theory analogous to that of H\'{a}jek and Le Cam for classical statistical problems. We give complementary optimality results,…
Several variations of the classical Kalman-Yakubovich-Popov Lemma, as well the associated minimax theorem are presented.
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…
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…