Related papers: Asymptotically Optimal Adversarial Strategies for …
We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…
An alternative method of detection-loophole-free Bell test is proposed using local hidden variable (LHV) models with optimal detection efficiencies. A framework for constructing such optimal LHV models is presented. Optimal LHV models for…
We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…
A classical problem in digital communications is to evaluate the symbol error probability (SEP) and bit error probability (BEP) of a multidimensional constellation over an additive white Gaussian noise channel. In this paper, we revisit…
This paper studies performative risk minimization, a formulation of stochastic optimization under decision-dependent distributions. We consider the general case where the performative risk can be non-convex, for which we develop efficient…
The paper offers a novel unified approach to studying the accuracy of parameter estimation by the quasi likelihood method. Important features of the approach are: (1) The underlying model {is not assumed to be parametric}. (2) No conditions…
We develop a semidefinite programming method for the optimization of quantum networks, including both causal networks and networks with indefinite causal structure. Our method applies to a broad class of performance measures, defined…
Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…
The main purpose of this paper is to provide an asymptotically optimal test. The proposed statistic is of Neyman-Pearson-type when the parameters are estimated with a particular kind of estimators. It is shown that the proposed estimators…
We study a class of iterated empirical risk minimization (ERM) procedures in which two successive ERMs are performed on the same dataset, and the predictions of the first estimator enter as an argument in the loss function of the second.…
Bell experiment in the network gives rise to a form of quantum nonlocality which is conceptually different from traditional multipartite Bell nonlocality. Conventional multipartite Bell experiment features a single source that distributes…
We deduce the non-asymptotical bilateral estimates for moment inequalities for sums of non-negative independent random variables, based on the correspondent estimates for the so-called Bell functions and the Poisson distribution.
The paper deals with asymptotic properties of the adaptive procedure proposed in the author paper (2007) for estimation of unknown nonparametric regression. We prove that this procedure is asymptotically efficient for a quadratic risk. It…
This paper addresses the question whether model knowledge can guide a defender to appropriate decisions, or not, when an attacker intrudes into control systems. The model-based defense scheme considered in this study, namely Bayesian…
A key objective in conducting a Bell test is to quantify the statistical evidence against a local-hidden variable model (LHVM) given that we can collect only a finite number of trials in any experiment. The notion of statistical evidence is…
The statistical finite element method (StatFEM) is an emerging probabilistic method that allows observations of a physical system to be synthesised with the numerical solution of a PDE intended to describe it in a coherent statistical…
Motivated by the recent success of reinforcement learning in games such as Go and Dota2, we formulate Bell non-local games as a reinforcement learning problem. Such a formulation helps us to explore Bell non-locality in a range of…
Bell inequalities reveal the fundamentally nonlocal character of quantum mechanics. In this regard, one of the interesting problems is to explore all possible Bell inequalities that demonstrate a gap between local and nonlocal quantum…
In this work, we revisit the one- and two-sample testing problems: binary hypothesis testing in which one or both distributions are unknown. For the one-sample test, we provide a more streamlined proof of the asymptotic optimality of…
Machine Learning models have been shown to be vulnerable to adversarial examples, ie. the manipulation of data by a attacker to defeat a defender's classifier at test time. We present a novel probabilistic definition of adversarial examples…