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In this paper we consider the problem of multiple testing when the hypotheses are dependent. In most of the existing literature, either Bayesian or non-Bayesian, the decision rules mainly focus on the validity of the test procedure rather…

Methodology · Statistics 2018-07-10 Noirrit K. Chandra , Sourabh Bhattacharya

The task of binary quantum hypothesis testing is to determine the state of a quantum system via measurements on it, given the side information that it is in one of two possible states, say $\rho$ and $\sigma$. This task is generally studied…

Quantum Physics · Physics 2021-04-21 Robert Salzmann , Nilanjana Datta

The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…

Information Theory · Computer Science 2024-05-30 Valentinian Lungu , Ioannis Kontoyiannis

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…

Information Theory · Computer Science 2014-10-28 Dennis Wei , Kush R. Varshney

We study a distributed hypothesis testing setup where peripheral nodes send quantized data to the fusion center in a memoryless fashion. The \emph{expected} number of bits sent by each node under the null hypothesis is kept limited. We…

Information Theory · Computer Science 2022-06-27 Yunus Inan , Mert Kayaalp , Ali H. Sayed , Emre Telatar

The problem of robust binary hypothesis testing is studied. Under both hypotheses, the data-generating distributions are assumed to belong to uncertainty sets constructed through moments; in particular, the sets contain distributions whose…

Statistics Theory · Mathematics 2024-01-09 Akshayaa Magesh , Zhongchang Sun , Venugopal V. Veeravalli , Shaofeng Zou

We analyze hypotheses tests using classical results on large deviations to compare two models, each one described by a different H\"older Gibbs probability measure. One main difference to the classical hypothesis tests in Decision Theory is…

Statistics Theory · Mathematics 2021-12-28 Hermes H. Ferreira , Artur O. Lopes , Silvia R. C. Lopes

In this paper we deal with the problem of sequential testing of multiple hypotheses. The main goal is minimizing the expected sample size (ESS) under restrictions on the error probabilities. We take, as a criterion of minimization, a…

Methodology · Statistics 2023-04-14 Andrey Novikov

We consider the classical sequential binary hypothesis testing problem in which there are two hypotheses governed respectively by distributions $P_0$ and $P_1$ and we would like to decide which hypothesis is true using a sequential test. It…

Information Theory · Computer Science 2020-07-01 Yonglong Li , Vincent Y. F. Tan

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…

Statistics Theory · Mathematics 2021-03-29 Michael Bell , Yuval Kochman

In a Bayesian analysis, the likelihood that specific candidate parameters govern the evolution of a quantum system are conditioned on the outcome of measurements which, in turn, cause measurement backaction on the state of the system [M.…

Quantum Physics · Physics 2018-08-08 Alexander Holm Kiilerich , Klaus Mølmer

We suggest to construct infinite stochastic binary sequences by associating one of the two symbols of the sequence with the renewal times of an underlying renewal process. Focusing on stationary binary sequences corresponding to delayed…

Mathematical Physics · Physics 2023-04-24 Marco Zamparo

We consider the problem of binary classification with abstention in the relatively less studied \emph{bounded-rate} setting. We begin by obtaining a characterization of the Bayes optimal classifier for an arbitrary input-label distribution…

Machine Learning · Computer Science 2019-05-24 Shubhanshu Shekhar , Mohammad Ghavamzadeh , Tara Javidi

For any pair of quantum states (the hypotheses), the task of binary quantum hypotheses testing is to derive the tradeoff relation between the probability $p_{01}$ of rejecting the null hypothesis and $p_{10}$ of accepting the alternative…

Quantum Physics · Physics 2020-09-16 Le Phuc Thinh , Michele Dall'Arno , Valerio Scarani

Bounding the best achievable error probability for binary classification problems is relevant to many applications including machine learning, signal processing, and information theory. Many bounds on the Bayes binary classification error…

Information Theory · Computer Science 2018-10-03 Salimeh Yasaei Sekeh , Morteza Noshad , Kevin R. Moon , Alfred O. Hero

Statistical machine learning theory often tries to give generalization guarantees of machine learning models. Those models naturally underlie some fluctuation, as they are based on a data sample. If we were unlucky, and gathered a sample…

Machine Learning · Computer Science 2022-11-21 Alexander Mey

We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one…

Probability · Mathematics 2018-05-23 Gennady Samorodnitsky , Yizao Wang

Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…

Logic in Computer Science · Computer Science 2018-06-12 Dimitrios Milios , Guido Sanguinetti , David Schnoerr

In this paper the numerical approximation of solutions of Liouville-Master Equations for time-dependent distribution functions of Piecewise Deterministic Processes with memory is considered. These equations are linear hyperbolic PDEs with…

Numerical Analysis · Mathematics 2007-05-23 Mario Annunziato

This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error…

Quantum Physics · Physics 2018-03-14 J. Prabhu Tej , Syed Raunaq Ahmed , A. R. Usha Devi , A. K. Rajagopal