Related papers: Interpolating between symmetric and asymmetric hyp…
Quantum hypothesis testing (QHT) concerns the statistical inference of unknown quantum states. In the general setting of composite hypotheses, the goal of QHT is to determine whether an unknown quantum state belongs to one or another of two…
We introduce a game-theoretic framework to study the hypothesis testing problem, in the presence of an adversary aiming at preventing a correct decision. Specifically, the paper considers a scenario in which an analyst has to decide whether…
The trade-off between the two types of errors in binary state discrimination may be quantified in the asymptotics by various error exponents. In the case of simple i.i.d. hypotheses, each of these exponents is equal to a divergence…
This article is concerned with decentralized sequential testing of a normal mean $\mu$ with two-sided alternatives. It is assumed that in a single-sensor network system with limited local memory, i.i.d. normal raw observations are observed…
Making binary decisions is a common data analytical task in scientific research and industrial applications. In data sciences, there are two related but distinct strategies: hypothesis testing and binary classification. In practice, how to…
We consider the problem of hypothesis testing in the situation when the first hypothesis is simple and the second one is local one-sided composite. We describe the choice of the thresholds and the power functions of the Score Function test,…
As small quantum computers are becoming available on different physical platforms, a benchmarking task known as cross-platform verification has been proposed that aims to estimate the fidelity of states prepared on two quantum computers.…
In the problem of asymptotic binary i.i.d. state discrimination, the optimal asymptotics of the type I and the type II error probabilities is in general an exponential decrease to zero as a function of the number of samples; the set of…
In this paper we consider the problem of uniformity testing with limited memory. We observe a sequence of independent identically distributed random variables drawn from a distribution $p$ over $[n]$, which is either uniform or is…
This paper revisits the universal asymmetric $1 \to 2$ quantum cloning problem. We identify the symmetry properties of this optimisation problem, giving us access to the optimal quantum cloning map. Furthermore, we use the bipolar theorem,…
We study the problem of conditional two-sample testing, which aims to determine whether two populations have the same distribution after accounting for confounding factors. This problem commonly arises in various applications, such as…
We consider the problem of two-sample testing in a semi-supervised setting with abundant unlabeled covariate data. Standard two-sample tests neglect covariate information, which has the potential to significantly boost performance. However,…
In the binary hypothesis testing problem, it is well known that sequentiality in taking samples eradicates the trade-off between two error exponents, yet implementing the optimal test requires the knowledge of the underlying distributions,…
The $\beta$-model has been extensively utilized to model degree heterogeneity in networks, wherein each node is assigned a unique parameter. In this article, we consider the hypothesis testing problem that two nodes $i$ and $j$ of a…
The problem of discriminating with minimum error between two mixed quantum states is reviewed, with emphasize on the detection operators necessary for performing the measurement. An analytical result is derived for the minimum probability…
Quantum systems exhibit particle-like or wave-like behaviour depending on the experimental apparatus they are confronted by. This wave-particle duality is at the heart of quantum mechanics, and is fully captured in Wheeler's famous delayed…
We study the adversarial binary hypothesis testing problem in the sequential setting. Associated with each hypothesis is a closed, convex set of distributions. Given the hypothesis, each observation is generated according to a distribution…
This paper addresses the problem of distributed hypothesis testing in multi-agent networks, where agents repeatedly collect local observations about an unknown state of the world, and try to collaboratively detect the true state through…
The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in…
Simultaneous tests of superiority and non-inferiority hypotheses on multiple endpoints are often performed in clinical trials to demonstrate that a new treatment is superior over a control on at least one endpoint and non-inferior on the…