Related papers: Non-iid hypothesis testing: from classical to quan…
Testing hypothesis of independence between two random elements on a joint alphabet is a fundamental exercise in statistics. Pearson's chi-squared test is an effective test for such a situation when the contingency table is relatively small.…
We introduce credal two-sample testing, a new hypothesis testing framework for comparing credal sets -- convex sets of probability measures where each element captures aleatoric uncertainty and the set itself represents epistemic…
The problem of hypothesis testing is examined from both the historical and Bayesian points of view in the case that sampling is from an underlying joint probability distribution and the hypotheses tested for are those of independence and…
Consider two random variables contaminated by two unknown transformations. The aim of this paper is to test the equality of those transformations. Two cases are distinguished: first, the two random variables have known distributions.…
In spite of its fundamental importance in quantum science and technology, the experimental certification of nonclassicality is still a challenging task, especially in realistic scenarios where losses and noise imbue the system. Here, we…
We introduce a framework for distributed quantum inference under communication constraints. In our model, $m$ distributed nodes each receive one copy of an unknown $d$-dimensional quantum state $\rho$, before communicating via a constrained…
We revisit the outlier hypothesis testing framework of Li \emph{et al.} (TIT 2014) and derive fundamental limits for the optimal test under the generalized Neyman-Pearson criterion. In outlier hypothesis testing, one is given multiple…
The generalized quantum Stein's lemma characterizes the optimal asymptotic exponent of the type-II error in quantum hypothesis testing for an independent and identically distributed (IID) null hypothesis against a composite alternative…
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.…
The sample complexity of simple binary hypothesis testing is the smallest number of i.i.d.\ samples required to distinguish between two distributions $p$ and $q$ in either: (i) the prior-free setting, with type-I error at most $\alpha$ and…
We consider the problem of testing the equality of conditional distributions of a response variable given a vector of covariates between two populations. Such a hypothesis testing problem can be motivated from various machine learning and…
We discuss several tests for whether a given set of independent and identically distributed (i.i.d.) draws does not come from a specified probability density function. The most commonly used are Kolmogorov-Smirnov tests, particularly…
When data analysts train a classifier and check if its accuracy is significantly different from chance, they are implicitly performing a two-sample test. We investigate the statistical properties of this flexible approach in the…
A new method based on the rejection sampling for finding statistical tests is proposed. This method is conceptually intuitive, easy to implement, and applicable for arbitrary dimension. To illustrate its potential applicability, three…
This paper studies the problem of discriminating two multivariate Gaussian distributions in a distributed manner. Specifically, it characterizes in a special case the optimal typeII error exponent as a function of the available…
In the common time series model $X_{i,n} = \mu (i/n) + \varepsilon_{i,n}$ with non-stationary errors we consider the problem of detecting a significant deviation of the mean function $\mu$ from a benchmark $g (\mu )$ (such as the initial…
Suppose we have a distribution of interest, with density $p(x),x\in {\cal X}$ say, and an algorithm claimed to generate samples from $p(x)$. Moreover, assume we have available a Metropolis--Hastings transition kernel fulfilling detail…
We study the following independence testing problem: given access to samples from a distribution $P$ over $\{0,1\}^n$, decide whether $P$ is a product distribution or whether it is $\varepsilon$-far in total variation distance from any…
We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting…
The aim of this expos\'e is to make explicit the analogy between the classical notion of non-independent probability distribution and the quantum notion of entangled state. To bring that analogy forth, we consider a classical systems with…