Related papers: A complete characterization of testable hypotheses
Quantum correlations in Bell and prepare-and-measure experiments are central resources for probing nonclassicality and enabling device-based quantum information protocols. In the absence of shared public randomness (i.e., without run-to-run…
Hypothesis testing in the linear regression model is a fundamental statistical problem. We consider linear regression in the high-dimensional regime where the number of parameters exceeds the number of samples ($p> n$). In order to make…
A strong mode of a probability measure on a normed space $X$ can be defined as a point $u$ such that the mass of the ball centred at $u$ uniformly dominates the mass of all other balls in the small-radius limit. Helin and Burger weakened…
Let $Q$ denote the space of signed measures on the Borel $\sigma$-algebra of a separable complete space $X$. We endow $Q$ with the norm $\|q\|=\sup|\int\phi dq|$, where the supremum is taken over all Lipschitz with constant 1 functions…
Existing guarantees for algorithms sampling from nonlogconcave measures on $\mathbb{R}^d$ are generally inexplicit or unscalable. Even for the class of measures with logdensities that have bounded Hessians and are strongly concave outside a…
We study distribution testing without direct access to a source of relevant data, but rather to one where only a tiny fraction is relevant. To enable this, we introduce the following verification query model. The goal is to perform a…
The contribution of this work is twofold. The first part deals with a Hilbert-space version of McCann's celebrated result on the existence and uniqueness of monotone measure-preserving maps: given two probability measures $\rm P$ and $\rm…
Let $L$ be a linear space of real bounded random variables on the probability space $(\Omega,\mathcal{A},P_0)$. There is a finitely additive probability $P$ on $\mathcal{A}$, such that $P\sim P_0$ and $E_P(X)=0$ for all $X\in L$, if and…
Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as conditional distributions of a single probability measure on…
Is this paper we study penalisations of diffusions satisfying some technical conditions, generalizing a result obtained by Najnudel, Roynette and Yor. If one of these diffusions has probability distribution $\mathbb{P}$, then our result can…
Testing uniformity on the $p$-dimensional unit sphere is arguably the most fundamental problem in directional statistics. In this paper, we consider this problem in the framework of axial data, that is, under the assumption that the $n$…
Quantum Analogical Modeling (QAM) works under the assumption that the correct exemplar-based description for a system of behavior minimizes the overall uncertainty of the system. The measure used in QAM differs from the traditional…
Consider a binary statistical hypothesis testing problem, where $n$ independent and identically distributed random variables $Z^n$ are either distributed according to the null hypothesis $P$ or the alternative hypothesis $Q$, and only $P$…
For every non-hyper-FC-central countable amenable group and every $k\geq 2$, we provide a sequence of symmetric, fully supported probability measures such that their convex combination is non-Liouville (that is it admits a non-constant…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional relationship between the dimension (say, $p$) and the sample size (say,…
We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, $t$-designs, and $t$-wise…
We discuss measures, invariant measures on definable groups, and genericity, often in an NIP (failure of the independence property) environment. We complete the proof of the third author's conjectures relating definably compact groups $G$…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
Large scale discrete uniform and homogeneous $P$-values often arise in applications with multiple testing. For example, this occurs in genome wide association studies whenever a nonparametric one-sample (or two-sample) test is applied…
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…