Related papers: A transference method in quantum probability
One of the goals of probabilistic inference is to decide whether an empirically observed distribution is compatible with a candidate Bayesian network. However, Bayesian networks with hidden variables give rise to highly non-trivial…
This paper studies the construction of p-values for nonparametric outlier detection, taking a multiple-testing perspective. The goal is to test whether new independent samples belong to the same distribution as a reference data set or are…
We show that the presented real-number quantum theories, compatible with the independent source assumption, require the inclusion of a nonlocal map. This means that if the independent source assumption holds, in these models, complex-number…
Inspired by the theory of p-adic differential equations, this paper introduces an analogous theory for q-difference equations over a local field, when |q|=1. We define some basic concepts, for instance the generic radius of convergence,…
In this paper, we introduce a flexible and widely applicable nonparametric entropy-based testing procedure that can be used to assess the validity of simple hypotheses about a specific parametric population distribution. The testing…
We find a new finite algorithm for evaluation of Lipschitz-free $p$-space norm in finite-dimensional Lipschitz-free $p$-spaces. We use this algorithm to deal with the problem of whether given $p$-metric spaces $N\subset M$, the canonical…
Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…
We conduct a KL-divergence based procedure for testing elliptical distributions. The procedure simultaneously takes into account the two defining properties of an elliptically distributed random vector: independence between length and…
Given a random sample of size $n$ from a $p$ dimensional random vector, where both $n$ and $p$ are large, we are interested in testing whether the $p$ components of the random vector are mutually independent. This is the so-called complete…
Classical information loading is an essential task for many processing quantum algorithms, constituting a cornerstone in the field of quantum machine learning. In particular, the embedding techniques based on Hamiltonian simulation…
We consider the problem of inference in shift-share research designs. The choice between existing approaches that allow for unrestricted spatial correlation involves tradeoffs, varying in terms of their validity when there are relatively…
The limitation of permutation tests is that they assume exchangeability. It is shown that in generalized linear models one can construct permutation tests from score statistics in particular cases. When under the null hypothesis the…
In their usual form, representation independence metatheorems provide an external guarantee that two implementations of an abstract interface are interchangeable when they are related by an operation-preserving correspondence. If our…
In this paper, we examine how various notions of independence in non-commutative probability theory arise in bi-free probability. We exhibit how Boolean and monotone independence occur from bi-free pairs of faces and establish a Kac/Loeve…
Comparing probability distributions is a core challenge across the natural, social, and computational sciences. Existing methods, such as Maximum Mean Discrepancy (MMD), struggle in high-dimensional and non-compact domains. Here we…
We state a quantum version of Bayes's rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state…
We propose a novel statistical test to assess the mutual independence of multidimensional random vectors. Our approach is based on the $L_1$-distance between the joint density function and the product of the marginal densities associated…
Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is…
Re-sampling based statistical tests are known to be computationally heavy, but reliable when small sample sizes are available. Despite their nice theoretical properties not much effort has been put to make them efficient. In this paper we…
We consider the random matrix model $X_n = P_n + i Q_n$, where $P_n$ and $Q_n$ are independently Haar-unitary rotated Hermitian matrices with at most $2$ atoms in their spectra. Let $(M, \tau)$ be a tracial von Neumann algebra and let $p, q…