Related papers: Approximate null distribution of the largest root …

Let X be a n*p matrix and l_1 the largest eigenvalue of the covariance matrix X^{*}*X. The "null case" where X_{i,j} are independent Normal(0,1) is of particular interest for principal component analysis. For this model, when n, p tend to…

Relational models for contingency tables are generalizations of log-linear models, allowing effects associated with arbitrary subsets of cells in a possibly incomplete table, and not necessarily containing the overall effect. In this…

The property of perfectness plays an important role in the theory of Bayesian networks. First, the existence of perfect distributions for arbitrary sets of variables and directed acyclic graphs implies that various methods for reading…

In the framework of semiparametric distribution regression, we consider the problem of comparing the conditional distribution functions corresponding to two samples. In contrast to testing for exact equality, we are interested in the (null)…

In a multifidelity setting, data are available under the same conditions from two (or more) sources, e.g. computer codes, one being lower-fidelity but computationally cheaper, and the other higher-fidelity and more expensive. This work…

In many practical situations we would like to estimate the covariance matrix of a set of variables from an insufficient amount of data. More specifically, if we have a set of $N$ independent, identically distributed measurements of an $M$…

Let (X,d_X) be an n-point metric space. We show that there exists a distribution D over non-contractive embeddings into trees f:X-->T such that for every x in X, the expectation with respect to D of the maximum over y in X of the ratio…

The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference,…

Information diffusion in networks can be used to model many real-world phenomena, including rumor spreading on online social networks, epidemics in human beings, and malware on the Internet. Informally speaking, the source localization…

Let $A$ be a real skew-symmetric Gaussian random matrix whose upper triangular elements are independently distributed according to the standard normal distribution. We provide the distribution of the largest singular value $\sigma_1$ of…

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

In this paper, we address the problem of approximating a multivariate function defined on a general domain in $d$ dimensions from sample points. We consider weighted least-squares approximation in an arbitrary finite-dimensional space $P$…

The paper deals with studying a connection of the Littlewood--Offord problem with estimating the concentration functions of some symmetric infinitely divisible distributions. It is shown that the values at zero of the concentration…

A taxonomy is a standardized framework to classify and organize items into categories. Hierarchical taxonomies are ubiquitous, ranging from the classification of organisms to the file system on a computer. Characterizing the typical…

Let $\mathbb{A}_p=\frac{\mathbb{Y}\mathbb{Y}^*}{m}$ and $\mathbb{B}_p=\frac{\mathbb{X}\mathbb{X}^*}{n}$ be two independent random matrices where $\mathbb{X}=(X_{ij})_{p \times n}$ and $\mathbb{Y}=(Y_{ij})_{p \times m}$ respectively consist…

Many machine learning models appear to deploy effortlessly under distribution shift, and perform well on a target distribution that is considerably different from the training distribution. Yet, learning theory of distribution shift bounds…

The Galton--Watson process is the simplest example of a branching process. The relationship between the offspring distribution, and, when the extinction occurs almost surely, the distribution of the total progeny is well known. In this…

The best-known and most commonly used distribution-property estimation technique uses a plug-in estimator, with empirical frequency replacing the underlying distribution. We present novel linear-time-computable estimators that significantly…

In this article, we define a matrix multinomial distribution. We prove some properties of the matrix multinomial distribution. We prove that the matrix Poisson distribution can be used as an approximation to the matrix multinomial…

The nullity of a graph is the multiplicity of the eigenvalue zero in its adjacency spectrum. In this paper, we give a closed formula for the minimum and maximum nullity among trees with the same degree sequence, using the notion of matching…