Related papers: The maximal correlation coefficient associated wit…
Given a statistical model, the maximum likelihood degree is the number of complex solutions to the likelihood equations for generic data. We consider discrete algebraic statistical models and study the solutions to the likelihood equations…
Correlations in Bell and noncontextuality inequalities can be expressed as a positive linear combination of probabilities of events. Exclusive events can be represented as adjacent vertices of a graph, so correlations can be associated to a…
Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian…
Consider a setting with $N$ independent individuals, each with an unknown parameter, $p_i \in [0, 1]$ drawn from some unknown distribution $P^\star$. After observing the outcomes of $t$ independent Bernoulli trials, i.e., $X_i \sim…
This paper deals with empirical processes of the type \[C_n(B)=\sqrt{n}\{\mu_n(B)-P(X_{n+1}\in B\mid X_1,...,X_n)\},\] where $(X_n)$ is a sequence of random variables and $\mu_n=(1/n)\sum_{i=1}^n\delta_{X_i}$ the empirical measure.…
The maximum likelihood threshold of a statistical model is the minimum number of datapoints required to fit the model via maximum likelihood estimation. In this paper we determine the maximum likelihood thresholds of generic linear…
Chatterjee's rank correlation coefficient $\xi_n$ is an empirical index for detecting functional dependencies between two variables $X$ and $Y$. It is an estimator for a theoretical quantity $\xi$ that is zero for independence and one if…
Quantifying the dependence between high-dimensional random variables is central to statistical learning and inference. Two classical methods are canonical correlation analysis (CCA), which identifies maximally correlated projected versions…
In this paper we present a method for exact generation of multivariate samples with pre-specified marginal distributions and a given correlation matrix, based on a mixture of Fr\'echet-Hoeffding bounds and marginal products. The bivariate…
In the ultraviolet (UV) scattering communication, the received signals exhibit the characteristics of discrete photoelectrons due to path loss. The synchronization is based on maximum Pulse Number-Sequence correlation problem. First of all,…
In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…
We show that the reciprocal maximal likelihood degree (rmld) of a diagonal linear concentration model $\mathcal L \subseteq \mathbb{C}^n$ of dimension $r$ is equal to $(-2)^r\chi_M( \textstyle\frac{1}{2})$, where $\chi_M$ is the…
We present an algorithm to obtain the maximum likelihood estimates of the correlation parameters of elliptical copulas. Previously existing methods for this task were either fast but only approximate or exact but very time-consuming,…
The relationship between a response variable and its covariates can vary significantly, especially in scenarios where covariates take on extremely high or low values. This paper introduces a max-linear tail regression model specifically…
We study the properties of the giant connected component in random graphs with arbitrary degree distribution. We concentrate on the degree-degree correlations. We show that the adjoining nodes in the giant connected component are correlated…
This paper considers a variation of the full-information secretary problem where the random variables to be observed are independent but not necessary identically distributed. The main result is a sharp lower bound for the optimal win…
The bivariate normal density with unit variance and correlation $\rho$ is well-known. We show that by integrating out $\rho$, the result is a function of the maximum norm. The Bayesian interpretation of this result is that if we put a…
Let $X_{i,n},n\in \mathbb{N},1\leq i\leq n$, be a triangular array of independent $\mathbb{R}^d$-valued Gaussian random vectors with correlation matrices $\Sigma_{i,n}$. We give necessary conditions under which the row-wise maxima converge…
In this short note we prove a maximal concentration lemma for sub-Gaussian random variables stating that for independent sub-Gaussian random variables we have \[P<(\max_{1\le i\le N}S_{i}>\epsilon>)…
Total correlation (TC) is a fundamental concept in information theory that measures statistical dependency among multiple random variables. Recently, TC has shown noticeable effectiveness as a regularizer in many learning tasks, where the…