Related papers: Some Counterexamples Concerning Maximal Correlatio…
A matching $M$ of a graph $G$ is maximal if it is not a proper subset of any other matching in $G$. Maximal matchings are much less known and researched than their maximum and perfect counterparts. In particular, almost nothing is known…
Non-local correlations are usually understood through the outcomes of alternative measurements (on two or more parts of a system) that cannot altogether actually be carried out in an experiment. Indeed, a joint input/output -- e.g.,…
Linear approximations to the decision boundary of a complex model have become one of the most popular tools for interpreting predictions. In this paper, we study such linear explanations produced either post-hoc by a few recent methods or…
The recent "correlation breakdown" in the modeling of credit default swaps, in which model correlations had to exceed 100% in order to reproduce market prices of supersenior tranches, is analyzed and argued to be a fundamental market…
We describe a Bayesian model for social learning of a random variable in which agents might observe each other over a directed network. The outcomes produced are compared to those from a model in which observations occur randomly over a…
Logistic regression is a classical model for describing the probabilistic dependence of binary responses to multivariate covariates. We consider the predictive performance of the maximum likelihood estimator (MLE) for logistic regression,…
We study how correlations in the design matrix influence Lasso prediction. First, we argue that the higher the correlations are, the smaller the optimal tuning parameter is. This implies in particular that the standard tuning parameters,…
Being the limits of copulas of componentwise maxima in independent random samples, extreme-value copulas can be considered to provide appropriate models for the dependence structure between rare events. Extreme-value copulas not only arise…
Estimating large covariance and precision matrices are fundamental in modern multivariate analysis. The problems arise from statistical analysis of large panel economics and finance data. The covariance matrix reveals marginal correlations…
A formal likelihood ratio hypothesis test for the validity of a parametric regression function is proposed, using a large-dimensional, nonparametric double cone alternative. For example, the test against a constant function uses the…
A general theory is presented for the spatial correlations in the intensity of the radiation emitted by a random medium in thermal equilibrium. We find that a non-zero correlation persists over distances large compared to the transverse…
It is shown that the resurrection axiom and the maximality principle may be consistently combined for various iterable forcing classes. The extent to which resurrection and maximality overlap is explored via the local maximality principle.
We consider the hypothesis testing problem of deciding whether an observed high-dimensional vector has independent normal components or, alternatively, if it has a small subset of correlated components. The correlated components may have a…
We study the number of linear extensions of a partial order with a given proportion of comparable pairs of elements, and estimate the maximum and minimum possible numbers. We also consider a random interval partial order on $n$ elements,…
Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theory suggests the use of max-stable models…
Monotone linear relations play important roles in variational inequality problems and quadratic optimizations. In this paper, we give explicit maximally monotone linear subspace extensions of a monotone linear relation in finite dimensional…
This paper demonstrates many immediate connections between adaptive control and optimization methods commonly employed in machine learning. Starting from common output error formulations, similarities in update law modifications are…
We establish sharp tail asymptotics for component-wise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the…
We study the maximal correlation coefficient $R(X,Y)$ between two stochastic processes $X$ and $Y$. In the case when $(X,Y)$ is a random walk, we find $R(X,Y)$ using the Cs\'{a}ki-Fischer identity and the lower semicontinuity of the map…
Generalising the concept of Bell nonlocality to networks leads to novel forms of correlations, the characterization of which is however challenging. Here we investigate constraints on correlations in networks under the two natural…