Related papers: U-Processes, U-Quantile Processes and Generalized …

Many multivariate statistical analysis methods and their corresponding probabilistic counterparts have been adopted to develop process monitoring models in recent decades. However, the insightful connections between them have rarely been…

We consider large non-Hermitian random matrices $X$ with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having…

We prove tail and moment inequalities for multiple stochastic integrals on the Poisson space and for Poisson $U$-statistics. We use them to demonstrate the Law of the Iterated Logarithm for these processes when the intensity of the Poisson…

Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…

In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the…

U-statistics are widely used in fields such as economics, machine learning, and statistics. However, while they enjoy desirable statistical properties, they have an obvious drawback in that the computation becomes impractical as the data…

Uncertainty quantification has been a core of the statistical machine learning, but its computational bottleneck has been a serious challenge for both Bayesians and frequentists. We propose a model-based framework in quantifying…

Modern data sets in various domains often include units that were sampled non-randomly from the population and have a latent correlation structure. Here we investigate a common form of this setting, where every unit is associated with a…

We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…

Let $\{X_n, n \ge 1\}$ be a sequence of stationary associated random variables. We discuss another set of conditions under which a central limit theorem for U-statistics based on $\{X_n, n \ge 1\}$ holds. We look at U-statistics based on…

Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…

Higher-order $U$-statistics abound in fields such as statistics, machine learning, and computer science, but are known to be highly time-consuming to compute in practice. Despite their widespread appearance, a comprehensive study of their…

Let $(G(X_j))_{j\geq1}$ be a multivariate subordinated Gaussian process, which exhibits long-range dependence. We study the asymptotic behaviour of the corresponding sequential empirical process under two different types of subordination.…

We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in…

We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…

We consider the problem of calculating learning curves (i.e., average generalization performance) of Gaussian processes used for regression. On the basis of a simple expression for the generalization error, in terms of the eigenvalue…

We establish normal approximation in the Wasserstein metric for both non-degenerate and degenerate second-order U-statistics under cross-sectional dependence using Stein's method. For the non-degenerate case, our results extend recent…

We deduce the non-asymptotical (bilateral) estimates for moment inequalities for multiple sums of non-negative (more precisely, non-negative) independent random variables, on the other words, the well known U or V-statistics. Our…

This paper considers generalized linear models using rule-based features, also referred to as rule ensembles, for regression and probabilistic classification. Rules facilitate model interpretation while also capturing nonlinear dependences…

We compute the exact asymptotics for the cumulants of linear statistics associated with the zeros counting measure of a large class of real Gaussian processes. Precisely, we show that if the underlying covariance function is regular and…