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The Hirschfeld-Gebelein-R\'enyi (HGR) correlation coefficient is an extension of Pearson's correlation that is not limited to linear correlations, with potential applications in algorithmic fairness, scientific analysis, and causal…

Graphical Gaussian models have proven to be useful tools for exploring network structures based on multivariate data. Applications to studies of gene expression have generated substantial interest in these models, and resulting recent…

Feed-forward neural networks (NN) are a staple machine learning method widely used in many areas of science and technology. While even a single-hidden layer NN is a universal approximator, its expressive power is limited by the use of…

In times where more and more data become available and where the data exhibit rather complex structures (significant departure from symmetry, heavy or light tails), flexible modelling has become an essential task for statisticians as well…

Many variables in the social, physical, and biosciences, including neuroscience, are non-normally distributed. To improve the statistical properties of such data, or to allow parametric testing, logarithmic or logit transformations are…

A Gaussian process is proposed as a model for the posterior distribution of the local predictive ability of a model or expert, conditional on a vector of covariates, from historical predictions in the form of log predictive scores. Assuming…

A new distribution is introduced, which we call the twin-t distribution. This distribution is heavy-tailed like the t distribution, but closer to normality in the central part of the curve. Its properties are described, e.g. the pdf, the…

We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization…

Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…

For the task of relevance analysis, the conventional Tukey's test may be applied to the set of all pairwise comparisons. However, there were few studies that discuss both nonparametric k-sample comparisons and relevance analysis in high…

Skewness is often present in a wide range of spatial prediction problems, and modeling it in the spatial context remains a challenging problem. In this study a skew-Gaussian random field is considered. The skew-Gaussian random field is…

Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various…

We develop a class of nearest-neighbor mixture models that provide direct, computationally efficient, probabilistic modeling for non-Gaussian geospatial data. The class is defined over a directed acyclic graph, which implies conditional…

The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

Extending computational harmonic analysis tools from the classical setting of regular lattices to the more general setting of graphs and networks is very important and much research has been done recently. The Generalized Haar-Walsh…

Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…

The generalized negative binomial distribution (GNB) is a new flexible family of discrete distributions that are mixed Poisson laws with the mixing generalized gamma (GG) distributions. This family of discrete distributions is very wide and…

We develop a class of non-Gaussian translation processes that extend classical stochastic differential equations (SDEs) by prescribing arbitrary absolutely continuous marginal distributions. Our approach uses a copula-based transformation…

Many approximate Bayesian inference methods assume a particular parametric form for approximating the posterior distribution. A multivariate Gaussian distribution provides a convenient density for such approaches; examples include the…