Related papers: The Multivariate Generalised von Mises distributio…
Non-Gaussian mixture models are gaining increasing attention for mixture model-based clustering particularly when dealing with data that exhibit features such as skewness and heavy tails. Here, such a mixture distribution is presented,…
The generalized inverse Gaussian, denoted $\mathrm{GIG}(p, a, b)$, is a flexible family of distributions that includes the gamma, inverse gamma, and inverse Gaussian distributions as special cases. In addition to its applications in…
Generalized variational inference (GVI) provides an optimization-theoretic framework for statistical estimation that encapsulates many traditional estimation procedures. The typical GVI problem is to compute a distribution of parameters…
We propose a probability distribution for multivariate binary random variables. The probability distribution is expressed as principal minors of the parameter matrix, which is a matrix analogous to the inverse covariance matrix in the…
Many datasets are observed on a finite set of equally spaced directions instead of the exact angles, such as the wind direction data. However, in the statistical literature, bivariate models are only available for continuous circular random…
In this paper, we propose cylindrical distributions obtained by combining the sine-skewed von Mises distribution (circular part) with the Weibull distribution (linear part). This new model, the WeiSSVM, enjoys numerous advantages: simple…
There is a need for new models for characterizing dependence in multivariate data. The multivariate Gaussian distribution is routinely used, but cannot characterize nonlinear relationships in the data. Most non-linear extensions tend to be…
This paper aims to examine the characteristics of the posterior distribution of covariance/precision matrices in a "large $p$, large $n$" scenario, where $p$ represents the number of variables and $n$ is the sample size. Our analysis…
Multivariate categorical data occur in many applications of machine learning. One of the main difficulties with these vectors of categorical variables is sparsity. The number of possible observations grows exponentially with vector length,…
A generalization of the classic Gaussian random variable to the family of Multi- Gaussian (MG) random variables characterized by shape parameter M > 0, in addition to the mean and the standard deviation, is introduced. The probability…
We introduce a new approach to a linear-circular regression problem that relates multiple linear predictors to a circular response. We follow a modeling approach of a wrapped normal distribution that describes angular variables and angular…
Fern\'andez-Dur\'an and Gregorio-Dom\'inguez (2014) defined a family of probability distributions for a vector of circular random variables by considering multiple nonnegative trigonometric sums. These distributions are highly flexible and…
This paper studies fundamental aspects of modelling data using multivariate Watson distributions. Although these distributions are natural for modelling axially symmetric data (i.e., unit vectors where $\pm \x$ are equivalent), for…
We propose a new distribution, called the soft tMVN distribution, which provides a smooth approximation to the truncated multivariate normal (tMVN) distribution with linear constraints. An efficient blocked Gibbs sampler is developed to…
We propose a method for inference in generalised linear mixed models (GLMMs) and several extensions of these models. First, we extend the GLMM by allowing the distribution of the random components to be non-Gaussian, that is, assuming an…
Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…
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,…
The need for regression models to predict circular values arises in many scientific fields. In this work we explore a family of expressive and interpretable distributions over circle-valued random functions related to Gaussian processes…
Graphical models are a key class of probabilistic models for studying the conditional independence structure of a set of random variables. Circular variables are special variables, characterized by periodicity, arising in several contexts…
This tutorial aims to provide an intuitive introduction to Gaussian process regression (GPR). GPR models have been widely used in machine learning applications due to their representation flexibility and inherent capability to quantify…