The Multivariate Generalised von Mises distribution: Inference and applications
Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by extending some standard probabilistic modelling tools to the circular domain. First we introduce a new multivariate distribution over circular variables, called the multivariate Generalised von Mises (mGvM) distribution. This distribution can be constructed by restricting and renormalising a general multivariate Gaussian distribution to the unit hyper-torus. Previously proposed multivariate circular distributions are shown to be special cases of this construction. Second, we introduce a new probabilistic model for circular regression, that is inspired by Gaussian Processes, and a method for probabilistic principal component analysis with circular hidden variables. These models can leverage standard modelling tools (e.g. covariance functions and methods for automatic relevance determination). Third, we show that the posterior distribution in these models is a mGvM distribution which enables development of an efficient variational free-energy scheme for performing approximate inference and approximate maximum-likelihood learning.
Code (0)
등록된 구현이 없습니다.
Tasks
Gaussian ProcessesSimilar Papers 제목 키워드 기반
Minimum message length estimation of mixtures of multivariate Gaussian and von Mises-Fisher distributions
Mixture modelling involves explaining some observed evidence using a combination of probability distributions. The crux of the problem is the inference of an optimal number of mixture components and their corresponding p…
Generalised Bayesian Inference for Discrete Intractable Likelihood
Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical…
Bayesian InferenceLearning Causal Response Representations through Direct Effect Analysis
We propose a novel approach for learning causal response representations. Our method aims to extract directions in which a multidimensional outcome is most directly caused by a treatment variable. By bridging conditional…
Representation LearningMultivariate Generalized Gaussian Process Models
We propose a family of multivariate Gaussian process models for correlated outputs, based on assuming that the likelihood function takes the generic form of the multivariate exponential family distribution (EFD). We deno…
regressionRobust Generalised Bayesian Inference for Intractable Likelihoods
Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. Here we consider …
Bayesian Inference