Related papers: Closed-form Inference and Prediction in Gaussian P…
In the gravitational-wave analysis of pulsar-timing-array datasets, parameter estimation is usually performed using Markov Chain Monte Carlo methods to explore posterior probability densities. We introduce an alternative procedure that…
Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…
Gaussian processes (GPs) are important probabilistic tools for inference and learning in spatio-temporal modelling problems such as those in climate science and epidemiology. However, existing GP approximations do not simultaneously support…
A conventional Bayesian approach to prediction uses the posterior distribution to integrate out parameters in a density for unobserved data conditional on the observed data and parameters. When the true posterior is intractable, it is…
This paper presents a new approach to automatically discovering accurate models of complex time series data. Working within a Bayesian nonparametric prior over a symbolic space of Gaussian process time series models, we present a novel…
We introduce a conceptually novel structured prediction model, GPstruct, which is kernelized, non-parametric and Bayesian, by design. We motivate the model with respect to existing approaches, among others, conditional random fields (CRFs),…
Modeling count-valued time series has been receiving increasing attention since count time series naturally arise in physical and social domains. Poisson gamma dynamical systems (PGDSs) are newly-developed methods, which can well capture…
We present an R package bssm for Bayesian non-linear/non-Gaussian state space modelling. Unlike the existing packages, bssm allows for easy-to-use approximate inference based on Gaussian approximations such as the Laplace approximation and…
Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric…
The Poisson-gamma state space (PGSS) models have been utilized in the analysis of non-negative integer-valued time series to sequentially obtain closed form filtering and predictive densities. In this study, we show the underlying mechanics…
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…
The recently introduced Gaussian Process State (GPS) provides a highly flexible, compact and physically insightful representation of quantum many-body states based on ideas from the zoo of machine learning approaches. In this work, we give…
The Gaussian Process Latent Variable Model (GP-LVM) is a non-linear probabilistic method of embedding a high dimensional dataset in terms low dimensional `latent' variables. In this paper we illustrate that maximum a posteriori (MAP)…
Latent space models (LSMs) are often used to analyze dynamic (time-varying) networks that evolve in continuous time. Existing approaches to Bayesian inference for these models rely on Markov chain Monte Carlo algorithms, which cannot handle…
Gaussian process (GP) regression with 1D inputs can often be performed in linear time via a stochastic differential equation formulation. However, for non-Gaussian likelihoods, this requires application of approximate inference methods…
This work studies the problem of stochastic dynamic filtering and state propagation with complex beliefs. The main contribution is GP-SUM, a filtering algorithm tailored to dynamic systems and observation models expressed as Gaussian…
We put forward a new Bayesian modeling strategy for spatiotemporal count data that enables efficient posterior sampling. Most previous models for such data decompose logarithms of the response Poisson rates into fixed effects and spatial…
The log-Gaussian Cox process is a flexible and popular class of point pattern models for capturing spatial and space-time dependence for point patterns. Model fitting requires approximation of stochastic integrals which is implemented…
In spite of the diverse literature on nonstationary spatial modeling and approximate Gaussian process (GP) methods, there are no general approaches for conducting fully Bayesian inference for moderately sized nonstationary spatial data sets…