Related papers: Gaussian Process Structural Equation Models with L…
Standard GPs offer a flexible modelling tool for well-behaved processes. However, deviations from Gaussianity are expected to appear in real world datasets, with structural outliers and shocks routinely observed. In these cases GPs can fail…
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…
Computer simulations often involve both qualitative and numerical inputs. Existing Gaussian process (GP) methods for handling this mainly assume a different response surface for each combination of levels of the qualitative factors and…
We introduce a Bayesian framework for inference with a supervised version of the Gaussian process latent variable model. The framework overcomes the high correlations between latent variables and hyperparameters by using an unbiased pseudo…
Longitudinal data are important in numerous fields, such as healthcare, sociology and seismology, but real-world datasets present notable challenges for practitioners because they can be high-dimensional, contain structured missingness…
Gaussian processes are a flexible Bayesian nonparametric modelling approach that has been widely applied but poses computational challenges. To address the poor scaling of exact inference methods, approximation methods based on sparse…
Our concern is selecting the concentration matrix's nonzero coefficients for a sparse Gaussian graphical model in a high-dimensional setting. This corresponds to estimating the graph of conditional dependencies between the variables. We…
Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in…
State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…
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,…
Causal learning has long concerned itself with the accurate recovery of underlying causal mechanisms. Such causal modelling enables better explanations of out-of-distribution data. Prior works on causal learning assume that the high-level…
The Dynamical Gaussian Process Latent Variable Models provide an elegant non-parametric framework for learning the low dimensional representations of the high-dimensional time-series. Real world observational studies, however, are often…
We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of…
The estimation of linear causal models (also known as structural equation models) from data is a well-known problem which has received much attention in the past. Most previous work has, however, made an explicit or implicit assumption of…
Gaussian process-based latent variable models are flexible and theoretically grounded tools for nonlinear dimension reduction, but generalizing to non-Gaussian data likelihoods within this nonlinear framework is statistically challenging.…
Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…
Recently there has been an increasing interest in methods that deal with multiple outputs. This has been motivated partly by frameworks like multitask learning, multisensor networks or structured output data. From a Gaussian processes…
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…
Suppose we observe samples of a subset of a collection of random variables. No additional information is provided about the number of latent variables, nor of the relationship between the latent and observed variables. Is it possible to…
An old problem in multivariate statistics is that linear Gaussian models are often unidentifiable, i.e. some parameters cannot be uniquely estimated. In factor (component) analysis, an orthogonal rotation of the factors is unidentifiable,…