Related papers: Latent Gaussian Processes for Distribution Estimat…

Recognizing the successes of treed Gaussian process (TGP) models as an interpretable and thrifty model for nonparametric regression, we seek to extend the model to classification. Both treed models and Gaussian processes (GPs) have,…

Unsupervised estimation of latent variable models is a fundamental problem central to numerous applications of machine learning and statistics. This work presents a principled approach for estimating broad classes of such models, including…

Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…

We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to…

A representation of Gaussian distributed sparsely sampled longitudinal data in terms of predictive distributions for their functional principal component scores (FPCs) maps available data for each subject to a multivariate Gaussian…

Heteroscedastic regression considering the varying noises among observations has many applications in the fields like machine learning and statistics. Here we focus on the heteroscedastic Gaussian process (HGP) regression which integrates…

Real-world clinical problems are often characterized by multimodal data, usually associated with incomplete views and limited sample sizes in their cohorts, posing significant limitations for machine learning algorithms. In this work, we…

A large amount of observational data has been accumulated in various fields in recent times, and there is a growing need to estimate the generating processes of these data. A linear non-Gaussian acyclic model (LiNGAM) based on the…

The theory of Bayesian learning incorporates the use of Student-t Processes to model heavy-tailed distributions and datasets with outliers. However, despite Student-t Processes having a similar computational complexity as Gaussian…

When constructing a Bayesian Machine Learning model, we might be faced with multiple different prior distributions and thus are required to properly consider them in a sensible manner in our model. While this situation is reasonably well…

Clinical patient records are an example of high-dimensional data that is typically collected from disparate sources and comprises of multiple likelihoods with noisy as well as missing values. In this work, we propose an unsupervised…

This paper develops forecasting methodology and application of new classes of dynamic models for time series of non-negative counts. Novel univariate models synthesise dynamic generalized linear models for binary and conditionally Poisson…

We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random…

Accounting for the complexity of psychological theories requires methods that can predict not only changes in the means of latent variables -- such as personality factors, creativity, or intelligence -- but also changes in their variances.…

We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…

High-dimensional multivariate longitudinal data, which arise when many outcome variables are measured repeatedly over time, are becoming increasingly common in social, behavioral and health sciences. We propose a latent variable model for…

Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…

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…

The problem of missing values in multivariable time series is a key challenge in many applications such as clinical data mining. Although many imputation methods show their effectiveness in many applications, few of them are designed to…

Spatio-temporal prediction of levels of an environmental exposure is an important problem in environmental epidemiology. Our work is motivated by multiple studies on the spatio-temporal distribution of mobile source, or traffic related,…