Related papers: Applications of Gaussian Process Latent Variable M…
Latent Gaussian models (LGMs) are widely used in statistics and machine learning. Bayesian inference in non-conjugate LGMs is difficult due to intractable integrals involving the Gaussian prior and non-conjugate likelihoods. Algorithms…
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…
Gaussian processes (GPs) are important models in supervised machine learning. Training in Gaussian processes refers to selecting the covariance functions and the associated parameters in order to improve the outcome of predictions, the core…
Density modeling is notoriously difficult for high dimensional data. One approach to the problem is to search for a lower dimensional manifold which captures the main characteristics of the data. Recently, the Gaussian Process Latent…
In multivariate time series, the estimation of the covariance matrix of the observation innovations plays an important role in forecasting as it enables the computation of the standardized forecast error vectors as well as it enables the…
We propose a dynamic factor model (DFM) where the latent factors are linked to observed variables with unknown and potentially nonlinear functions. The key novelty and source of flexibility of our approach is a nonparametric observation…
Gaussian Process (GP) regression models typically assume that residuals are Gaussian and have the same variance for all observations. However, applications with input-dependent noise (heteroscedastic residuals) frequently arise in practice,…
Latent Gaussian Models (LGMs) are a subset of Bayesian Hierarchical models where Gaussian priors, conditional on variance parameters, are assigned to all effects in the model. LGMs are employed in many fields for their flexibility and…
We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…
Computer experiments involving both qualitative and quantitative (QQ) factors have attracted increasing attention. Gaussian process (GP) models have proven effective in this context by choosing specialized covariance functions for QQ…
Context-aware recommender systems (CARS) have gained increasing attention due to their ability to utilize contextual information. Compared to traditional recommender systems, CARS are, in general, able to generate more accurate…
The interpretation of complex high-dimensional data typically requires the use of dimensionality reduction techniques to extract explanatory low-dimensional representations. However, in many real-world problems these representations may not…
Gaussian graphical models (GGMs) are widely used to recover the conditional independence structure among random variables. Recent work has sought to incorporate auxiliary covariates to improve estimation, particularly in applications such…
Latent variable models (LVMs) learn probabilistic models of data manifolds lying in an \emph{ambient} Euclidean space. In a number of applications, a priori known spatial constraints can shrink the ambient space into a considerably smaller…
The random matrix theory method of planar Gaussian diagrammatic expansion is applied to find the mean spectral density of the Hermitian equal-time and non-Hermitian time-lagged cross-covariance estimators, firstly in the form of master…
Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear…
In this tutorial we explain the inference procedures developed for the sparse Gaussian process (GP) regression and Gaussian process latent variable model (GPLVM). Due to page limit the derivation given in Titsias (2009) and Titsias &…
We develop an automated variational method for inference in models with Gaussian process (GP) priors and general likelihoods. The method supports multiple outputs and multiple latent functions and does not require detailed knowledge of the…
We consider a class of semi-parametric dynamic models with strong white noise errors. This class of processes includes the standard Vector Autoregressive (VAR) model, the nonfundamental structural VAR, the mixed causal-noncausal models, as…
This work proposes a scalable probabilistic latent variable model based on Gaussian processes (Lawrence, 2004) in the context of multiple observation spaces. We focus on an application in astrophysics where data sets typically contain both…