Related papers: On Approximate Inference for Generalized Gaussian …
Generalized Gaussian processes (GGPs) are highly flexible models that combine latent GPs with potentially non-Gaussian likelihoods from the exponential family. GGPs can be used in a variety of settings, including GP classification,…
Gaussian Processes (GPs) are widely recognized as powerful non-parametric models for regression and classification. Traditional GP frameworks predominantly operate under the assumption that the inputs are either accurately known or subject…
This paper presents a method for approximate Gaussian process (GP) regression with tensor networks (TNs). A parametric approximation of a GP uses a linear combination of basis functions, where the accuracy of the approximation depends on…
Sparse variational Gaussian processes (GPs) construct tractable posterior approximations to GP models. At the core of these methods is the assumption that the true posterior distribution over training function values ${\bf f}$ and inducing…
Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. Such scenarios demand that GP decisions are not only accurate, but also robust to perturbations. In this…
Many inferential tasks involve fitting models to observed data and predicting outcomes at new covariate values, requiring interpolation or extrapolation. Conventional methods select a single best-fitting model, discarding fits that were…
In this paper we introduce deep Gaussian process (GP) models. Deep GPs are a deep belief network based on Gaussian process mappings. The data is modeled as the output of a multivariate GP. The inputs to that Gaussian process are then…
Gaussian Processes (GPs) have been widely used in machine learning to model distributions over functions, with applications including multi-modal regression, time-series prediction, and few-shot learning. GPs are particularly useful in the…
Mechanistic simulation models are inverted against observations in order to gain inference on modeled processes. However, with the increasing ability to collect high resolution observations, these observations represent more patterns of…
Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian…
We propose an Gaussian Mixture Model (GMM) learning algorithm, based on our previous work of GMM expansion idea. The new algorithm brings more robustness and simplicity than classic Expectation Maximization (EM) algorithm. It also improves…
This tutorial aims to provide an intuitive introduction to Gaussian process regression (GPR). GPR models have been widely used in machine learning applications due to their representation flexibility and inherent capability to quantify…
We propose a new method for simplification of Gaussian process (GP) models by projecting the information contained in the full encompassing model and selecting a reduced number of variables based on their predictive relevance. Our results…
Rich and complex time-series data, such as those generated from engineering systems, financial markets, videos or neural recordings, are now a common feature of modern data analysis. Explaining the phenomena underlying these diverse data…
This paper proposes an efficient general alternating-direction implicit (GADI) framework for solving large sparse linear systems. The convergence property of the GADI framework is discussed. Most of the existing ADI methods can be viewed as…
The proliferation of capable and efficient machine learning (ML) models marks one of the strongest methodological shifts in signal processing (SP) in its nearly 100-year history. ML models support the development of SP systems that…
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 order to scale standard Gaussian process (GP) regression to large-scale datasets, aggregation models employ factorized training process and then combine predictions from distributed experts. The state-of-the-art aggregation models,…
In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…
The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially…