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Related papers: Multivariate Generalized Gaussian Process Models

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In science and engineering, we often work with models designed for accurate prediction of variables of interest. Recognizing that these models are approximations of reality, it becomes desirable to apply multiple models to the same data and…

Machine Learning · Computer Science 2024-04-03 Marzieh Ajirak , Daniel Waxman , Fernando Llorente , Petar M. Djuric

Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too…

Machine Learning · Statistics 2016-04-12 Roberto Calandra , Jan Peters , Carl Edward Rasmussen , Marc Peter Deisenroth

From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing…

Data Analysis, Statistics and Probability · Physics 2010-10-19 Alexandre Souto Martinez , Rodrigo Silva Gonzalez , Cesar Augusto Sangaletti Tercariol

Markov chain Monte Carlo methods for exponential family models with intractable normalizing constant, such as the exchange algorithm, require simulations of the sufficient statistics at every iteration of the Markov chain, which often…

Computation · Statistics 2023-02-21 Quan Vu , Matthew T. Moores , Andrew Zammit-Mangion

A Gaussian process (GP)-based methodology is proposed to emulate complex dynamical computer models (or simulators). The method relies on emulating the numerical flow map of the system over an initial (short) time step, where the flow map is…

Methodology · Statistics 2024-11-26 Hossein Mohammadi , Peter Challenor , Marc Goodfellow

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…

Machine Learning · Computer Science 2025-06-27 Michalis K. Titsias

Neural Processes (NPs; Garnelo et al., 2018a,b) are a rich class of models for meta-learning that map data sets directly to predictive stochastic processes. We provide a rigorous analysis of the standard maximum-likelihood objective used to…

Machine Learning · Statistics 2021-01-12 Wessel P. Bruinsma , James Requeima , Andrew Y. K. Foong , Jonathan Gordon , Richard E. Turner

A simple and widely adopted approach to extend Gaussian processes (GPs) to multiple outputs is to model each output as a linear combination of a collection of shared, unobserved latent GPs. An issue with this approach is choosing the number…

Machine Learning · Statistics 2019-12-18 Pavel Berkovich , Eric Perim , Wessel Bruinsma

This paper presents a Gaussian process (GP) model for estimating piecewise continuous regression functions. In scientific and engineering applications of regression analysis, the underlying regression functions are piecewise continuous in…

Methodology · Statistics 2021-04-15 Chiwoo Park

We present elliptical processes, a family of non-parametric probabilistic models that subsume Gaussian processes and Student's t processes. This generalization includes a range of new heavy-tailed behaviors while retaining computational…

Machine Learning · Computer Science 2023-11-23 Maria Bånkestad , Jens Sjölund , Jalil Taghia , Thomas B. Schöon

We address the problem of continual learning in multi-task Gaussian process (GP) models for handling sequential input-output observations. Our approach extends the existing prior-posterior recursion of online Bayesian inference, i.e.\ past…

Machine Learning · Statistics 2019-11-04 Pablo Moreno-Muñoz , Antonio Artés-Rodríguez , Mauricio A. Álvarez

Multi-task learning models using Gaussian processes (GP) have been developed and successfully applied in various applications. The main difficulty with this approach is the computational cost of inference using the union of examples from…

Machine Learning · Computer Science 2012-11-29 Yuyang Wang , Roni Khardon

Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by…

Machine Learning · Statistics 2017-08-10 Alexandre K. W. Navarro , Jes Frellsen , Richard E. Turner

Deep Gaussian Processes (DGPs) are hierarchical generalizations of Gaussian Processes that combine well calibrated uncertainty estimates with the high flexibility of multilayer models. One of the biggest challenges with these models is that…

Machine Learning · Statistics 2018-11-13 Marton Havasi , José Miguel Hernández-Lobato , Juan José Murillo-Fuentes

Latent Gaussian process (GP) models are flexible probabilistic non-parametric function models. Vecchia approximations are accurate approximations for GPs to overcome computational bottlenecks for large data, and the Laplace approximation is…

Methodology · Statistics 2024-12-09 Pascal Kündig , Fabio Sigrist

This paper generalises the exponential family GLM to allow arbitrary distributions for the response variable. This is achieved by combining the model-assisted regression approach from survey sampling with the GLM scoring algorithm, weighted…

Methodology · Statistics 2019-01-10 Murray Aitkin

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…

Machine Learning · Statistics 2020-12-29 Martin Jankowiak , Geoff Pleiss , Jacob R. Gardner

Motivated by deep neural networks, the deep Gaussian process (DGP) generalizes the standard GP by stacking multiple layers of GPs. Despite the enhanced expressiveness, GP, as an $L_2$ regularization prior, tends to be over-smooth and…

Machine Learning · Statistics 2024-10-30 Zhi Chang , Chukwudi Obite , Shuang Zhou , Shiwei Lan

This research proposes a flexible Bayesian extension of the composite Gaussian process (CGP) model of Ba and Joseph (2012) for predicting (stationary or) non-stationary $y(\mathbf{x})$. The CGP generalizes the regression plus stationary…

Methodology · Statistics 2019-06-27 Casey B. Davis , Christopher M. Hans , Thomas J. Santner

For multivariate spatial Gaussian process (GP) models, customary specifications of cross-covariance functions do not exploit relational inter-variable graphs to ensure process-level conditional independence among the variables. This is…

Methodology · Statistics 2021-11-19 Debangan Dey , Abhirup Datta , Sudipto Banerjee