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Previous results pertaining to algebraic state and parameter estimation of linear systems based on a special construction of a forward-backward kernel representation of linear differential invariants are extended to handle large noise in…

Systems and Control · Electrical Eng. & Systems 2021-02-02 Debarshi Patanjali Ghoshal , Hannah Michalska

Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…

Methodology · Statistics 2025-04-29 Blake Hansen , Alejandra Avalos-Pacheco , Massimiliano Russo , Roberta De Vito

Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…

Machine Learning · Statistics 2017-12-08 Luca Ambrogioni , Eric Maris

We introduce a novel kernel that models input-dependent couplings across multiple latent processes. The pairwise joint kernel measures covariance along inputs and across different latent signals in a mutually-dependent fashion. A latent…

Machine Learning · Statistics 2017-10-04 Sami Remes , Markus Heinonen , Samuel Kaski

Gaussian processes (GPs) are crucial in machine learning for quantifying uncertainty in predictions. However, their associated covariance matrices, defined by kernel functions, are typically dense and large-scale, posing significant…

Machine Learning · Computer Science 2025-04-02 Theresa Wagner , Tianshi Xu , Franziska Nestler , Yuanzhe Xi , Martin Stoll

We generalize the log Gaussian Cox process (LGCP) framework to model multiple correlated point data jointly. The observations are treated as realizations of multiple LGCPs, whose log intensities are given by linear combinations of latent…

Machine Learning · Statistics 2019-03-18 Virginia Aglietti , Theodoros Damoulas , Edwin Bonilla

The integration of physical relationships into stochastic models is of major interest e.g. in data assimilation. Here, a multivariate Gaussian random field formulation is introduced, which represents the differential relations of the…

Applications · Statistics 2018-02-14 Rüdiger Hewer , Petra Friederichs , Andreas Hense , Martin Schlather

Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…

Machine Learning · Computer Science 2020-06-09 Jarred Barber

One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these kernel…

Machine Learning · Computer Science 2024-04-29 Theresa Wagner , Franziska Nestler , Martin Stoll

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…

Machine Learning · Statistics 2018-07-23 Martin Tegner , Benjamin Bloem-Reddy , Stephen Roberts

We present a novel scheme to accurately predict atomic forces as vector quantities, rather than sets of scalar components, by Gaussian Process (GP) Regression. This is based on matrix-valued kernel functions, on which we impose the…

Chemical Physics · Physics 2017-06-14 Aldo Glielmo , Peter Sollich , Alessandro De Vita

We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in…

Machine Learning · Statistics 2019-01-04 Pablo Moreno-Muñoz , Antonio Artés-Rodríguez , Mauricio A. Álvarez

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…

Gaussian processes are flexible function approximators, with inductive biases controlled by a covariance kernel. Learning the kernel is the key to representation learning and strong predictive performance. In this paper, we develop…

Machine Learning · Computer Science 2019-10-31 Gregory W. Benton , Wesley J. Maddox , Jayson P. Salkey , Julio Albinati , Andrew Gordon Wilson

Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation…

Machine Learning · Computer Science 2025-02-25 Lulu Kang , Minshen Xu

Kernel-based modeling of dynamic systems has garnered a significant amount of attention in the system identification literature since its introduction to the field. While the method was originally applied to linear impulse response…

Systems and Control · Computer Science 2017-10-27 Jeremy Stoddard , Georgios Birpoutsoukis

To speed up Gaussian process inference, a number of fast kernel matrix-vector multiplication (MVM) approximation algorithms have been proposed over the years. In this paper, we establish an exact fast kernel MVM algorithm based on exact…

Machine Learning · Statistics 2025-08-05 Nicolas Langrené , Xavier Warin , Pierre Gruet

The high efficiency of a recently proposed method for computing with Gaussian processes relies on expanding a (translationally invariant) covariance kernel into complex exponentials, with frequencies lying on a Cartesian equispaced grid.…

Numerical Analysis · Mathematics 2023-05-19 Alex Barnett , Philip Greengard , Manas Rachh

This article is concerned with learning and stochastic control in physical systems which contain unknown input signals. These unknown signals are modeled as Gaussian processes (GP) with certain parametrized covariance structures. The…

Systems and Control · Computer Science 2018-08-15 Simo Särkkä , Mauricio A. Álvarez , Neil D. Lawrence

This work considers stationary vector count time series models defined via deterministic functions of a latent stationary vector Gaussian series. The construction is very general and ensures a pre-specified marginal distribution for the…

Statistics Theory · Mathematics 2023-10-31 Marie-Christine Düker , Robert Lund , Vladas Pipiras