Related papers: Efficient non-conjugate Gaussian process factor mo…

Gaussian processes scale prohibitively with the size of the dataset. In response, many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited…

We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix…

Gaussian process regression networks (GPRN) are powerful Bayesian models for multi-output regression, but their inference is intractable. To address this issue, existing methods use a fully factorized structure (or a mixture of such…

The Gaussian process latent variable model (GPLVM) is a popular probabilistic method used for nonlinear dimension reduction, matrix factorization, and state-space modeling. Inference for GPLVMs is computationally tractable only when the…

This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…

Gaussian process regression (GPR) is a non-parametric Bayesian technique for interpolating or fitting data. The main barrier to further uptake of this powerful tool rests in the computational costs associated with the matrices which arise…

We introduce the probabilistic sequential matrix factorization (PSMF) method for factorizing time-varying and non-stationary datasets consisting of high-dimensional time-series. In particular, we consider nonlinear Gaussian state-space…

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…

The Gaussian Process Latent Variable Model (GP-LVM) is a non-linear probabilistic method of embedding a high dimensional dataset in terms low dimensional `latent' variables. In this paper we illustrate that maximum a posteriori (MAP)…

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…

We propose a lower bound on the log marginal likelihood of Gaussian process regression models that can be computed without matrix factorisation of the full kernel matrix. We show that approximate maximum likelihood learning of model…

Gaussian processes (GPs) are flexible non-parametric models, with a capacity that grows with the available data. However, computational constraints with standard inference procedures have limited exact GPs to problems with fewer than about…

A common approach to analyze a covariate-sample count matrix, an element of which represents how many times a covariate appears in a sample, is to factorize it under the Poisson likelihood. We show its limitation in capturing the tendency…

Gaussian process regression is a machine learning approach which has been shown its power for estimation of unknown functions. However, Gaussian processes suffer from high computational complexity, as in a basic form they scale cubically…

Likelihood-free inference (LFI) methods, such as approximate Bayesian computation, have become commonplace for conducting inference in complex models. Many approaches are based on summary statistics or discrepancies derived from synthetic…

Gaussian processes are flexible, probabilistic, non-parametric models widely used in machine learning and statistics. However, their scalability to large data sets is limited by computational constraints. To overcome these challenges, we…

Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…

Scalable Gaussian process (GP) inference is essential for sequential decision-making tasks, yet improving GP scalability remains a challenging problem with many open avenues of research. This paper focuses on iterative GPs, where iterative…

Gaussian process (GP) regression with 1D inputs can often be performed in linear time via a stochastic differential equation formulation. However, for non-Gaussian likelihoods, this requires application of approximate inference methods…

Gaussian processes (GPs) play an essential role in biostatistics, scientific machine learning, and Bayesian optimization for their ability to provide probabilistic predictions and model uncertainty. However, GP inference struggles to scale…