Related papers: On the Identifiability and Interpretability of Gau…

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…

Mixtures of Gaussian process experts is a class of models that can simultaneously address two of the key limitations inherent in standard Gaussian processes: scalability and predictive performance. In particular, models that use Dirichlet…

Kernel methods play an important role in machine learning applications due to their conceptual simplicity and superior performance on numerous machine learning tasks. Expressivity of a machine learning model, referring to the ability of the…

The generalization properties of Gaussian processes depend heavily on the choice of kernel, and this choice remains a dark art. We present the Neural Kernel Network (NKN), a flexible family of kernels represented by a neural network. The…

Gaussian Process (GP) models are widely utilized as surrogate models in scientific and engineering fields. However, standard GP models are limited to continuous variables due to the difficulties in establishing correlation structures for…

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…

We introduce Gaussian Process Topic Models (GPTMs), a new family of topic models which can leverage a kernel among documents while extracting correlated topics. GPTMs can be considered a systematic generalization of the Correlated Topic…

Gaussian processes (GPs) are widely-used tools in spatial statistics and machine learning and the formulae for the mean function and covariance kernel of a GP $T u$ that is the image of another GP $u$ under a linear transformation $T$…

Spectral mixture (SM) kernels comprise a powerful class of generalized kernels for Gaussian processes (GPs) to describe complex patterns. This paper introduces model compression and time- and phase (TP) modulated dependency structures to…

Kernels representing limiting cases of neural network architectures have recently gained popularity. However, the application and performance of these new kernels compared to existing options, such as the Matern kernel, is not well studied.…

A network of independently trained Gaussian processes (StackedGP) is introduced to obtain predictions of quantities of interest with quantified uncertainties. The main applications of the StackedGP framework are to integrate different…

Gaussian processes (GPs) are widely used as distributions of random effects in linear mixed models, which are fit using the restricted likelihood or the closely-related Bayesian analysis. This article addresses two problems. First, we…

Gaussian processes are typically used for smoothing and interpolation on small datasets. We introduce a new Bayesian nonparametric framework -- GPatt -- enabling automatic pattern extrapolation with Gaussian processes on large…

Gaussian processes (GPs) produce good probabilistic models of functions, but most GP kernels require $O((n+m)n^2)$ time, where $n$ is the number of data points and $m$ the number of predictive locations. We present a new kernel that allows…

Kernel based methods including Gaussian process regression (GPR) and generally kernel ridge regression (KRR) have been finding increasing use in computational chemistry, including the fitting of potential energy surfaces and density…

We present a scalable Gaussian process model for identifying and characterizing smooth multidimensional changepoints, and automatically learning changes in expressive covariance structure. We use Random Kitchen Sink features to flexibly…

Variational Quantum Algorithms (VQAs) aim at solving classical or quantum optimization problems by optimizing parametrized trial states on a quantum device, based on the outcomes of noisy projective measurements. The associated optimization…

We show that Gaussian process regression (GPR) allows representing multivariate functions with low-dimensional terms via kernel design. When using a kernel built with HDMR (High-dimensional model representation), one obtains a similar type…

In recent years, there has been considerable interest in developing machine learning models on graphs to account for topological inductive biases. In particular, recent attention has been given to Gaussian processes on such structures since…

Transformers have increasingly become the de facto method to model sequential data with state-of-the-art performance. Due to its widespread use, being able to estimate and calibrate its modeling uncertainty is important to understand and…