Related papers: Fast Gaussian process inference by exact Mat\'ern …
Variational Bayes (VB) is a critical method in machine learning and statistics, underpinning the recent success of Bayesian deep learning. The natural gradient is an essential component of efficient VB estimation, but it is prohibitively…
A Gaussian process (GP) is a powerful and widely used regression technique. The main building block of a GP regression is the covariance kernel, which characterizes the relationship between pairs in the random field. The optimization to…
We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian…
This paper presents a variational Bayesian kernel selection (VBKS) algorithm for sparse Gaussian process regression (SGPR) models. In contrast to existing GP kernel selection algorithms that aim to select only one kernel with the highest…
Despite the increasing importance of stochastic processes on linear networks and graphs, current literature on multivariate (vector-valued) Gaussian random fields on metric graphs is elusive. This paper challenges several aspects related to…
Subgradient algorithms for training support vector machines have been quite successful for solving large-scale and online learning problems. However, they have been restricted to linear kernels and strongly convex formulations. This paper…
Varying coefficient models (VCMs) are widely used for estimating nonlinear regression functions for functional data. Their Bayesian variants using Gaussian process priors on the functional coefficients, however, have received limited…
We investigate training and using Gaussian kernel SVMs by approximating the kernel with an explicit finite- dimensional polynomial feature representation based on the Taylor expansion of the exponential. Although not as efficient as the…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…
Acquiring labels are often costly, whereas unlabeled data are usually easy to obtain in modern machine learning applications. Semi-supervised learning provides a principled machine learning framework to address such situations, and has been…
Common workflows in machine learning and statistics rely on the ability to partition the information in a data set into independent portions. Recent work has shown that this may be possible even when conventional sample splitting is not…
Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward…
Reliable prediction of protein variant effects is crucial for both protein optimization and for advancing biological understanding. For practical use in protein engineering, it is important that we can also provide reliable uncertainty…
Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…
Gaussian processes offer a flexible kernel method for regression. While Gaussian processes have many useful theoretical properties and have proven practically useful, they suffer from poor scaling in the number of observations. In…
We propose a principled way to define Gaussian process priors on various sets of unweighted graphs: directed or undirected, with or without loops. We endow each of these sets with a geometric structure, inducing the notions of closeness and…
Regularized least-squares (kernel-ridge / Gaussian process) regression is a fundamental algorithm of statistics and machine learning. Because generic algorithms for the exact solution have cubic complexity in the number of datapoints, large…
We propose a pointwise inference algorithm for high-dimensional linear models with time-varying coefficients. The method is based on a novel combination of the nonparametric kernel smoothing technique and a Lasso bias-corrected ridge…
We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…