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Learning expressive kernels while retaining tractable inference remains a central challenge in scaling Gaussian processes (GPs) to large and complex datasets. We propose a scalable GP regressor based on deep basis kernels (DBKs). Our DBK is…
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…
In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The…
Gaussian Process (GP) regression is a popular and sample-efficient approach for many engineering applications, where observations are expensive to acquire, and is also a central ingredient of Bayesian optimization (BO), a highly prevailing…
Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We…
A Gaussian process has been one of the important approaches for emulating computer simulations. However, the stationarity assumption for a Gaussian process and the intractability for large-scale dataset limit its availability in practice.…
Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of…
Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…
Kernel-based models such as kernel ridge regression and Gaussian processes are ubiquitous in machine learning applications for regression and optimization. It is well known that a major downside for kernel-based models is the high…
Recent works on Hierarchical Clustering (HC), a well-studied problem in exploratory data analysis, have focused on optimizing various objective functions for this problem under arbitrary similarity measures. In this paper we take the first…
Automating statistical modelling is a challenging problem in artificial intelligence. The Automatic Statistician takes a first step in this direction, by employing a kernel search algorithm with Gaussian Processes (GP) to provide…
In this paper, we formulate a new generalized reference kernel hoping to improve the original base kernel using a set of reference vectors. Depending on the selected reference vectors, our formulation shows similarities to approximate…
Gaussian process (GP) methods have been widely studied recently, especially for large-scale systems with big data and even more extreme cases when data is sparse. Key advantages of these methods consist in: 1) the ability to provide…
This paper presents a method for building a preconditioner for a kernel ridge regression problem, where the preconditioner is not only effective in its ability to reduce the condition number substantially, but also efficient in its…
Learning the kernel parameters for Gaussian processes is often the computational bottleneck in applications such as online learning, Bayesian optimization, or active learning. Amortizing parameter inference over different datasets is a…
Gaussian processes (GPs) are used to make medical and scientific decisions, including in cardiac care and monitoring of atmospheric carbon dioxide levels. Notably, the choice of GP kernel is often somewhat arbitrary. In particular,…
Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs…
Despite the growing popularity of explainable and interpretable machine learning, there is still surprisingly limited work on inherently interpretable clustering methods. Recently, there has been a surge of interest in explaining the…
Multiple datasets containing different types of features may be available for a given task. For instance, users' profiles can be used to group users for recommendation systems. In addition, a model can also use users' historical behaviors…
Kernel methods on discrete domains have shown great promise for many challenging data types, for instance, biological sequence data and molecular structure data. Scalable kernel methods like Support Vector Machines may offer good predictive…