Related papers: Process convolution approaches for modeling intera…

Recently there has been an increasing interest in methods that deal with multiple outputs. This has been motivated partly by frameworks like multitask learning, multisensor networks or structured output data. From a Gaussian processes…

Research on Poisson regression analysis for dependent data has been developed rapidly in the last decade. One of difficult problems in a multivariate case is how to construct a cross-correlation structure and at the meantime make sure that…

We propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input…

Link prediction aims to reveal missing edges in a graph. We address this task with a Gaussian process that is transformed using simplified graph convolutions to better leverage the inductive bias of the domain. To scale the Gaussian process…

Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…

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…

Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic…

Gaussian processes (GPs) are pervasive in functional data analysis, machine learning, and spatial statistics for modeling complex dependencies. Modern scientific data sets are typically heterogeneous and often contain multiple known…

Neural processes are a family of models which use neural networks to directly parametrise a map from data sets to predictions. Directly parametrising this map enables the use of expressive neural networks in small-data problems where neural…

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…

Graph classification is a fundamental but challenging issue for numerous real-world applications. Despite recent great progress in image/video classification, convolutional neural networks (CNNs) cannot yet cater to graphs well because of…

Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…

Improved communication systems, shrinking battery sizes and the price drop of tracking devices have led to an increasing availability of trajectory tracking data. These data are often analyzed to understand animal behavior. In this work, we…

We develop a Gaussian process framework for learning interaction kernels in multi-species interacting particle systems from trajectory data. Such systems provide a canonical setting for multiscale modeling, where simple microscopic…

We consider a modification of the covariance function in Gaussian processes to correctly account for known linear constraints. By modelling the target function as a transformation of an underlying function, the constraints are explicitly…

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…

Biological data objects often have both of the following features: (i) they are functions rather than single numbers or vectors, and (ii) they are correlated due to phylogenetic relationships. In this paper we give a flexible statistical…

Graph convolutional networks adapt the architecture of convolutional neural networks to learn rich representations of data supported on arbitrary graphs by replacing the convolution operations of convolutional neural networks with…