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We propose practical deep Gaussian process models on Riemannian manifolds, similar in spirit to residual neural networks. With manifold-to-manifold hidden layers and an arbitrary last layer, they can model manifold- and scalar-valued…
Gaussian processes (GPs) are non-linear probabilistic models popular in many applications. However, na\"ive GP realizations require quadratic memory to store the covariance matrix and cubic computation to perform inference or evaluate the…
Many applications in speech, robotics, finance, and biology deal with sequential data, where ordering matters and recurrent structures are common. However, this structure cannot be easily captured by standard kernel functions. To model such…
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…
This paper introduces an active learning framework for manifold Gaussian Process (GP) regression, combining manifold learning with strategic data selection to improve accuracy in high-dimensional spaces. Our method jointly optimizes a…
Gaussian Process (GP) regression has seen widespread use in robotics due to its generality, simplicity of use, and the utility of Bayesian predictions. The predominant implementation of GP regression is a nonparameteric kernel-based…
Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost and it is difficult to design nonstationary GP priors in practice. In this paper, we propose…
We propose a new approach to inverse reinforcement learning (IRL) based on the deep Gaussian process (deep GP) model, which is capable of learning complicated reward structures with few demonstrations. Our model stacks multiple latent GP…
Gaussian Processes (GPs) are flexible, nonparametric Bayesian models widely used for regression and classification because of their ability to capture complex data patterns and quantify predictive uncertainty. However, the O(n^3)…
Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator,…
We introduce a scalable Bayesian preference learning method for identifying convincing arguments in the absence of gold-standard rat- ings or rankings. In contrast to previous work, we avoid the need for separate methods to perform quality…
In this paper we introduce a novel framework for making exact nonparametric Bayesian inference on latent functions, that is particularly suitable for Big Data tasks. Firstly, we introduce a class of stochastic processes we refer to as…
Gaussian process training decomposes into inference of the (approximate) posterior and learning of the hyperparameters. For non-Gaussian (non-conjugate) likelihoods, two common choices for approximate inference are Expectation Propagation…
We study wide Bayesian neural networks focusing on the rare but statistically dominant fluctuations that govern posterior concentration, beyond Gaussian-process limits. Large-deviation theory provides explicit variational objectives-rate…
The analytic inference, e.g. predictive distribution being in closed form, may be an appealing benefit for machine learning practitioners when they treat wide neural networks as Gaussian process in Bayesian setting. The realistic widths,…
Physical phenomena are observed in many fields (sciences and engineering) and are often studied by time-consuming computer codes. These codes are analyzed with statistical models, often called emulators. In many situations, the physical…
A multi-layer deep Gaussian process (DGP) model is a hierarchical composition of GP models with a greater expressive power. Exact DGP inference is intractable, which has motivated the recent development of deterministic and stochastic…
In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…
In many areas of science and engineering, discovering the governing differential equations from the noisy experimental data is an essential challenge. It is also a critical step in understanding the physical phenomena and prediction of the…
Bayesian inference and kernel methods are well established in machine learning. The neural network Gaussian process in particular provides a concept to investigate neural networks in the limit of infinitely wide hidden layers by using…