Sparse pseudo-point approximations for Gaussian process (GP) models provide a suite of methods that support deployment of GPs in the large data regime and enable analytic intractabilities to be sidestepped. However, the field lacks a principled method to handle streaming data in which both the posterior distribution over function values and the hyperparameter estimates are updated in an online ...

This paper proposes the application of bagging to obtain more robust and accurate predictions using Gaussian process regression models. The training data is re-sampled using the bootstrap method to form several training sets, from which multiple Gaussian process models are developed and combined through weighting to provide predictions. A number of weighting methods for model combination are di...

High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear probabilistic approaches to this data are required. In this paper we introduce the variational Gaussian process dynamical system. Our work builds on recent varia...

Generalized autoregressive conditional heteroscedasticity (GARCH) models have long been considered as one of the most successful families of approaches for volatility modeling in financial return series. In this paper, we propose an alternative approach based on methodologies widely used in the field of statistical machine learning. Specifically, we propose a novel nonparametric Bayesian mixtur...

Peter Bartlett RSISE Australian National University Canberra, ACT, 0200 [email protected] We present a simple sparse greedy technique to approximate the maximum a posteriori estimate of Gaussian Processes with much improved scaling behaviour in the sample size m. In particular, computational requirements are O(n2m), storage is O(nm), the cost for prediction is 0 ( n) and the cost to com...

Many applications in machine learning require optimizing unknown functions defined over a high-dimensional space from noisy samples that are expensive to obtain. We address this notoriously hard challenge, under the assumptions that the function varies only along some low-dimensional subspace and is smooth (i.e., it has a low norm in a Reproducible Kernel Hilbert Space). In particular, we prese...

We present a new sparse Gaussian Process (GP) model for regression. The key novel idea is to sparsify the spectral representation of the GP. This leads to a simple, practical algorithm for regression tasks. We compare the achievable trade-offs between predictive accuracy and computational requirements, and show that these are typically superior to existing state-of-the-art sparse approximations...

How should we design experiments to maximize performance of a complexsystem, taking into account uncontrollable environmental conditions? Howshould we select relevant documents (ads) to display, given information about theuser? These tasks can be formalized as contextual bandit problems, where at eachround, we receive context (about the experimental conditions, the query), and<l...

We propose an efficient stochastic variational approach to Gaussian Process (GP) classification building on Pólya-Gamma data augmentation and inducing points, which is based on closed-form updates of natural gradients. We evaluate the algorithm on real-world datasets containing up to 11 million data points and demonstrate that it is up to two orders of magnitude faster than the state-of-the-art...