We propose a Standing Wave Decomposition (SWD) approximation to Gaussian Process regression (GP). GP involves a costly matrix inversion operation, which limits applicability to large data analysis. For an input space that can be approximated by a grid and when correlations among data are short-ranged, the kernel matrix inversion can be replaced by analytic diagonalization using the SWD. We show...

•Combine Bayesian change point detection with Gaussian Processes to define a nonstationary time series model. •Central aim is to react to underlying regime changes in an online manner. •Able to integrate out all latent variables and optimize hyperparameters sequentially. •Explore three alternative ways of augmenting GP models to handle nonstationarity (GPTS, ARGPCP and NSGP – see below). •A Bay...

This paper explores nonparametric and semiparametric nonstationary modeling methodologies that couple stationary Gaussian processes and (limiting) linear models with treed partitioning. Partitioning is a simple but effective method for dealing with nonstationarity. Mixing between full Gaussian processes and simple linear models can yield a more parsimonious spatial model while significantly red...

Echo state networks (ESNs) constitute a novel approach to recurrent neural network (RNN) training, with an RNN (the reservoir) being generated randomly, and only a readout being trained using a simple, computationally efficient algorithm. ESNs have greatly facilitated the practical application of RNNs, outperforming classical approaches on a number of benchmark tasks. In this paper, we introduc...

Gaussian process prior with an appropriate likelihood function is a flexible non-parametric model for a variety of learning tasks. One important and standard task is multi-class classification, which is the categorization of an item into one of several fixed classes. A usual likelihood function for this is the multinomial logistic likelihood function. However, exact inference with this model ha...

Standard Gaussian processes (GPs) model observations’ noise as constant throughout input space. This is often a too restrictive assumption, but one that is needed for GP inference to be tractable. In this work we present a non-standard variational approximation that allows accurate inference in heteroscedastic GPs (i.e., under inputdependent noise conditions). Computational cost is roughly twic...

The Gaussian process latent variable model (GPLVM) is an unsupervised probabilistic model for nonlinear dimensionality reduction. A supervised extension, called discriminative GPLVM (DGPLVM), incorporates supervisory information into GPLVM to enhance the classification performance. However, its limitation of the latent space dimensionality to at most C − 1 (C is the number of classes) leads to ...

Consider the situation where we have some pre-trained classification models for bike rental stations (or any other spatially located data). Given a new rental station (deployment context), we imagine that there might be some rental stations that are more similar to this station in terms of the daily usage patterns, whether or not these stations are close by or not. We propose to use a Gaussian ...

Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires O(n) logic gates. We show that the quantum linear systems algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] can be applied to Gaussian process regression (GPR), leading to an exponential reduction in computation time in some inst...

Learning accurate models of complex clinical time-series data is critical for understanding the disease and its dynamics. Modeling of clinical time-series is particularly challenging because: observations are made at irregular time intervals and may be missing for long periods of time. In this work, we propose a new model of clinical time series data that is optimized to handle irregularly samp...