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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…
The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Processes are a popular class of models used for this purpose…
Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…
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…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…
Most machine learning methods require careful selection of hyper-parameters in order to train a high performing model with good generalization abilities. Hence, several automatic selection algorithms have been introduced to overcome tedious…
Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we…
Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
Gaussian processes offer a flexible kernel method for regression. While Gaussian processes have many useful theoretical properties and have proven practically useful, they suffer from poor scaling in the number of observations. In…
This paper is concerned with the problem of how to speed up computation for Gaussian process models trained on autocorrelated data. The Gaussian process model is a powerful tool commonly used in nonlinear regression applications. Standard…
Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become…
Gaussian Processes are used in many applications to model spatial phenomena. Within this context, a key issue is to decide the set of locations where to take measurements so as to obtain a better approximation of the underlying function.…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
We introduce fully scalable Gaussian processes, an implementation scheme that tackles the problem of treating a high number of training instances together with high dimensional input data. Our key idea is a representation trick over the…
Gaussian processes (GP) provide a prior over functions and allow finding complex regularities in data. Gaussian processes are successfully used for classification/regression problems and dimensionality reduction. In this work we consider…