Blitzkriging: Kronecker-structured Stochastic Gaussian Processes

By T. Nickson, Tom Gunter, Chris M. Lloyd, Michael A. Osborne, Stephen J. Roberts. 2015

22 citations recorded by the source corpus.

We present Blitzkriging, a new approach to fast inference for Gaussian processes, applicable to regression, optimisation and classication. State-of-the-art (stochastic) inference for Gaussian processes on very large datasets scales cubically in the number of ‘inducing inputs’, variables introduced to factorise the model. Blitzkriging shares state-of-the-art scaling with data, but reduces the scaling in the number of inducing points to approximately linear. Further, in contrast to other methods, Blitzkriging: does not force the data to conform to any particular structure (including grid-like); reduces reliance on error-prone optimisation of inducing point locations; and is able to learn rich (covariance) structure from the data. We demonstrate the benets of our approach on real data in regression, time-series prediction and signal-interpolation experiments.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Statistical and Nonlinear Physics

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Citations in the corpus

Stochastic Variational Deep Kernel Learning (2016, background): “, [19, 11]), and some of the most recent work in this area applied variational auto-encoders [15] for coupled variational updates (aka back constraints) [5, 2].”
When Gaussian Process Meets Big Data: A Review of Scalable GPs (2018, background): “8 Finally, the scalability of SVGP can be further reduced to nearly O(m) by introducing Kronecker structures for inducing points and the variance of q( fm | y) [83], [84].”
Scalable Gaussian Processes with Billions of Inducing Inputs via Tensor Train Decomposition (2017, methodology): “L G ] 1 9 O ct 2 for the expectation µ of the variational distribution over the values u of the process at inducing inputs Z. Nickson et al. (2015) showed that using Kronecker format for Σ does not substantially affect the predictive performance of GP regression, while allowing for computational…”