Blitzkriging: Kronecker-structured Stochastic Gaussian Processes
This addresses a computational bottleneck for Gaussian processes in large datasets, applicable to regression, optimization, and classification, though it appears incremental as it builds on existing stochastic inference methods.
The paper tackles the cubic scaling of state-of-the-art Gaussian process inference with inducing points by introducing Blitzkriging, which reduces this scaling to approximately linear while maintaining data scaling and enabling learning of rich covariance structures without structural constraints.
We present Blitzkriging, a new approach to fast inference for Gaussian processes, applicable to regression, optimisation and classification. 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 benefits of our approach on real data in regression, time-series prediction and signal-interpolation experiments.