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A Generalized Stochastic Variational Bayesian Hyperparameter Learning Framework for Sparse Spectrum Gaussian Process Regression | | Quang Minh Hoang
; Trong Nghia Hoang
; Kian Hsiang Low
; | | Date: |
18 Nov 2016 | | Abstract: | While much research effort has been dedicated to scaling up sparse Gaussian
process (GP) models based on inducing variables for big data, little attention
is afforded to the other less explored class of low-rank GP approximations that
exploit the sparse spectral representation of a GP kernel. This paper presents
such an effort to advance the state of the art of sparse spectrum GP models to
achieve competitive predictive performance for massive datasets. Our
generalized framework of stochastic variational Bayesian sparse spectrum GP
(sVBSSGP) models addresses their shortcomings by adopting a Bayesian treatment
of the spectral frequencies to avoid overfitting, modeling these frequencies
jointly in its variational distribution to enable their interaction a
posteriori, and exploiting local data for boosting the predictive performance.
However, such structural improvements result in a variational lower bound that
is intractable to be optimized. To resolve this, we exploit a variational
parameterization trick to make it amenable to stochastic optimization.
Interestingly, the resulting stochastic gradient has a linearly decomposable
structure that can be exploited to refine our stochastic optimization method to
incur constant time per iteration while preserving its property of being an
unbiased estimator of the exact gradient of the variational lower bound.
Empirical evaluation on real-world datasets shows that sVBSSGP outperforms
state-of-the-art stochastic implementations of sparse GP models. | | Source: | arXiv, 1611.6080 | | Services: | Forum | Review | PDF | Favorites | |
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