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While much research effort has been dedicated to scaling up sparse Gaussianprocess (GP) models based on inducing variables for big data, little attentionis afforded to the other less explored class of low-rank GP approximations thatexploit the sparse spectral representation of a GP kernel. This paper presentssuch an effort to advance the state of the art of sparse spectrum GP models toachieve competitive predictive performance for massive datasets. Ourgeneralized framework of stochastic variational Bayesian sparse spectrum GP(sVBSSGP) models addresses their shortcomings by adopting a Bayesian treatmentof the spectral frequencies to avoid overfitting, modeling these frequenciesjointly in its variational distribution to enable their interaction aposteriori, and exploiting local data for boosting the predictive performance.However, such structural improvements result in a variational lower bound thatis intractable to be optimized. To resolve this, we exploit a variationalparameterization trick to make it amenable to stochastic optimization.Interestingly, the resulting stochastic gradient has a linearly decomposablestructure that can be exploited to refine our stochastic optimization method toincur constant time per iteration while preserving its property of being anunbiased estimator of the exact gradient of the variational lower bound.Empirical evaluation on real-world datasets shows that sVBSSGP outperformsstate-of-the-art stochastic implementations of sparse GP models.

A Generalized Stochastic Variational Bayesian Hyperparameter Learning Framework for Sparse Spectrum Gaussian Process Regression