Revisiting the Sample Complexity of Sparse Spectrum Approximation of Gaussian Processes

Part of Advances in Neural Information Processing Systems 33 (NeurIPS 2020)

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Minh Hoang, Nghia Hoang, Hai Pham, David Woodruff


We introduce a new scalable approximation for Gaussian processes with provable guarantees which holds simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse spectrum Gaussian processes (SSGPs). In particular, our analysis shows that under a certain data disentangling condition, an SSGP's prediction and model evidence (for training) can well-approximate those of a full GP with low sample complexity. We also develop a new auto-encoding algorithm that finds a latent space to disentangle latent input coordinates into well-separated clusters, which is amenable to our sample complexity analysis. We validate our proposed method on several benchmarks with promising results supporting our theoretical analysis.