Sparse Gaussian Processes with Spherical Harmonic Features Revisited
This work provides an incremental improvement for researchers and practitioners using Gaussian processes in machine learning applications requiring high-dimensional inputs.
The authors tackled the challenge of scaling Gaussian processes with spherical harmonic features to higher dimensions and learning high-frequency variations by introducing sparseness in the eigenbasis through variational learning of phases. They validated their approach on benchmark datasets, achieving improved scalability and performance.
We revisit the Gaussian process model with spherical harmonic features and study connections between the associated RKHS, its eigenstructure and deep models. Based on this, we introduce a new class of kernels which correspond to deep models of continuous depth. In our formulation, depth can be estimated as a kernel hyper-parameter by optimizing the evidence lower bound. Further, we introduce sparseness in the eigenbasis by variational learning of the spherical harmonic phases. This enables scaling to larger input dimensions than previously, while also allowing for learning of high frequency variations. We validate our approach on machine learning benchmark datasets.