Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Rates of Convergence for Sparse Variational Gaussian Process Regression
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use eigenfunction inducing features with M=\BigO(\log N) | Sparse variational GP · Squared exponential kernel with Gaussian inputs (1D) | KL divergence: M=\BigO(\log N) | Helped |
| Use inducing points with approximate k-DPP initialization and M=\BigO(\log^D N) | Sparse variational GP · Squared exponential ARD kernel with Gaussian inputs (D dimensions) | KL divergence: M=\BigO(\log^D N) | Helped |
| Use eigenfunction features for a Matérn k+1/2 kernel | Sparse variational GP · Uniform inputs on an interval (1D) | inducing features for KL convergence: M=N^{\alpha} with \alpha>\frac{1}{2k+1} | Helped |
| Use inducing points with approximate k-DPP initialization instead of eigenfunction features | Sparse variational GP · Matérn k+1/2 kernel with uniform inputs (1D) | inducing variables for KL convergence: M=N^{\alpha} with \alpha > 1/(2k); M=N^{\alpha} with \alpha > 1/(2k+1) | Mixed |
| Increase the number of inducing variables as the dataset grows | Sparse variational GP · GP regression with fixed input interval | expected KL divergence: \frac{t}{2\sn^{2}}\leq \E_y [\KL{Q}{\hat{P}} ] \leq \frac{t}{\sn^2} | Helped |
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