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Understanding Probabilistic Sparse Gaussian Process Approximations
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use VFE instead of FITC for sparse GP regression | sparse Gaussian process regression · Snelson dataset, 100-point subset | predictive distribution fidelity to the full GP | Helped |
| Use FITC instead of VFE | sparse Gaussian process regression · Snelson dataset, 100-point subset | noise variance calibration: σn = 1.93 · 10−4; σn = 0.286; full GP σn = 0.274 | Hurt |
| Increase the number of inducing inputs | VFE · sparse GP regression | marginal likelihood bound | Helped |
| Increase the number of inducing inputs | FITC · sparse GP regression | marginal likelihood objective | Mixed |
| Add inducing inputs without further hyperparameter optimization | FITC · Snelson dataset, 200 points | data fit | Hurt |
| Allow inducing inputs to clump on top of one another | FITC · Snelson dataset | recovery of the full GP posterior: 33.8923 -> 28.3869 | Hurt |
| Optimize inducing inputs from the exact-posterior configuration | FITC · Snelson dataset, 100-point subset | NLML: 33.8923 -> 28.3869 | Helped |
| Optimize inducing inputs from the exact-posterior configuration | VFE · Snelson dataset, 100-point subset | NLML: 33.8923 -> 33.8923 | No clear effect |
| Initialize VFE by freezing hyperparameters initially (ablation) | VFE on pumadyn32nm · pumadyn32nm | RMSE: 0.979 -> 0.276 | Helped |
| Initialize VFE with the FITC solution (ablation) | VFE on pumadyn32nm · pumadyn32nm | RMSE: 0.979 -> 0.212 | Helped |
| Jointly optimize VFE hyperparameters and inducing inputs from random initial conditions | VFE on pumadyn32nm · pumadyn32nm | RMSE: 0.209 -> 0.979 | Hurt |
| Use VFE rather than FITC with 40 inducing inputs | sparse GP regression · pumadyn32nm | noise variance calibration: 0.004; 1 | Mixed |
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