Research map / Probabilistic and scientific modeling / Variational and generative sampling
Measuring Sample Quality with Kernels
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use IMQ kernel (beta=-1/2, c=1) instead of Gaussian kernel for KSD one-sample test | KSD one-sample hypothesis test · Multivariate normality test, d=2 to 25, n=500 | power: power 1.0 vs 0.02 at d=25; 1.0 vs 0.12 at d=20 | Helped |
| Use Gaussian base kernel in KSD (versus IMQ) for off-target sequences in dimension d>=3 | Gaussian KSD · Off-target sequence, P=N(0,I_d) | KSD value | Hurt |
| IMQ kernel with beta in (-1,0) versus light-tailed kernels (Gaussian, Matern, compact) | KSD sample quality measure · Theory: Gaussian/Matern/compactly supported kernels, d>=3 | detects non-convergence | Helped |
| Select approximate slice sampler tolerance using IMQ KSD instead of ESS | Approximate slice sampler hyperparameter epsilon · Bimodal Gaussian mixture posterior | selected epsilon: KSD selects 1e-2; ESS selects 1e-1 | Helped |
| KSD computation vs graph Stein discrepancy computation time | IMQ KSD · i.i.d. target samples, d=4 | computation time: 10 to 1000 times faster when d=4 | Helped |
| Use IMQ kernel with beta=-1/2 in KSD, versus Gaussian kernel in sample improvement objective | Sample quality improvement (Liu & Lee 2016) · Gaussian target N(0,I_d), n=100, mean estimation MSE | mean squared error of mean estimate | Helped |
| Use SGFS-d sampler (diagonal) instead of SGFS-f (full matrix) | Stochastic Gradient Fisher Scoring samplers · Bayesian logistic regression on MNIST (d=51) | IMQ KSD and per-sample time: 0.0017s vs 0.0019s per sample | Hurt |
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