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SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the inverse Langevin generator as the kernel operator | LAWGD · Targets with a discrete spectrum satisfying a Poincaré inequality | KL divergence: D_KL(μ_t ∥ π) ≤ (D_KL(μ_0 ∥ π) ∧ 2) e^{-t}, for all t ≥ 1 | Helped |
| Use the identity operator for the kernelized chi-squared gradient flow | Chi-squared gradient flow · Targets satisfying a Poincaré inequality | KL divergence: D_KL(μ_t ∥ π) ≤ D_KL(μ_0 ∥ π) e^{-2t/C_P}, ∀ t ≥ 0 | Helped |
| Use the identity operator for the kernelized chi-squared gradient flow | Chi-squared gradient flow · Targets satisfying a Poincaré inequality | Chi-squared divergence: χ²(μ_t ∥ π) ≤ χ²(μ_0 ∥ π) ∧ (9C_P/(8t))² | Helped |
| Use the identity operator for the kernelized chi-squared gradient flow | Chi-squared gradient flow · Log-concave targets | Chi-squared divergence: χ²(μ_t ∥ π) ≤ χ²(μ_0 ∥ π) e^{-t/(2C_P)} | Helped |
| Use the identity operator for the kernelized chi-squared gradient flow | Chi-squared gradient flow · Targets satisfying a log-Sobolev inequality | Chi-squared divergence: χ²(μ_t ∥ π) ≤ (χ²(μ_0 ∥ π) ∧ 2) e^{-t/(9C_LSI)}, for all t ≥ 7C_LSI | Helped |
| Use a constant step size rather than a decreasing step size | SVGD · Two-dimensional Gaussian mixture with less favorable initialization | Particle convergence | Hurt |
| Use a truncated spectral kernel with the bottom 100 eigenvalues and eigenfunctions | LAWGD · Two-dimensional Gaussian mixture | Sampling performance | No clear effect |
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