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A Non-Asymptotic Analysis for Stein Variational Gradient Descent
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply discrete-time SVGD with a sufficiently small step size under the stated boundedness and smoothness assumptions | SVGD · Population regime | KL divergence: KL(μ_{n+1}|π)-KL(μ_n|π)≤ -γ (1- γ ((α² + M)B²)/2) I_stein(μ_n|π) | Helped |
| Use discrete-time SVGD with the stated step-size assumptions | SVGD · Population regime | Average Stein Fisher Information: 1/n ∑_{k=1}^n I_Stein(μ_k|π)≤ KL(μ_0|π)/(c_γ n) | Helped |
| Use N interacting particles to approximate population SVGD | Finite-particle SVGD · Finite-particle approximation | Expected squared W₂ distance to population distribution: E[W₂²(μ_n,μ̂_n)]≤ 1/2(1/√N √var(μ_0)e^{LT})(e^{2LT}-1) | Helped |
| Assume the Stein log-Sobolev inequality | SVGD gradient flow · Continuous-time population regime | KL divergence: KL(μ_t|π)≤ e^{-2λt}KL(μ_0|π) | Helped |
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