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About this paper
Tianle Liu, Promit Ghosal, Krishnakumar Balasubramanian, Natesh S. Pillai
Analyzing Stein Variational Gradient Descent (SVGD) projected onto Gaussian distributions with bilinear kernels, this work from Harvard and MIT determines linear convergence rates for mean-field and finite-particle systems and unifies several Gaussian Variational Inference algorithms.
Key insights
- SVGD dynamics with bilinear kernels, when initialized with a Gaussian distribution, preserve Gaussianity for Gaussian targets, enabling closed-form ODE analysis for the mean and covariance.
- The empirical measure of finite particles in Gaussian–SVGD converges uniformly in time to its mean-field limit for Gaussian targets, improving upon previous time-dependent bounds for general SVGD.
- Several existing Gaussian Variational Inference (GVI) algorithms can be unified and understood as specific cases of Gaussian–SVGD by choosing different bilinear kernels.
Summary by alphaXiv.
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