
Stein Variational Gradient Descent as Gradient Flow
Stein variational gradient descent (SVGD) is a deterministic sampling al...
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Approximation beats concentration? An approximation view on inference with smooth radial kernels
Positive definite kernels and their associated Reproducing Kernel Hilber...
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Analyzing and Improving Stein Variational Gradient Descent for Highdimensional Marginal Inference
Stein variational gradient descent (SVGD) is a nonparametric inference m...
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On the geometry of Stein variational gradient descent
Bayesian inference problems require sampling or approximating highdimen...
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Gradient descent with identity initialization efficiently learns positive definite linear transformations by deep residual networks
We analyze algorithms for approximating a function f(x) = Φ x mapping ^d...
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Stein Variational Gradient Descent With MatrixValued Kernels
Stein variational gradient descent (SVGD) is a particlebased inference ...
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Stein Variational Gradient Descent as Moment Matching
Stein variational gradient descent (SVGD) is a nonparametric inference algorithm that evolves a set of particles to fit a given distribution of interest. We analyze the nonasymptotic properties of SVGD, showing that there exists a set of functions, which we call the Stein matching set, whose expectations are exactly estimated by any set of particles that satisfies the fixed point equation of SVGD. This set is the image of Stein operator applied on the feature maps of the positive definite kernel used in SVGD. Our results provide a theoretical framework for analyzing the properties of SVGD with different kernels, shedding insight into optimal kernel choice. In particular, we show that SVGD with linear kernels yields exact estimation of means and variances on Gaussian distributions, while random Fourier features enable probabilistic bounds for distributional approximation. Our results offer a refreshing view of the classical inference problem as fitting Stein's identity or solving the Stein equation, which may motivate more efficient algorithms.
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