Stein Variational Gradient Descent



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In this work, we study an approach for variational Bayesian inference based on smooth diffeomorphic transformations. This approach is referred to as Stein Variational Gradient Descent (SVGD). The basic idea is to compute a diffeomorphic transport map that pushes forward a reference distribution (that is easy to manipulate) to a target distribution. This diffeomorphic transport map is found by minimizing the Kullback--Leibler divergence between the target and reference distribution. We compute first-order variations of the objective functional with respect to perturbations of the diffeomorphic map. This provides us with gradient information used to update particles to approximate the target distribution. The expression of the gradient can be significantly simplified by modeling the diffeomorphic transport map in a reproducing kernel Hilbert space. We showcase results for our implementation of the SVGD algorithm for one- and two-dimensional particles.



Mathematics, Computer science