Density Estimation-based Stein Variational Gradient Descent

Abstract Approximating a target distribution is important in many statistical problems, such as Bayesian inference. We introduce a variant of Stein variational gradient descent, called the density estimation-based Stein variational gradient descent (DESVGD). DESVGD utilizes kernel density estimation techniques to replace the empirical measure in SVGD with its continuous counterpart, which allows direct computation of the KL divergence between the current approximation and the target and thereby helps monitoring the numerical convergence of the iterative optimization process. DESVGD also offers derivatives of the KL divergence, which can be used to better design learning rates and thus to achieve faster convergence. By simply replacing the kernel used in SVGD with its weighted average, the implementation of DESVGD reduces to that of SVGD. Our numerical experiments demonstrate that DESVGD well approximates the target distribution and that it outperforms the original SVGD in terms of approximation quality.