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Stein Variational Gradient Descent (SVGD) can transport particles alongtrajectories that reduce the KL divergence between the target and particledistribution but requires the target score function to compute the update. Weintroduce a new perspective on SVGD that views it as a local estimator of thereversed KL gradient flow. This perspective inspires us to propose newestimators that use local linear models to achieve the same purpose. Theproposed estimators can be computed using only samples from the target andparticle distribution without needing the target score function. Our proposedvariational gradient estimators utilize local linear models, resulting incomputational simplicity while maintaining effectiveness comparable to SVGD interms of estimation biases. Additionally, we demonstrate that under a mildassumption, the estimation of high-dimensional gradient flow can be translatedinto a lower-dimensional estimation problem, leading to improved estimationaccuracy. We validate our claims with experiments on both simulated andreal-world datasets.

Variational Gradient Descent using Local Linear Models