Neural transport augmented samplers have been subsequently extended by Hoffman et al. (2019) While, Duncan et al. (2019) have studied the Another contribution of this paper is learning equivariant Energy-Based Models using equivariant Stein variational gradient descent. Energy Based Models have witnessed a revival recently. As far as the authors are aware. Figure 8: Recommended to view in color . Translucent yellow dots represent the distribution.

We first introduce Equivari-ant Stein V ariational Gradient Descent algorithm - an equivariant sampling method based on Stein's identity for sampling from densities with symmetries.

We focus on the problem of efficient sampling and learning of probability densities by incorporating symmetries in probabilistic models. We first introduce Equivariant Stein Variational Gradient Descent algorithm -- an equivariant sampling method based on Stein's identity for sampling from densities with symmetries. Equivariant SVGD explicitly incorporates symmetry information in a density through equivariant kernels which makes the resultant sampler efficient both in terms of sample complexity and the quality of generated samples. Subsequently, we define equivariant energy based models to model invariant densities that are learned using contrastive divergence. By utilizing our equivariant SVGD for training equivariant EBMs, we propose new ways of improving and scaling up training of energy based models. We apply these equivariant energy models for modelling joint densities in regression and classification tasks for image datasets, many-body particle systems and molecular structure generation.