Our initial investigation identifies which distributions accurately characterize the feature space, subsequently leveraging this priori to guide the alignment of the weakly supervised embeddings. Specifically, we analyze the superiority of the mixture of von Mises-Fisher distributions (moVMF) among several common distribution candidates.

This section describes Stein variational gradient descent (SVGD) by Liu and Wang [19]. The overview is meant as supplementary material for Section 5, where we propose to use SVGD for inferring the DiBS posteriors p(Z | D) and p(Z, Θ | D). In contrast to sampling-based MCMC or optimizationbased variational inference methods, SVGD iteratively transports a fixed set of particles to closely match a target distribution, akin to the gradient descent algorithm in optimization. We refer the reader to Liu and Wang [19] for additional details. Let p(x) with x X be a differentiable density that we want to sample from, e.g., to estimate an expectation.