Title: Pareto Variational Autoencoder
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Keywords: Variational autoencoder, Pareto distribution, Information geometry, Heavy-tail learning, Heavy-tail Modeling

Abstract: Incorporating robustness in generative modeling has enticed many researchers of the field.
To this end, we introduce a new class of multivariate power-law distributions---the symmetric Pareto (symPareto) distribution---which can be viewed as an $\ell_1$-norm-based counterpart of the multivariate $t$ distribution.
The symPareto distribution possesses many attractive information-geometric properties with respect to the $\gamma$-power divergence that naturally populates power-law families.
Leveraging on the joint minimization view of variational inference, we propose the ParetoVAE, a probabilistic autoencoder that minimizes the $\gamma$-power divergence between two statistical manifolds.
ParetoVAE employs the symPareto distribution for both prior and encoder, with flexible decoder options including Student's $t$ and symPareto distributions.  Empirical evidences demonstrate ParetoVAE's effectiveness across multiple domains through varying the types of the decoder. The $t$ decoder achieves superior performance in sparse, heavy-tailed data reconstruction and word frequency analysis; the symPareto decoder enables robust high-dimensional denoising.