Markov Chain Decoders Overcome the Heavy-Tail Limitations of Lipschitz Generative Models
Heavy-tailed distributions are prevalent in performance evaluation, network traffic, and risk modeling. This behavior poses a fundamental challenge for modern deep generative models. Standard Variational Autoencoders (VAEs) employ Gaussian decoder likelihoods and Lipschitz-constrained neural networks, a combination that is structurally incapable of producing heavy-tailed outputs: the Gaussian tail decays exponentially, and Lipschitz continuity prevents the decoder from amplifying rare events from the latent space input to sufficiently overcome this decay. We provide both a theoretical characterization of this limitation and a controlled empirical demonstration using synthetic Pareto data ...
| Authors | Abdelhakim Ziani, Andras Horvath, Paolo Ballarini |
|---|---|
| Primary category | stat.ML |
| Published | 18 May 2026 |
| Last updated at source | 3 June 2026 |
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