Phase-Type Variational Autoencoders for Heavy-Tailed Data

• URL: http://arxiv.org/abs/2603.01800v1
• Date: Mon, 02 Mar 2026 12:32:42 GMT
• Title: Phase-Type Variational Autoencoders for Heavy-Tailed Data
• Authors: Abdelhakim Ziani, András Horváth, Paolo Ballarini,
• Abstract summary: Heavy-tailed distributions are ubiquitous in real-world data, where rare but extreme events dominate risk and variability.<n>We propose the Phase-Type Variational Autoencoder (PH-VAE), whose decoder distribution is a latent-conditioned Phase-Type (PH) distribution.<n> Experiments on synthetic and real-world benchmarks demonstrate that PH-VAE accurately recovers diverse heavy-tailed distributions.
• Score: 0.20854674413792754
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Heavy-tailed distributions are ubiquitous in real-world data, where rare but extreme events dominate risk and variability. However, standard Variational Autoencoders (VAEs) employ simple decoder distributions (e.g., Gaussian) that fail to capture heavy-tailed behavior, while existing heavy-tail-aware extensions remain restricted to predefined parametric families whose tail behavior is fixed a priori. We propose the Phase-Type Variational Autoencoder (PH-VAE), whose decoder distribution is a latent-conditioned Phase-Type (PH) distribution defined as the absorption time of a continuous-time Markov chain (CTMC). This formulation composes multiple exponential time scales, yielding a flexible and analytically tractable decoder that adapts its tail behavior directly from the observed data. Experiments on synthetic and real-world benchmarks demonstrate that PH-VAE accurately recovers diverse heavy-tailed distributions, significantly outperforming Gaussian, Student-t, and extreme-value-based VAE decoders in modeling tail behavior and extreme quantiles. In multivariate settings, PH-VAE captures realistic cross-dimensional tail dependence through its shared latent representation. To our knowledge, this is the first work to integrate Phase-Type distributions into deep generative modeling, bridging applied probability and representation learning.

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