HTGAN: heavy-tail GAN for multivariate dependent extremes via latent-dimensional control

Dealing with extreme values is a key challenge in probabilistic modeling, relevant to economics, engineering, and life sciences. Standard GANs, built on light-tailed noise, fail to capture heavy-tail behavior and dependence in extreme regions. We propose HTGAN, a modified GAN with heavy-tailed input noise. Using the stable tail dependence function (stdf) from extreme-value theory, we derive a worst-case error bound for approximating the stdf of the target, scaling as (Formula presented.), where N is the latent noise dimension and the data dimension. Thus, higher latent dimension improves dependence estimation. Experiments on synthetic and real heavy-tailed datasets confirm that HTGAN better reproduces extreme dependence than classical light-tailed GANs, with accuracy improving as latent dimension increases.