Zhiwei Tong
University of Iowa
Title
Generative Modeling and Latent Cross-Entropy Importance Sampling for Multivariate Rare Events
Abstract
Rare-event analysis of multivariate data requires an accurate model of the joint distribution and an efficient method for estimating tail quantities. We combine a generative adversarial network (GAN) with latent cross-entropy importance sampling to estimate event probabilities, conditional tail means, and component allocations. The GAN represents the multivariate distribution using a differentiable generator with standard Gaussian inputs. We use the generator Jacobian to locate a minimum-norm design point in the latent space, then adapt a Gaussian-mixture proposal toward the event region using likelihood-weighted pilot samples. Because the latent densities are available in closed form, importance weights can be computed exactly under the fitted distribution, without evaluating the output density or requiring an invertible generator. Under suitable latent tail regularity conditions, the retained design-point shift yields a logarithmically efficient estimator of event probabilities. We evaluate accuracy and efficiency using Gaussian scale-mixture models with heavy-tailed marginals and different dependence structures commonly used in default risk modeling. Across all test models, the GAN produces lower mean absolute errors in the tail quantities than the best of six matched vine copulas. Latent importance sampling also substantially reduces estimated variance compared with ordinary Monte Carlo.
