Title: Adversarial Variational Bayes Methods for Tweedie Compound Poisson Mixed Models,
Abstract: The Tweedie Compound Poisson-Gamma model is routinely used for modeling
non-negative continuous data with a discrete probability mass at zero. Mixed
models with random effects account for the covariance structure related to the
grouping hierarchy in the data. An important application of Tweedie mixed
models is pricing the insurance policies, e.g. car insurance. However, the
intractable likelihood function, the unknown variance function, and the
hierarchical structure of mixed effects have presented considerable challenges
for drawing inferences on Tweedie. In this study, we tackle the Bayesian
Tweedie mixed-effects models via variational inference approaches. In
particular, we empower the posterior approximation by implicit models trained
in an adversarial setting. To reduce the variance of gradients, we
reparameterize random effects, and integrate out one local latent variable of
Tweedie. We also employ a flexible hyper prior to ensure the richness of the
approximation. Our method is evaluated on both simulated and real-world data.
Results show that the proposed method has smaller estimation bias on the random
effects compared to traditional inference methods including MCMC; it also
achieves a state-of-the-art predictive performance, meanwhile offering a richer
estimation of the variance function.