Adversarial Variational Inference for Tweedie Compound Poisson Models
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Tweedie Compound Poisson models are heavily used for modelling non-negative continuous data with a discrete probability spike at zero. An important practice is the modelling of the aggregate claim loss for insurance policies in actuarial science. However, the intractable density function and the unknown variance function have presented considerable challenges for Tweedie regression models. Previous studies are focused on numerical approximations to the density function. In this study, we tackle the Bayesian Tweedie regression problem via a Variational approach. In particular, we empower the posterior approximation by an implicit model trained in the adversarial setting, introduce the hyper prior by making the parameters of the prior distribution trainable, and integrate out one local latent variable in Tweedie model to reduce the variance. Our method is evaluated on the application of predicting the losses for auto insurance policies. Results show that the proposed method enjoys a state-of-the-art performance among traditional inference methods, while having a richer estimation of the variance function.
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