Marginal Tail-Adaptive Normalizing Flows
This work addresses a critical issue in deep generative modeling for applications like weather and climate, where accurate tail modeling is essential, though it is incremental in improving existing normalizing flow methods.
The paper tackles the problem of learning tail behavior in distributions, which is difficult due to limited tail samples, by improving normalizing flows to capture tails more accurately, resulting in enhanced accuracy, especially on distribution tails, and the ability to generate heavy-tailed data.
Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of the distribution. In this paper, we focus on improving the ability of normalizing flows to correctly capture the tail behavior and, thus, form more accurate models. We prove that the marginal tailedness of an autoregressive flow can be controlled via the tailedness of the marginals of its base distribution. This theoretical insight leads us to a novel type of flows based on flexible base distributions and data-driven linear layers. An empirical analysis shows that the proposed method improves on the accuracy -- especially on the tails of the distribution -- and is able to generate heavy-tailed data. We demonstrate its application on a weather and climate example, in which capturing the tail behavior is essential.