Fat-Tailed Variational Inference with Anisotropic Tail Adaptive Flows
This work addresses a fundamental limitation in flow-based methods for robust modeling, enabling more accurate variational inference in domains with anisotropic tails, though it is incremental in improving existing theory and methods.
The paper tackles the challenge of accurately modeling fat-tailed distributions in variational inference, where Gaussian-based methods often fail, by proposing anisotropic tail-adaptive flows (ATAF) that address tail-anisotropy, and experimental results show ATAF is competitive with prior work while capturing appropriate tail-anisotropy.
While fat-tailed densities commonly arise as posterior and marginal distributions in robust models and scale mixtures, they present challenges when Gaussian-based variational inference fails to capture tail decay accurately. We first improve previous theory on tails of Lipschitz flows by quantifying how the tails affect the rate of tail decay and by expanding the theory to non-Lipschitz polynomial flows. Then, we develop an alternative theory for multivariate tail parameters which is sensitive to tail-anisotropy. In doing so, we unveil a fundamental problem which plagues many existing flow-based methods: they can only model tail-isotropic distributions (i.e., distributions having the same tail parameter in every direction). To mitigate this and enable modeling of tail-anisotropic targets, we propose anisotropic tail-adaptive flows (ATAF). Experimental results on both synthetic and real-world targets confirm that ATAF is competitive with prior work while also exhibiting appropriate tail-anisotropy.