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Title: Testing normalizing flows for posteriors in variational Bayes Authors:  Tim Kutzker - Humboldt University Berlin (Germany) [presenting]
Nadja Klein - Humboldt University Berlin (Germany)
Abstract: Normalizing flows (NFs) model complex probability density functions as concatenations of invertible (backward) transformations of simple densities with sound statistical characteristics. Data generation in return requires forward transformations. The ability to approximate and sample from arbitrary densities sufficiently well also brought NFs more and more into the spotlight to serve as variational densities in approximating complex posterior distributions through variational Bayes. To be practical in applications and to compete with existing methods such as MCMC, however, NFs must be sufficiently fast and efficient in both the forward and backward direction, which usually oppose each other. We propose a statistical test that first ensures that the NF approximates the probability density function sufficiently well and second follows the principle of parsimony ensuring the data is generated as fast as possible. For this purpose, we scale the multidimensional (density) test problem to the univariate (two-sample) Kolmogorov-Smirnov test approach by considering a standard uniformly distributed transformation of the highest probability density region, while retaining computational efficiency. We highlight the merits of our tests in a detailed MC study and a real data example.