A1156
Title: Quantifying model complexity in normalizing flows
Authors: Alexander Ritz - Clausthal University of Technology (Germany) [presenting]
Benjamin Saefken - Clausthal University of Technology (Germany)
Abstract: Normalizing flows offer a flexible and interpretable way to obtain conditional density estimates based on a transformation model. While there is an intuitive relation between the parameterisation chosen for the underlying transformation function and the complexity of the model, an exact quantification has not been derived so far. Within the literature, there appears to be no clear justification for a particular choice of model other than the expressiveness of the transformation (universality being preferred usually) and its numerical or analytic convenience. While these are important concerns, deriving a more formalised motivation could help avoid over- and underfitting, allowing researchers to base their model selection on a more objective measure. One way to construct such a model choice criterion may be formulated analogously to established covariance penalties for prediction error estimates, utilizing the underlying normal distribution of the model class. The performance of such an approach is then assessed by means of a simulation study; evaluating the impact of the derived model choice criterion on the prediction error of the chosen model. Likewise, the chosen models' transformation complexity in terms of parameter count and expressiveness is assessed in order to judge their parsimony.
