How Inverse Conditional Flows Can Serve as a Substitute for Distributional Regression

Lucas Kook, Chris Kolb, Philipp Schiele, Daniel Dold, Marcel Arpogaus, Cornelius Fritz, Philipp F. M. Baumann, Philipp Kopper, Tobias Pielok, Emilio Dorigatti, David Rügamer

Keywords: Normalizing Flows, Distribution Regression, Transformation Models, Aleatoric Uncertainty

Abstract: Neural network representations of simple models, such as linear regression, are being studied increasingly to better understand the underlying principles of deep learning algorithms. However, neural representations of distributional regression models, such as the Cox model, have received little attention so far. We close this gap by proposing a framework for distributional regression using inverse flow transformations (DRIFT), which includes neural representations of the aforementioned models. We empirically demonstrate that the neural representations of models in DRIFT can serve as a substitute for their classical statistical counterparts in several applications involving continuous, ordered, time-series, and survival outcomes. We confirm that models in DRIFT empirically match the performance of several statistical methods in terms of estimation of partial effects, prediction, and aleatoric uncertainty quantification. DRIFT covers both interpretable statistical models and flexible neural networks opening up new avenues in both statistical modeling and deep learning.

List Of Authors: Kook, Lucas and Kolb, Chris and Schiele, Philipp and Dold, Daniel and Arpogaus, Marcel and Fritz, Cornelius and Baumann, Philipp and Kopper, Philipp and Pielok, Tobias and Dorigatti, Emilio and Ruegamer, David

Submission Number: 134