How Inverse Conditional Flows Can Serve as a Substitute for Distributional Regression
This work addresses the gap in neural representations for distributional regression, offering a substitute for statistical models in applications like survival analysis, though it appears incremental as it builds on existing flow transformations.
The authors tackled the lack of neural network representations for distributional regression models like the Cox model by proposing DRIFT, a framework using inverse flow transformations, and demonstrated that it matches classical statistical methods in performance for various outcomes.
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.