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

TL;DR

This paper introduces DRIFT, a neural framework for distributional regression using inverse flow transformations, capable of replacing classical models like the Cox model in various applications involving continuous and survival data.

Contribution

The paper proposes DRIFT, a novel neural-based framework for distributional regression that encompasses traditional models and demonstrates comparable performance in multiple tasks.

Findings

Neural representations in DRIFT can substitute classical statistical models.

DRIFT matches traditional models in estimation, prediction, and uncertainty quantification.

The framework applies to diverse data types including survival and time-series.

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.