Fully Heteroscedastic Count Regression with Deep Double Poisson Networks

TL;DR

This paper introduces the Deep Double Poisson Network (DDPN), a novel neural count regression model that effectively captures input-dependent uncertainty and outperforms existing methods in accuracy and calibration.

Contribution

The paper proposes DDPN, the first neural count regression model with heteroscedastic uncertainty modeling and improved epistemic uncertainty estimation, advancing count data analysis.

Findings

DDPN outperforms baselines in accuracy and calibration.

DDPN provides robust uncertainty estimates for count data.

DDPN achieves state-of-the-art results in deep count regression.

Abstract

Neural networks capable of accurate, input-conditional uncertainty representation are essential for real-world AI systems. Deep ensembles of Gaussian networks have proven highly effective for continuous regression due to their ability to flexibly represent aleatoric uncertainty via unrestricted heteroscedastic variance, which in turn enables accurate epistemic uncertainty estimation. However, no analogous approach exists for count regression, despite many important applications. To address this gap, we propose the Deep Double Poisson Network (DDPN), a novel neural discrete count regression model that outputs the parameters of the Double Poisson distribution, enabling arbitrarily high or low predictive aleatoric uncertainty for count data and improving epistemic uncertainty estimation when ensembled. We formalize and prove that DDPN exhibits robust regression properties similar to heteroscedastic Gaussian models via learnable loss attenuation, and introduce a simple loss modification to control this behavior. Experiments on diverse datasets demonstrate that DDPN outperforms current baselines in accuracy, calibration, and out-of-distribution detection, establishing a new state-of-the-art in deep count regression.