Fully Heteroscedastic Count Regression with Deep Double Poisson Networks
This addresses the problem of uncertainty estimation in count regression for AI systems, providing a novel method for applications where count data is critical, though it is incremental as it adapts existing heteroscedastic Gaussian approaches to a new domain.
The paper tackled the lack of neural networks for accurate uncertainty representation in count regression by proposing the Deep Double Poisson Network (DDPN), which outputs Double Poisson distribution parameters to enable flexible aleatoric uncertainty and improves epistemic uncertainty estimation when ensembled, outperforming current baselines in accuracy, calibration, and out-of-distribution detection.
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.