Flexible Heteroscedastic Count Regression with Deep Double Poisson Networks (2406.09262v2)

Abstract: Neural networks that can produce accurate, input-conditional uncertainty representations are critical for real-world applications. Recent progress on heteroscedastic continuous regression has shown great promise for calibrated uncertainty quantification on complex tasks, like image regression. However, when these methods are applied to discrete regression tasks, such as crowd counting, ratings prediction, or inventory estimation, they tend to produce predictive distributions with numerous pathologies. Moreover, discrete models based on the Generalized Linear Model (GLM) framework either cannot process complex input or are not fully heterosedastic. To address these issues we propose the Deep Double Poisson Network (DDPN). In contrast to networks trained to minimize Gaussian negative log likelihood (NLL), discrete network parameterizations (i.e., Poisson, Negative binomial), and GLMs, DDPN can produce discrete predictive distributions of arbitrary flexibility. Additionally, we propose a technique to tune the prioritization of mean fit and probabilistic calibration during training. We show DDPN 1) vastly outperforms existing discrete models; 2) meets or exceeds the accuracy and flexibility of networks trained with Gaussian NLL; 3) produces proper predictive distributions over discrete counts; and 4) exhibits superior out-of-distribution detection. DDPN can easily be applied to a variety of count regression datasets including tabular, image, point cloud, and text data.