Fully Heteroscedastic Count Regression with Deep Double Poisson Networks

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 $\textit{count}$ 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.

Many real-world problems involve predicting counts — like how many people are in a photo or how many items will sell tomorrow. But it’s not enough to just predict a number; we also need to know how confident the model is in its prediction. Most existing tools struggle to provide reliable uncertainty for count data, especially when that uncertainty varies across inputs. In this work, we introduce a new neural network model that not only predicts counts accurately, but also captures how uncertain those predictions are — adapting to each situation. Our approach sets a new standard for reliability in count-based forecasting tasks, with strong performance across vision, medical, and retail datasets. This makes it easier to trust AI systems in settings where stakes are high and decisions depend on more than just a number.