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. We propose to address these
issues by training a neural network to output the parameters of a Double
Poisson distribution, which we call the Deep Double Poisson Network (DDPN). In
contrast to existing methods that are trained to minimize Gaussian negative log
likelihood (NLL), DDPNs produce a proper probability mass function over
discrete output. Additionally, DDPNs naturally model under-, over-, and
equi-dispersion, unlike networks trained with the more rigid Poisson and
Negative Binomial parameterizations. We show DDPNs 1) vastly outperform
existing discrete models; 2) meet or exceed the accuracy and flexibility of
networks trained with Gaussian NLL; 3) produce proper predictive distributions
over discrete counts; and 4) exhibit superior out-of-distribution detection.
DDPNs can easily be applied to a variety of count regression datasets including
tabular, image, point cloud, and text data.

神经网络可以准确地产生需要的、与输入相关的不确定性表示，这对现实世界的应用至关重要。最近在异方差连续回归方面取得的进展显示了在复杂任务（如图像回归）上进行校准的不确定性量化的巨大潜力。然而，当将这些方法应用于离散回归任务（如人群计数、评级预测或库存估计）时，它们往往会产生具有许多病态的预测分布。我们提出通过训练神经网络输出双泊松分布的参数来解决这些问题，我们将其称为深度双泊松网络（DDPN）。与现有方法不同，它们是经过训练以最小化高斯负对数似然（NLL）的，DDPNs 会生成离散输出上的正确概率质量函数。此外，DDPNs 自然地对低、高和等离散度建模，而不像使用更严格的泊松和负二项参数化进行训练的网络。我们展示了 DDPNs：1）远远优于现有的离散模型；2）实现或超过使用高斯 NLL 进行训练的网络的准确性和灵活性；3）产生适当的离散计数的预测分布；4）具有优秀的超出分布检测能力。DDPNs 可以轻松应用于各种计数回归数据集，包括表格、图像、点云和文本数据。