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.

翻译：能够产生准确、输入条件不确定性表示的神经网络对于现实应用至关重要。异方差连续回归的最新进展在复杂任务（如图像回归）的校准不确定性量化方面展现出巨大潜力。然而，当这些方法应用于离散回归任务（如人群计数、评分预测或库存估计）时，往往会产生具有多种病理特征的预测分布。我们提出通过训练神经网络输出双泊松分布参数来解决这些问题，该网络被称为深度双泊松网络（DDPN）。与现有通过最小化高斯负对数似然（NLL）进行训练的方法不同，DDPN能够生成离散输出的恰当概率质量函数。此外，相较于采用更严格泊松和负二项式参数化训练的网络，DDPN能够自然地建模欠离散、过离散和等离散现象。我们证明DDPN具有以下优势：1）显著优于现有离散模型；2）在准确性和灵活性方面达到或超过高斯NLL训练的网络；3）生成离散计数的恰当预测分布；4）展现出卓越的分布外检测能力。DDPN可轻松应用于多种计数回归数据集，包括表格数据、图像数据、点云数据和文本数据。