  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.
