  Effective decision making requires understanding the uncertainty inherent in
a prediction. In regression, this uncertainty can be estimated by a variety of
methods; however, many of these methods are laborious to tune, generate
overconfident uncertainty intervals, or lack sharpness (give imprecise
intervals). We address these challenges by proposing a novel method to capture
predictive distributions in regression by defining two neural networks with two
distinct loss functions. Specifically, one network approximates the cumulative
distribution function, and the second network approximates its inverse. We
refer to this method as Collaborating Networks (CN). Theoretical analysis
demonstrates that a fixed point of the optimization is at the idealized
solution, and that the method is asymptotically consistent to the ground truth
distribution. Empirically, learning is straightforward and robust. We benchmark
CN against several common approaches on two synthetic and six real-world
datasets, including forecasting A1c values in diabetic patients from electronic
health records, where uncertainty is critical. In the synthetic data, the
proposed approach essentially matches ground truth. In the real-world datasets,
CN improves results on many performance metrics, including log-likelihood
estimates, mean absolute errors, coverage estimates, and prediction interval
widths.
