US Patent 11531917 Probabilistic forecasting with nonparametric quantile functions

Techniques are described for a time series probabilistic forecasting framework that combines recurrent neural networks (RNNs) with a flexible, nonparametric representation of the output distribution. The representation is based on the nonparametric quantile function (instead of, for example, a parametric density function) and is trained by minimizing a continuous ranked probability score (CRPS) derived from the quantile function. Unlike methods based on parametric probability density functions and maximum likelihood estimation, the techniques described herein can flexibly adapt to different output distributions without manual intervention. Furthermore, the nonparametric nature of the quantile function provides a significant boost in the approach's robustness, making it more readily applicable to a wide variety of time series datasets.