Abstract: Methods, systems, and apparatus, including computer storage media, for performing multi-horizon forecasting on time-series data. A method includes determining short-term temporal characteristics for respective forecasting horizons of one or more time-steps. The determining can include generating, using RNN encoders, encoder vectors based on static covariates, and time-varying input data; and predicting using one or more RNN decoders, a short-term pattern for a respective future time period. The method can also include capturing long-term temporal characteristics for the respective forecasting horizons based on the static covariates, the time-varying input data captured during the respective past time-periods, and the time-varying known future input data.

Abstract: A method for regression and time series forecasting includes obtaining a set of hierarchical time series, each time series in the set of hierarchical time series including a plurality of time series data values. The method includes determining, using the set of hierarchical time series, a basis regularization of the set of hierarchical time series and an embedding regularization of the set of hierarchical time series. The method also includes training a model using the set of hierarchical time series and a loss function based on the basis regularization and the embedding regularization. The method includes forecasting, using the trained model and one of the time series in the set of hierarchical time series, an expected time series data value in the one of the time series.