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.