Reconciling Predictions in the Regression Setting: An Application to Bus Travel Time Prediction

In different application areas, the prediction of values that are hierarchically related is required. As an example, consider predicting the revenue per month and per year of a company where the prediction of the year should be equal to the sum of the predictions of the months of that year. The idea of reconciliation of prediction on grouped time-series has been previously proposed to provide optimal forecasts based on such data. This method in effect, models the time-series collectively rather than providing a separate model for time-series at each level. While originally, the idea of reconciliation is applicable on data of time-series nature, it is not clear if such an approach can also be applicable to regression settings where multi-attribute data is available. In this paper, we address such a problem by proposing Reconciliation for Regression (R4R), a two-step approach for prediction and reconciliation. In order to evaluate this method, we test its applicability in the context of Travel Time Prediction (TTP) of bus trips where two levels of values need to be calculated: (i) travel times of the links between consecutive bus-stops; and (ii) total trip travel time. The results show that R4R can improve the overall results in terms of both link TTP performance and reconciliation between the sum of the link TTPs and the total trip travel time. We compare the results acquired when using group-based reconciliation methods and show that the proposed reconciliation approach in a regression setting can provide better results in some cases. This method can be generalized to other domains as well.