Loss Attenuation for Time Series Prediction Respecting Categories of Values

Forecasting future values is a core task in many applications dealing with multivariate time series data. In pollution monitoring, for example, forecasting future PM\(_{\boldsymbol{2.5}}\) values in air is very common, which is a crucial indicator of the air quality index (AQI). These values in time series are sometimes affiliated with category information for easy understanding. As an illustration, it is often to categorize the PM\(_{\boldsymbol{2.5}}\) values to indicate the levels of health concern or health risk based on pre-defined category intervals. Forecasting future values without considering the categories leads to potential inconsistency between the categories of predicted values and real values. The underlying reason is that the objective during training is to minimize the overall prediction error, e.g., mean square error, which does not respect the category information. We propose a category adaptive loss attenuation method with respect to training samples in stochastic gradient descent for multi-horizon time series forecasting. The proposed weighting strategy considers training samples’ closeness to category boundaries in a parameterized cost-sensitive manner. The results from extensive experiments demonstrate that the weighting method can improve the overall performance of category-aware time series prediction.