Tensor extrapolation: an adaptation to data sets with missing entries

Abstract

Abstract Background Contemporary data sets are frequently relational in nature. In retail, for example, data sets are more granular than traditional data, often indexing individual products, outlets, or even users, rather than aggregating them at the group level. Tensor extrapolation is used to forecast relational time series data; it combines tensor decompositions and time series extrapolation. However, previous approaches to tensor extrapolation are restricted to complete data sets. This paper adapts tensor extrapolation to situations with missing entries and examines the method’s performance in terms of forecast accuracy. Findings To base the evaluation on time series with both diverse and controllable characteristics, the paper develops a synthetic data set closely related to the context of retailing. Calculations performed on these data demonstrate that tensor extrapolation outperforms the univariate baseline. Furthermore, a preparatory completion of the data set is not necessary. The higher the fraction of missing data, the greater the superiority of tensor extrapolation in terms of prediction error. Conclusions Forecasting plays a key role in the optimization of business processes and enables data-driven decision making. As such, tensor extrapolation should be part of the forecaster’s toolkit: Even if large parts of the data are missing, the proposed method is able to extract meaningful, latent structure, and to use this information in prediction.

Keywords

• Forecast accuracy
• Missing values
• Relational data
• Tensor decomposition
• Time series analysis