Theoretical analysis of transfer learning for temporally dependent observations

Transfer learning has become increasingly important in recent years as it enables models to quickly adapt to new tasks, environments and data sets. It can improve the accuracy of machine learning models and reduce the training time required for them. However, theoretical foundation of transfer learning algorithms is rather scarce, particularly for time series models. In this work, we focus on high-dimensional vector autoregressive models and provide a two-step procedure to conduct transfer learning utilizing auxiliary data sets followed by constructing confidence intervals for model parameters in the high-dimensional regime. Further, a new method to select informative sets from auxiliary sets is introduced. Finally, two debiasing techniques are developed to perform inference for model parameters. Theoretical properties of all proposed algorithms are established under mild conditions which allow for heavy-tailed distributions and dependence among auxiliary and target data sets. Given certain level of similarity between the informative models and the target model, it is shown that the proposed algorithm achieves the minimax rate. Lastly, the empirical performance of proposed methods is tested through analyzing both simulated data as well as an EEG data set.