Multivariate Online Regression Analysis with Heterogeneous Streaming Data


New data collection and storage technologies have given rise to a new field of streaming data analytics, including real-time statistical methodology for online data analyses. Most existing online learning methods are based on homogeneity assumption such that the sequence of samples are independent and identical. However, inter-data batch correlation and dynamically evolved batch-specific effects are among the key defining features in real-world streaming data such as electronic health records and mobile health data. This paper is built in the framework of state space mixed models in which the observed data stream is driven by a latent state process that follows a Markov process. In this setting, online maximum likelihood estimation is challenged by high-dimensional integrals and complex covariance structures. In this paper, we develop a Kalman filter based real-time regression analysis method that enables to update both point estimates and standard errors of the fixed population average effects while adjusting for dynamic hidden effects. Both theoretical justification and numerical experiments have demonstrated that our proposed online method has similar statistical properties to its offline counterpart but enjoys great computation efficiency. We also apply this method to analyze an electronic health record data example.

The Canadian Journal of Statistics