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Abstract:
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New data collection and storage technologies have given rise to a new field of streaming data analytics. 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. This talk centers around the 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 project, 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 and enjoys great computational efficiency.
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