Adaptive Regression Analysis of Heterogeneous Data Streams via Models with Dynamic Effects

Abstract

Streaming data sequences arise from various areas in the era of big data, and it is challenging to explore efficient online models that adapt to them. To address the potential heterogeneity, we introduce a new online estimation procedure to analyze the constantly incoming streaming datasets. The underlying model structures are assumed to be the generalized linear models with dynamic regression coefficients. Our key idea lies in introducing a vector of unknown parameters to measure the differences between batch-specific regression coefficients from adjacent data blocks. This is followed by the usage of the adaptive lasso penalization methodology to accurately select nonzero components, which indicates the existence of dynamic coefficients. We provide detailed derivations to demonstrate how our proposed method not only fits within the online updating framework in which the old estimator is recursively replaced with a new one based solely on the current individual-level samples and historical summary statistics but also adaptively avoids undesirable estimation biases coming from the potential changes in model parameters of interest. Computational issues are also discussed in detail to facilitate implementation. Its practical performance is demonstrated through both extensive simulations and a real case study. In summary, we contribute to a novel online method that efficiently adapts to streaming data environment, addresses potential heterogeneity, and mitigates estimation biases from changes in coefficients.

Keywords

• adaptive lasso
• data streams
• dynamic coefficients
• online estimation
• regression analysis