Efficient estimation and selection for regularized dynamic logistic regression

In various data science applications, the relationship between predictor variables and the response is dynamic in the sense that the corresponding model parameters are varying coefficients. Estimation and variable selection for such dynamic models are challenging with a large number of parameters and complex optimization. In this work, we propose a regularized dynamic logistic regression for efficient variable selection and model estimation. The proposed method considers a combination of fused and group regularization to estimate varying effects of important predictors on responses in the presence of irrelevant predictors. Specifically, we select the important variable with dynamic impact on responses through the selection of the entire group of piecewise constant functions for parameters, which can characterize dynamic impacts of predictor variables. Moreover, we develop an efficient algorithm based on the alternating direction method of multipliers for parameter estimation. The performance of the proposed method is evaluated by both simulations and real case studies.