Robust and efficient subsampling algorithms for massive data logistic regression.

Datasets that are big with regard to their volume, variety and velocity are becoming increasingly common. However, limitations in computer processing can often restrict analysis performed on them. Nonuniform subsampling methods are effective in reducing computational loads for massive data. However, the variance of the estimator of nonuniform subsampling methods becomes large when the subsampling probabilities are highly heterogenous. To this end, we develop two new algorithms to improve the estimation method for massive data logistic regression based on a chosen hard threshold value and combining subsamples, respectively. The basic idea of the hard threshold method is to carefully select a threshold value and then replace subsampling probabilities lower than the threshold value with the chosen value itself. The main idea behind the combining subsamples method is to better exploit information in the data without hitting the computation bottleneck by generating many subsamples and then combining estimates constructed from the subsamples. The combining subsamples method obtains the standard error of the parameter estimator without estimating the sandwich matrix, which provides convenience for statistical inference in massive data, and can significantly improve the estimation efficiency. Asymptotic properties of the resultant estimators are established. Simulations and analysis of real data are conducted to assess and showcase the practical performance of the proposed methods.

Causal Responsibility Division of Chronological Continuous Treatment Based on Change-Point Detection.

This paper introduces a novel approach, called causal relation quantification, based on change-point detection to address the issue of harmonic responsibility division in power systems. The proposed method focuses on determining the causal effect of chronological continuous treatment, enabling the identification of crucial treatment intervals. Within each interval, three propensity-score-based algorithms are executed to assess their respective causal effects. By integrating the results from each interval, the overall causal effect of a chronological continuous treatment variable can be calculated. This calculated overall causal effect represents the causal responsibility of each harmonic customer. The effectiveness of the proposed method is evaluated through a simulation study and demonstrated in an empirical harmonic application. The results of the simulation study indicate that our method provides accurate and robust estimates, while the calculated results in the harmonic application align closely with the real-world scenario as verified by on-site investigations.