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optimal Poisson subsampling for Softmax Regression

系统科学与复杂性学报:英文版 2023年第4期36卷 1609-1625页

作者： YAO Yaqiong ZOU Jiahui WANG Haiying Department of Statistics University of ConnecticutStorrsCT06269USA School of Statistics Capital University of Economics and BusinessBeijing 100070China

Softmax regression,which is also called multinomial logistic regression,is widely used in various fields for modeling the relationship between covariates and categorical responses with multiple *** increasing volumes of data bring new challenges for parameter estimation in softmax regression,and the optimal subsampling method is an effective way to solve ***,optimal subsampling with replacement requires to access all the sampling probabilities simultaneously to draw a subsample,and the resultant subsample could contain duplicate *** this paper,the authors consider Poisson subsampling for its higher estimation accuracy and applicability in the scenario that the data exceed the memory *** authors derive the asymptotic properties of the general Poisson subsampling estimator and obtain optimal subsampling probabilities by minimizing the asymptotic variance-covariance matrix under both A-and L-optimality *** optimal subsampling probabilities contain unknown quantities from the full dataset,so the authors suggest an approximately optimal Poisson subsampling algorithm which contains two sampling steps,with the first step as a pilot *** authors demonstrate the performance of our optimal Poisson subsampling algorithm through numerical simulations and real data examples.

关键词： Multinomial logistic regression optimality criterion optimal subsampling

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Analyzing the Dissemination of News by Model Averaging and subsampling

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Journal of Systems Science & Complexity 2024年第5期37卷 2104-2131页

作者： ZOU Jiahui School of Statistics Capital University of Economics and Business

The dissemination of news is a vital topic in management science, social science and data science. With the development of technology, the sample sizes and dimensions of digital news data increase remarkably. To alleviate the computational burden in big data, this paper proposes a method to deal with massive and moderate-dimensional data for linear regression models via combing model averaging and subsampling methodologies. The author first samples a subsample from the full data according to some special probabilities and split covariates into several groups to construct candidate models. Then, the author solves each candidate model and calculates the model-averaging weights to combine these estimators based on this subsample. Additionally, the asymptotic optimality in subsampling form is proved and the way to calculate optimal subsampling probabilities is *** author also illustrates the proposed method via simulations, which shows it takes less running time than that of the full data and generates more accurate estimations than uniform subsampling. Finally,the author applies the proposed method to analyze and predict the sharing number of news, and finds the topic, vocabulary and dissemination time are the determinants.

关键词： Asymptotic optimality dissemination of news linear regression models model averaging optimal subsampling

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