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随着计算机技术的发展，各行各业累积和存储了丰富的数据。这些数据往往具有来源差异性、高维性特点，基于这些特征的多源数据建模是统计学的热点问题。针对多源异质数据，本文提出深度神经网络整合分析模型(IADNN)。该模型建立了L1-CMCP惩罚，以识别重要特征以及处理数据的异质性，其中外层MCP识别对多源数据集整体显著的特征；中层MCP识别特征在数据集层面的异质性；内层Lasso识别DNN节点的异质性。这种嵌套设计旨在促进数据集间的信息共享。本文对L1-CMCP进行局部线性近似，再采用近端梯度下降算法进行模型估计。模拟分析表明，IADNN在特征选择和分类预测方面均有良好表现。当多源数据部分异质时，所提方法的F1分数、FPR等评估指标均优于各数据集独立建模和合并建模的方法；在多源数据完全异质或完全同质时，所提方法取得了与理论最佳模型相近的效果。最后，将IADNN应用于不同经济发展水平地区的信用违约数据，发现该模型在风险指标选择和违约预测方面具备有效性。
Abstract：With the development of computer technology,all walks of life have accumulated and stored rich data.They often have characteristics of source diversity and high dimensionality,and modeling multi-source data based on these characteristics is a popular topic in statistics.For the multi-source heterogeneous data,the study proposes the Integrative Analysis Deep Neural Network (IADNN),which employs the L1-CMCP penalty to identify significant feature variables and address data heterogeneity.The outer layer of L1-CMCP identifies features that significantly impact the entire multi-source data,the middle layer identifies the heterogeneity of features at the dataset level,and the inner Lasso layer detects heterogeneity among DNN nodes.This nested design is intended to enhance information sharing.For model estimation,a local linear approximation and a proximal gradient descent algorithm are adopted.Simulation study shows that the proposed IADNN performs satisfactorily in terms of feature selection and classification prediction.When the multi-source data are partially heterogeneous,the evaluation metrics of the IADNN model,such as the F1 score and the FPR,outperform both independent modeling and merged modeling approaches.When the multi-source data are completely heterogeneous or homogeneous,IADNN performance is similar to the theoretical best model.Lastly,the application of IADNN to credit default data from regions with different economic levels demonstrates its effectiveness in selecting risk indicators and predicting default.
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(1)因篇幅所限，模拟结果以附表1~4展示，见《统计研究》网站所列附件。下同。
(2)因篇幅所限，不同重叠情形的F1均值以附图1展示。
(1)因篇幅所限，美国三大地区的划分以附表5展示。
(1)因篇幅所限，前30个高频特征以附表6展示。
(2)因篇幅所限，不同方法下各地区的重要特征重叠数以附表7展示。
基本信息:
DOI：10.19343/j.cnki.11-1302/c.2025.02.010
中图分类号:F831.2;TP183;TP311.13
引用信息:
[1]王小燕,冮建伟,王洁丹,等.多源异质数据下深度神经网络的整合分析及其应用[J].统计研究,2025,42(02):122-134.DOI:10.19343/j.cnki.11-1302/c.2025.02.010.
基金信息:
国家自然科学基金面上项目“多源数据融合的高维整合分析分类模型及其信用风险应用”（72271088）; 教育部人文社会科学基金规划项目“面向超高频金融数据的函数型分类预测方法及应用研究”（22YJAZH099）; 湖南省研究生科研创新项目“多源数据的深度神经网络及其应用”（CX20230418）; 国家社会科学基金后期资助重点项目“金融市场函数型数据挖掘的统计方法及应用研究”（24FTJA001）
2025-03-04
2025-03-04
2025-03-04