通过反向传播方法估计同步方程模型,使用随机梯度下降方法
Belén Pérez-Sánchez1, Carmen Perea1, Guillem Duran Ballester2
1Center of Operations Research, Universidad Miguel Hernández de Elche, Elche, Alicante, Spain.
PeerJ. Computer science
|December 9, 2024
概括
本研究介绍了人工神经网络 (ANN) 作为解决同时方程模型 (SEM) 的新方法. 通过将 SEM 变量视为 ANN 神经元和系数视为连接重量,它提出了随机梯度下降 (SGD) 的反向传播以估计系数.
科学领域:
- 计量经济学 计量经济学
- 计算统计学 计算统计学
- 人工智能的人工智能
背景情况:
- 同时方程模型 (SEM) 在计量经济学和其他科学中对于分析双向和同时变量关系至关重要.
- 传统的SEM估计方法包括两阶段最小平方 (2SLS),三阶段最小平方 (3SLS) 和间接最小平方 (ILS).
- 现有的研究比较基于预测错误,计算成本和经典和贝叶斯统计等统计范式的SEM估计.
研究的目的:
- 提出和研究人工神经网络 (ANN) 作为解决同时方程模型 (SEM) 的新框架.
- 建立SEM变量和ANN神经元,SEM系数和神经网络连接重量之间的类比.
- 探索反向传播方法与随机梯度下降 (SGD) 的有效性,以估计SEM系数.
主要方法:
- 将同时方程模型 (SEM) 概念化为人工神经网络 (ANN) 的特定架构.
- 将SEM变量映射到ANN神经元,并将SEM系数映射到神经网络连接的权重.
- 应用反向传播算法,由随机梯度下降 (SGD) 驱动,用于估计SEM系数.
主要成果:
- 证明在ANN框架内代表SEM的可行性.
- 成功地应用了SGD的反向传播算法来估计SEM系数.
- 建立了一个新的计算方法来解决SEM.
结论:
- 人工神经网络为模拟并发方程提供了可行和创新的替代方案.
- 使用SGD的反向传播方法提供了一种有效的技术,用于估计SEM中的系数.
- 这项研究将计量经济学与机器学习联系起来,为SEM分析开辟了新的途径.
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