将因子模型与神经网络结合，高效处理高维复杂数据。
Generalized Factor Neural Network Model for High-dimensional Regression
- 引入PCA与软PCA层，可在任意位置嵌入神经网络中
- 在金融预测与宏观经济估计任务中表现优于基线方法
- 适合处理具有层级结构的高维数据，如金融时间序列
我们针对高维数据建模中的挑战展开研究，尤其关注隐藏在复杂非线性、噪声关系中的潜在低维结构。提出的方法实现了非参数回归、因子模型与神经网络的无缝融合。通过在神经网络任意阶段嵌入主成分分析（PCA）和软主成分分析（Soft PCA）层，使模型能在因子建模与非线性变换之间交替，提升对层级组合型数据的处理能力。我们对比了多种施加低秩结构于神经网络的技术，并研究了架构设计对性能的影响。实验表明，该方法在模拟数据、股票型ETF指数价格走势预测及宏观经济即时估计任务中均表现出色。
原文摘要 · Abstract (English)
We tackle the challenges of modeling high-dimensional data sets, particularly those with latent low-dimensional structures hidden within complex, non-linear, and noisy relationships. Our approach enables a seamless integration of concepts from non-parametric regression, factor models, and neural networks for high-dimensional regression. Our approach introduces PCA and Soft PCA layers, which can be embedded at any stage of a neural network architecture, allowing the model to alternate between factor modeling and non-linear transformations. This flexibility makes our method especially effective for processing hierarchical compositional data. We explore ours and other techniques for imposing low-rank structures on neural networks and examine how architectural design impacts model performance. The effectiveness of our method is demonstrated through simulation studies, as well as applications to forecasting future price movements of equity ETF indices and nowcasting with macroeconomic data.
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