用神经网络实现高效降维，精准识别数据核心结构。
Golden Ratio-Based Sufficient Dimension Reduction
- 基于神经网络逼近巴龙函数类，自动发现降维关键方向
- 能准确估计中心空间，计算成本低于已有方法
- 可扩展至实际场景，适合高维数据分析任务
许多机器学习应用涉及高维数据。为使计算可行且学习更高效，通常需要通过寻找预测变量的线性组合来降低输入变量的维度，以尽可能保留响应变量与原始预测变量间的关系信息。我们提出一种基于神经网络的充分降维方法，不仅能有效识别结构维度，还能良好估计中心空间。该方法利用神经网络对巴龙（Barron）类函数的逼近能力，相比文献中其他降维方法具有更低的计算成本。此外，该框架可扩展以适应实际降维需求，使方法在现实场景中更具适用性。
原文摘要 · Abstract (English)
Many machine learning applications deal with high dimensional data. To make computations feasible and learning more efficient, it is often desirable to reduce the dimensionality of the input variables by finding linear combinations of the predictors that can retain as much original information as possible in the relationship between the response and the original predictors. We propose a neural network based sufficient dimension reduction method that not only identifies the structural dimension effectively, but also estimates the central space well. It takes advantages of approximation capabilities of neural networks for functions in Barron classes and leads to reduced computation cost compared to other dimension reduction methods in the literature. Additionally, the framework can be extended to fit practical dimension reduction, making the methodology more applicable in practical settings.
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