Golden Ratio-Based Sufficient Dimension Reduction
This work addresses dimensionality reduction for machine learning practitioners, but it appears incremental as it builds on existing neural network capabilities and dimension reduction techniques.
The authors tackled the problem of high-dimensional data in machine learning by proposing a neural network-based sufficient dimension reduction method that effectively identifies structural dimensions and estimates the central space, leading to reduced computation costs compared to existing methods.
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.