# Golden Ratio-Based Sufficient Dimension Reduction

arXiv: https://arxiv.org/abs/2410.19300 · HTML: https://mlsanity.com/paper/2410.19300/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 37 references that are in the map.
- First posted on arXiv 25 Oct 2024.

## Builds on (most cited first, 8 of 8)

- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Approximation by Combinations of ReLU and Squared ReLU Ridge Functions with  ℓ1  and  ℓ0  Controls](https://mlsanity.com/paper/1607.07819/) (2016)
- [On the approximation of functions by tanh neural networks](https://mlsanity.com/paper/2104.08938/) (2021)
- [Deep vs. shallow networks : An approximation theory perspective](https://mlsanity.com/paper/1608.03287/) (2016)
- [Sufficient dimension reduction for classification using principal optimal transport direction](https://mlsanity.com/paper/2010.09921/) (2020)
- [Nonlinear Sufficient Dimension Reduction with a Stochastic Neural Network](https://mlsanity.com/paper/2210.04349/) (2022)
- [Level set learning with pseudo-reversible neural networks for nonlinear dimension reduction in function approximation](https://mlsanity.com/paper/2112.01438/) (2021)
- [On expectile-assisted inverse regression estimation for sufficient dimension reduction](https://mlsanity.com/paper/1910.10898/) (2019)

## Built on by (most cited first, 1 of 1)

- [FlowSDR: Sufficient Dimension Reduction via Conditional Normalizing Flows](https://mlsanity.com/paper/2606.01346/) (2026)

## Abstract (arXiv)

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.