# Sufficient Dimension Reduction for High-Dimensional Regression and Low-Dimensional Embedding: Tutorial and Survey

arXiv: https://arxiv.org/abs/2110.09620 · HTML: https://mlsanity.com/paper/2110.09620/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 76 references that are in the map.
- First posted on arXiv 18 Oct 2021.

## Builds on (most cited first, 10 of 10)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Eigenvalue and Generalized Eigenvalue Problems: Tutorial](https://mlsanity.com/paper/1903.11240/) (2019)
- [Reproducing Kernel Hilbert Space, Mercer's Theorem, Eigenfunctions, Nystr"om Method, and Use of Kernels in Machine Learning: Tutorial and Survey](https://mlsanity.com/paper/2106.08443/) (2021)
- [Factor Analysis, Probabilistic Principal Component Analysis, Variational Inference, and Variational Autoencoder: Tutorial and Survey](https://mlsanity.com/paper/2101.00734/) (2021)
- [KKT Conditions, First-Order and Second-Order Optimization, and Distributed Optimization: Tutorial and Survey](https://mlsanity.com/paper/2110.01858/) (2021)
- [Unsupervised and Supervised Principal Component Analysis: Tutorial](https://mlsanity.com/paper/1906.03148/) (2019)
- [Laplacian-Based Dimensionality Reduction Including Spectral Clustering, Laplacian Eigenmap, Locality Preserving Projection, Graph Embedding, and Diffusion Map: Tutorial and Survey](https://mlsanity.com/paper/2106.02154/) (2021)
- [Conditional Variance Estimator for Sufficient Dimension Reduction](https://mlsanity.com/paper/2102.08782/) (2021)
- [Deep Variational Sufficient Dimensionality Reduction](https://mlsanity.com/paper/1812.07641/) (2018)
- [Ensemble Conditional Variance Estimator for Sufficient Dimension Reduction](https://mlsanity.com/paper/2102.13435/) (2021)

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

- [Random-projection ensemble dimension reduction](https://mlsanity.com/paper/2410.04922/) (2024)

## Abstract (arXiv)

This is a tutorial and survey paper on various methods for Sufficient Dimension Reduction (SDR). We cover these methods with both statistical high-dimensional regression perspective and machine learning approach for dimensionality reduction. We start with introducing inverse regression methods including Sliced Inverse Regression (SIR), Sliced Average Variance Estimation (SAVE), contour regression, directional regression, Principal Fitted Components (PFC), Likelihood Acquired Direction (LAD), and graphical regression. Then, we introduce forward regression methods including Principal Hessian Directions (pHd), Minimum Average Variance Estimation (MAVE), Conditional Variance Estimation (CVE), and deep SDR methods. Finally, we explain Kernel Dimension Reduction (KDR) both for supervised and unsupervised learning. We also show that supervised KDR and supervised PCA are equivalent.