Survey on Algorithms for multi-index models
Machine Learning
2025-06-17 v2 Machine Learning
Methodology
Abstract
We review the literature on algorithms for estimating the index space in a multi-index model. The primary focus is on computationally efficient (polynomial-time) algorithms in Gaussian space, the assumptions under which consistency is guaranteed by these methods, and their sample complexity. In many cases, a gap is observed between the sample complexity of the best known computationally efficient methods and the information-theoretical minimum. We also review algorithms based on estimating the span of gradients using nonparametric methods, and algorithms based on fitting neural networks using gradient descent
Cite
@article{arxiv.2504.05426,
title = {Survey on Algorithms for multi-index models},
author = {Joan Bruna and Daniel Hsu},
journal= {arXiv preprint arXiv:2504.05426},
year = {2025}
}