Survey on Algorithms for multi-index models

Joan Bruna; Daniel Hsu

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arXiv · 2504.05426

Survey on Algorithms for multi-index models

Joan Bruna·Daniel Hsu

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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

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Joan Bruna, Daniel Hsu. 2025-04-07. Survey on Algorithms for multi-index models. https://arxiv.org/abs/2504.05426

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