Survey on Algorithms for multi-index models

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
View on arXiv@article{bruna2025_2504.05426, title={ Survey on Algorithms for multi-index models }, author={ Joan Bruna and Daniel Hsu }, journal={arXiv preprint arXiv:2504.05426}, year={ 2025 } }
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