综述多指标模型的高效算法与理论边界，揭示计算效率与样本需求间的差距。
Survey on Algorithms for multi-index models
- 基于梯度跨度估计和神经网络拟合的两类核心方法
- 高效算法样本复杂度高于信息论下限，存在理论间隙
- 适合关注统计学习理论与高效算法设计的研究者
我们综述了多指标模型中指数空间估计算法的文献。重点聚焦于高斯空间中的计算高效（多项式时间）算法，这些方法在何种假设下可保证一致性及其样本复杂度。许多情况下，现有最高效的算法样本复杂度显著高于信息论下限。此外，还回顾了利用非参数方法估计梯度张成空间的算法，以及通过梯度下降拟合神经网络的算法。
原文摘要 · Abstract (English)
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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