English(EN) Average Gradient Outer Product in kernel regression provably recovers the central subspace for multi-index models

核回归方法恢复多指标模型的中心子空间

作者 PulseAugur 编辑部 · [1 个来源] · 2026-05-14 17:05

研究人员开发了一种使用核岭回归和平均梯度外积（AGOP）的方法来识别数据中潜在的低维结构。该技术可以恢复多指标模型的中心子空间，即使在预测精度仍然很低的情况下也是如此。研究结果表明预测和表示之间存在分离，解释了迭代核方法（如递归特征机）的样本效率。 AI

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arXiv stat.ML TIER_1 English(EN) · Maryam Fazel · 2026-05-14 17:05

核回归中的平均梯度外积可证明地恢复多指标模型的中心子空间

We study a prototypical situation when a learned predictor can discover useful low-dimensional structure in data, while using fewer samples than are needed for accurate prediction. Specifically, we consider the problem of recovering a multi-index polynomial $f^*(x)=h(Ux)$, with $…