研究人员已经确定了使用带噪声的输入-输出数据学习Sobolev空间之间有界线性算子的统计和计算极限。该问题被重新构建为具有复杂多尺度结构的无限维矩阵回归。开发了一种新颖的块状最小二乘估计器，该估计器通过调整不同尺度的样本量，实现了最优速率和计算效率。 AI
排序理由 该集群包含一篇在arXiv上发表的学术论文，详细介绍了统计学和机器学习领域的理论研究。
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arXiv:2606.16913v1 Announce Type: cross Abstract: We study the statistical and computational limits of learning bounded linear operators between Sobolev spaces from noisy input-output data. In wavelet coordinates, the problem is recast as an infinite-dimensional matrix regression…
We study the statistical and computational limits of learning bounded linear operators between Sobolev spaces from noisy input-output data. In wavelet coordinates, the problem is recast as an infinite-dimensional matrix regression problem with a heterogeneous two-sided multiscale…