基于神经网络的主动学习：非参数统计学的见解
Active Learning with Neural Networks: Insights from Nonparametric Statistics
AI总结：
本文提出基于非参数统计学的深度主动学习方法，首次提供了近最优的标签复杂性保证，无需低噪声假设，并扩展至Radon BV²空间。
摘要：
深度神经网络具有强大的表示能力，但通常需要大量的训练示例。这促使了深度主动学习方法的出现，这些方法可以显著减少标注训练数据的数量。近年来，深度主动学习在文献中报告了实证成功，然而，深度主动学习的严格标签复杂性保证仍显得模糊。这构成了理论与实践之间的重大差距。本文通过提供深度主动学习的第一个近最优标签复杂性保证来解决这一差距。关键的见解是将深度主动学习从非参数分类的角度进行研究。在标准低噪声条件下，我们证明了使用神经网络的主动学习可以证明性地达到最小化标签复杂性，最多达到分歧系数和其他对数项。当配备放弃选项时，我们进一步开发了一个高效的深度主动学习算法，实现了polylog(1/ε)的标签复杂性，而无需任何低噪声假设。我们还扩展了我们的结果，超越了通常研究的Sobolev/Hölder空间，并为学习在Radon BV²空间中提供了标签复杂性保证，这些空间最近已被提出作为与神经网络相关的自然函数空间。
英文摘要：
Deep neural networks have great representation power, but typically require large numbers of training examples. This motivates deep active learning methods that can significantly reduce the amount of labeled training data. Empirical successes of deep active learning have been recently reported in the literature, however, rigorous label complexity guarantees of deep active learning have remained elusive. This constitutes a significant gap between theory and practice. This paper tackles this gap by providing the first near-optimal label complexity guarantees for deep active learning. The key insight is to study deep active learning from the nonparametric classification perspective. Under standard low noise conditions, we show that active learning with neural networks can provably achieve the minimax label complexity, up to disagreement coefficient and other logarithmic terms. When equipped with an abstention option, we further develop an efficient deep active learning algorithm that achieves $\mathsf{polylog}(\frac{1}ε)$ label complexity, without any low noise assumptions. We also provide extensions of our results beyond the commonly studied Sobolev/Hölder spaces and develop label complexity guarantees for learning in Radon $\mathsf{BV}^2$ spaces, which have recently been proposed as natural function spaces associated with neural networks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
