具有Lipschitz非线性的单神经元模型的主动学习
Active Learning for Single Neuron Models with Lipschitz Non-Linearities
AI总结：
本研究针对带对抗标签噪声的不可知场景下单神经元模型的主动学习问题，证明采用基于统计杠杆得分采样的线性函数主动学习策略可获强近似保证，且实验效果优于均匀采样。
摘要：
我们研究了不可知设置下（存在对抗性标签噪声时）单神经元模型（有时也被称为“脊函数”）的主动学习问题。这类模型已被证实在模拟物理现象、构建偏微分方程的数据驱动替代模型方面具有广泛有效性。\n 令人惊讶的是，我们证明对于带有任意Lipschitz非线性（例如ReLU、sigmoid、绝对值、低次多项式等）的单神经元模型，使用一种知名的、用于在不可知设置下拟合线性函数的主动学习策略，就能得到强可证明的近似保证。具体来说，我们可以通过统计杠杆得分采样来收集样本，该方法已被证实在其他主动学习场景中接近最优。我们通过仿真实验支撑了理论结果，实验表明我们提出的基于杠杆得分采样的主动学习策略在拟合单神经元模型时效果优于（普通）均匀采样。
英文摘要：
We consider the problem of active learning for single neuron models, also sometimes called ``ridge functions'', in the agnostic setting (under adversarial label noise). Such models have been shown to be broadly effective in modeling physical phenomena, and for constructing surrogate data-driven models for partial differential equations. Surprisingly, we show that for a single neuron model with any Lipschitz non-linearity (such as the ReLU, sigmoid, absolute value, low-degree polynomial, among others), strong provable approximation guarantees can be obtained using a well-known active learning strategy for fitting \emph{linear functions} in the agnostic setting. % -- i.e. for the case when there is no non-linearity. Namely, we can collect samples via statistical \emph{leverage score sampling}, which has been shown to be near-optimal in other active learning scenarios. We support our theoretical results with empirical simulations showing that our proposed active learning strategy based on leverage score sampling outperforms (ordinary) uniform sampling when fitting single neuron models.
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