论文标题
在结构化分布下学习具有Massart噪声的半空间
Learning Halfspaces with Massart Noise Under Structured Distributions
论文作者
论文摘要
我们研究了在分布特定PAC模型中学习与MassArt噪声学习半空间的问题。我们就广泛的分布族（包括对数符号分布）提供了第一个针对此问题的计算有效算法。这解决了许多先前的作品中提出的一个空旷的问题。我们的方法非常简单：我们确定了平滑的{\ em non-non-convex}替代损失与该损失的任何近似固定点的属性都定义了一个靠近目标半空间的半空间。鉴于这种结构性结果，我们可以使用SGD来解决潜在的学习问题。
We study the problem of learning halfspaces with Massart noise in the distribution-specific PAC model. We give the first computationally efficient algorithm for this problem with respect to a broad family of distributions, including log-concave distributions. This resolves an open question posed in a number of prior works. Our approach is extremely simple: We identify a smooth {\em non-convex} surrogate loss with the property that any approximate stationary point of this loss defines a halfspace that is close to the target halfspace. Given this structural result, we can use SGD to solve the underlying learning problem.
