There is a large body of work on convergence rates either in passive or active learning. Here we first outline some of the main results that have been obtained, more specifically in a nonparametric setting under assumptions about the smoothness of the regression function (or the boundary between classes) and the margin noise. We discuss the relative merits of these underlying assumptions by putting active learning in perspective with recent work on passive learning. We design an active learning algorithm with a rate of convergence better than in passive learning, using a particular smoothness assumption customized for k-nearest neighbors. Unlike previous active learning algorithms, we use a smoothness assumption that provides a dependence on the marginal distribution of the instance space. Additionally, our algorithm avoids the strong density assumption that supposes the existence of the density function of the marginal distribution of the instance space and is therefore more generally applicable.

中文翻译：

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局部平滑假设下的 K-NN 主动学习

在被动或主动学习中，有大量关于收敛率的工作。在这里，我们首先概述已经获得的一些主要结果，更具体地说是在关于回归函数（或类之间的边界）的平滑度和边缘噪声的假设下的非参数设置中。我们通过将主动学习与最近关于被动学习的工作相结合来讨论这些基本假设的相对优点。我们设计了一种主动学习算法，其收敛速度优于被动学习，使用为 k 最近邻定制的特定平滑度假设。与以前的主动学习算法不同，我们使用平滑度假设，该假设提供对实例空间边缘分布的依赖。此外，