We consider the problem of learning a manifold from a teacher's demonstration. Extending existing approaches of learning from randomly sampled data points, we consider contexts where data may be chosen by a teacher. We analyze learning from teachers who can provide structured data such as individual examples (isolated data points) and demonstrations (sequences of points). Our analysis shows that for the purpose of teaching the topology of a manifold, demonstrations can yield remarkable decreases in the amount of data points required in comparison to teaching with randomly sampled points. We also discuss the implications of our analysis for learning in humans and machines.

翻译：我们考虑的是从教师的演示中学习多方面内容的问题。我们扩展了从随机抽样数据点学习的现有方法,我们考虑了教师可以选择数据的背景。我们分析的是能够提供结构化数据的教师的学习,例如个别例子(单独数据点)和演示(分数顺序)。我们的分析表明,为了教授多重结构学的目的,演示可以使所需要的数据点数量与随机抽样点教学相比显著减少。我们还讨论了我们的分析对人和机器学习的影响。