Learning a manifold from a teacher's demonstrations

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.