## Abstract

This paper investigates the problem of active learning for binary label prediction on a graph. We introduce a simple and label-efficient algorithm called S^{2} for this task. At each step, S^{2} selects the vertex to be labeled based on the structure of the graph and all previously gathered labels. Specifically, S^{2} queries for the label of the vertex that bisects the shortest shortest path between any pair of oppositely labeled vertices. We present a theoretical estimate of the number of queries S^{2} needs in terms of a novel parametrization of the complexity of binary functions on graphs. We also present experimental results demonstrating the performance of S^{2} on both real and synthetic data. While other graph-based active learning algorithms have shown promise in practice, our algorithm is the first with both good performance and theoretical guarantees. Finally, we demonstrate the implications of the S^{2} algorithm to the theory of nonparametric active learning. In particular, we show that S^{2} achieves near minimax optimal excess risk for an important class of nonparametric classification problems.

Original language | English (US) |
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Journal | Journal of Machine Learning Research |

Volume | 40 |

Issue number | 2015 |

State | Published - Jan 1 2015 |

Externally published | Yes |

Event | 28th Conference on Learning Theory, COLT 2015 - Paris, France Duration: Jul 2 2015 → Jul 6 2015 |

## Keywords

- Active learning on graphs
- Nonparametric classification
- Query complexity of finding a cut

## ASJC Scopus subject areas

- Control and Systems Engineering
- Software
- Statistics and Probability
- Artificial Intelligence