Multi-View Active Learning in the Non-Realizable Case

TL;DR

This paper provides a theoretical analysis of multi-view active learning in non-realizable scenarios, showing significant improvements in sample complexity under certain noise conditions compared to single-view methods.

Contribution

It characterizes the sample complexity of multi-view active learning without the realizability assumption, revealing logarithmic and linear bounds under unbounded Tsybakov noise.

Findings

Sample complexity can be $ ilde{O}( ext{log}(1/\epsilon))$ with unbounded Tsybakov noise.

In general, sample complexity is $ ilde{O}(1/\epsilon)$, independent of Tsybakov noise parameters.

Contrasts with single-view setting where improvements are polynomial and dependent on noise parameters.

Abstract

The sample complexity of active learning under the realizability assumption has been well-studied. The realizability assumption, however, rarely holds in practice. In this paper, we theoretically characterize the sample complexity of active learning in the non-realizable case under multi-view setting. We prove that, with unbounded Tsybakov noise, the sample complexity of multi-view active learning can be $\widetilde{O}(\log\frac{1}{\epsilon})$, contrasting to single-view setting where the polynomial improvement is the best possible achievement. We also prove that in general multi-view setting the sample complexity of active learning with unbounded Tsybakov noise is $\widetilde{O}(\frac{1}{\epsilon})$, where the order of $1/\epsilon$ is independent of the parameter in Tsybakov noise, contrasting to previous polynomial bounds where the order of $1/\epsilon$ is related to the parameter in Tsybakov noise.