Obtaining labels can be costly and time-consuming. Active learning allows a learning algorithm to intelligently query samples to be labeled for efficient learning. Fisher information ratio (FIR) has been used as an objective for selecting queries in active learning. However, little is known about the theory behind the use of FIR for active learning. There is a gap between the underlying theory and the motivation of its usage in practice. In this paper, we attempt to fill this gap and provide a rigorous framework for analyzing the existing FIR-based active learning methods. In particular, we show that FIR can be asymptotically viewed as an upper bound of the expected variance of the log-likelihood ratio. Additionally, our analysis suggests a unifying framework that not only enables us to make theoretical comparisons among the existing querying methods based on FIR, but also gives more insight into the development of new active learning approaches based on this objective.

本研究提供了一种理论框架，分析了现有基于Fisher信息比率 (FIR) 的主动学习方法，并表明FIR可以渐近地被视为对数似然比的预期方差的上界，同时提出了一种更加统一的框架用于理论比较和开发基于该目标的新型主动学习方法。

基于 Fisher 信息的主动学习目标的渐近分析