Evolutionary symbolic regression (SR) fits a symbolic equation to data, which
gives a concise interpretable model. We explore using SR as a method to propose
which data to gather in an active learning setting with physical constraints.
SR with active learning proposes which experiments to do next. Active learning
is done with query by committee, where the Pareto frontier of equations is the
committee. The physical constraints improve proposed equations in very low data
settings. These approaches reduce the data required for SR and achieves state
of the art results in data required to rediscover known equations.

本文探讨使用进化符号回归作为方法来建议在受物理限制的主动学习环境中采集的数据，采用委员会查询的主动学习策略，物理约束提高了在极低数据条件下预测方程的质量。这些方法可以减少 SR 所需的数据，并在已知方程时达到了最先进的结果。

具有物理限制条件的符号回归中的主动学习性能

Active Learning in Symbolic Regression Performance with Physical  Constraints

We propose a new active learning (AL) framework, Active Learning++, which can
utilize an annotator's labels as well as its rationale. Annotators can provide
their rationale for choosing a label by ranking input features based on their
importance for a given query. To incorporate this additional input, we modified
the disagreement measure for a bagging-based Query by Committee (QBC) sampling
strategy. Instead of weighing all committee models equally to select the next
instance, we assign higher weight to the committee model with higher agreement
with the annotator's ranking. Specifically, we generated a feature
importance-based local explanation for each committee model. The similarity
score between feature rankings provided by the annotator and the local model
explanation is used to assign a weight to each corresponding committee model.
This approach is applicable to any kind of ML model using model-agnostic
techniques to generate local explanation such as LIME. With a simulation study,
we show that our framework significantly outperforms a QBC based vanilla AL
framework.

研究提出一种新的主动学习框架，称为 Active Learning++，其可以利用注释者的标签以及其理由，通过修改基于 Bagging 的 Query by Committee (QBC) 采样策略的不一致度量方法，将委员会模型的权重分配给具有更高一致性的注释者排序的委员会模型，在模拟研究中表明该框架显著优于 QBC based vanilla AL framework。