Neural Symbolic Regression using Control Variables
Xieting Chu Hongjue Zhao Enze Xu Hairong Qi Minghan Chen Huajie Shao
Symbolic regression (SR) is a powerful technique for discovering the
analytical mathematical expression from data, finding various applications in
natural sciences due to its good interpretability of results. However, existing
methods face scalability issues when dealing with complex equations involving
multiple variables. To address this challenge, we propose SRCV, a novel neural
symbolic regression method that leverages control variables to enhance both
accuracy and scalability. The core idea is to decompose multi-variable symbolic
regression into a set of single-variable SR problems, which are then combined
in a bottom-up manner. The proposed method involves a four-step process. First,
we learn a data generator from observed data using deep neural networks (DNNs).
Second, the data generator is used to generate samples for a certain variable
by controlling the input variables. Thirdly, single-variable symbolic
regression is applied to estimate the corresponding mathematical expression.
Lastly, we repeat steps 2 and 3 by gradually adding variables one by one until
completion. We evaluate the performance of our method on multiple benchmark
datasets. Experimental results demonstrate that the proposed SRCV significantly
outperforms state-of-the-art baselines in discovering mathematical expressions
with multiple variables. Moreover, it can substantially reduce the search space
for symbolic regression. The source code will be made publicly available upon
publication.