Original title: Improved identification accuracy in equation learning via comprehensive $\boldsymbol{R^2}$-elimination and Bayesian model selection
Authors: Daniel Nickelsen, Bubacarr Bah
In this article, researchers tackle the challenge of equation learning, where exhaustive exploration of all potential equations becomes impractical. They address issues with sparse regression and greedy algorithms, known for struggling with multicollinearity and overlooking crucial equation components, leading to reduced accuracy. Their innovative approach combines the strengths of $R^2$ and Bayesian model evidence, introducing a balanced method inspired by stepwise regression. Unlike traditional methods, theirs involves a comprehensive search while incrementally reducing the model space. They present three new avenues for equation learning, showcasing their approach across numerical experiments involving random polynomials and dynamic systems. Compared to four cutting-edge methods and two standard approaches, their comprehensive search method significantly outperforms others in identifying equations accurately. Notably, their novel approach using an overfitting penalty based solely on $R^2$ achieves the highest exact equation recovery rates, marking a substantial advancement in equation learning.
Original article: https://arxiv.org/abs/2311.13265