  Interpretable architectures can have advantages over black-box architectures,
and interpretability is essential for the application of machine learning in
critical settings, such as aviation or medicine. However, the simplest, most
commonly used interpretable architectures, such as LASSO or elastic net (EN),
are limited to linear predictions and have poor feature selection capabilities.
In this work, we introduce the LASSO-Clip-EN (LCEN) algorithm for the creation
of nonlinear, interpretable machine learning models. LCEN is tested on a wide
variety of artificial and empirical datasets, frequently creating more
accurate, sparser models than other architectures, including those for building
sparse, nonlinear models. LCEN is robust against many issues typically present
in datasets and modeling, including noise, multicollinearity, data scarcity,
and hyperparameter variance. LCEN is also able to rediscover multiple physical
laws from empirical data and, for processes with no known physical laws, LCEN
achieves better results than many other dense and sparse methods -- including
using 10.8-fold fewer features than dense methods and 8.1-fold fewer features
than EN on one dataset, and is comparable to or better than ANNs on multiple
datasets.
