Symbolic Regression is NP-hard
This is a foundational result for researchers in machine learning and optimization, as it establishes the computational hardness of a widely used task.
The paper tackled the problem of symbolic regression (SR), which involves learning mathematical expressions from data, by proving that SR is NP-hard, indicating no exact polynomial-time algorithm likely exists.
Symbolic regression (SR) is the task of learning a model of data in the form of a mathematical expression. By their nature, SR models have the potential to be accurate and human-interpretable at the same time. Unfortunately, finding such models, i.e., performing SR, appears to be a computationally intensive task. Historically, SR has been tackled with heuristics such as greedy or genetic algorithms and, while some works have hinted at the possible hardness of SR, no proof has yet been given that SR is, in fact, NP-hard. This begs the question: Is there an exact polynomial-time algorithm to compute SR models? We provide evidence suggesting that the answer is probably negative by showing that SR is NP-hard.