Popular decision tree algorithms are provably noise tolerant
This addresses the problem of noise robustness in widely used decision tree algorithms for machine learning practitioners, offering theoretical justification for their empirical success.
The paper proves that impurity-based decision tree algorithms like ID3, C4.5, and CART are highly noise tolerant under a strong noise model, providing near-matching bounds on allowable noise rates.
Using the framework of boosting, we prove that all impurity-based decision tree learning algorithms, including the classic ID3, C4.5, and CART, are highly noise tolerant. Our guarantees hold under the strongest noise model of nasty noise, and we provide near-matching upper and lower bounds on the allowable noise rate. We further show that these algorithms, which are simple and have long been central to everyday machine learning, enjoy provable guarantees in the noisy setting that are unmatched by existing algorithms in the theoretical literature on decision tree learning. Taken together, our results add to an ongoing line of research that seeks to place the empirical success of these practical decision tree algorithms on firm theoretical footing.