We introduce WildWood (WW), a new ensemble algorithm for supervised learning of Random Forest (RF) type. While standard RF algorithms use bootstrap out-of-bag samples to compute out-of-bag scores, WW uses these samples to produce improved predictions given by an aggregation of the predictions of all possible subtrees of each fully grown tree in the forest. This is achieved by aggregation with exponential weights computed over out-of-bag samples, that are computed exactly and very efficiently thanks to an algorithm called context tree weighting. This improvement, combined with a histogram strategy to accelerate split finding, makes WW fast and competitive compared with other well-established ensemble methods, such as standard RF and extreme gradient boosting algorithms.
This paper considers the problem of supervised learning with linear methods when both features and labels can be corrupted, either in the form of heavy tailed data and/or corrupted rows. We introduce a combination of coordinate gradient descent as a learning algorithm together with robust estimators of the partial derivatives. This leads to robust statistical learning methods that have a numerical complexity nearly identical to non-robust ones based on empirical risk minimization. The main idea is simple: while robust learning with gradient descent requires the computational cost of robustly estimating the whole gradient to update all parameters, a parameter can be updated immediately using a robust estimator of a single partial derivative in coordinate gradient descent. We prove upper bounds on the generalization error of the algorithms derived from this idea, that control both the optimization and statistical errors with and without a strong convexity assumption of the risk. Finally, we propose an efficient implementation of this approach in a new Python library called linlearn, and demonstrate through extensive numerical experiments that our approach introduces a new interesting compromise between robustness, statistical performance and numerical efficiency for this problem.
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