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An eager splitting strategy for online decision trees in ensembles

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Abstract

Decision tree ensembles are widely used in practice. In this work, we study in ensemble settings the effectiveness of replacing the split strategy for the state-of-the-art online tree learner, Hoeffding Tree, with a rigorous but more eager splitting strategy that we had previously published as Hoeffding AnyTime Tree. Hoeffding AnyTime Tree (HATT), uses the Hoeffding Test to determine whether the current best candidate split is superior to the current split, with the possibility of revision, while Hoeffding Tree aims to determine whether the top candidate is better than the second best and if a test is selected, fixes it for all posterity. HATT converges to the ideal batch tree while Hoeffding Tree does not. We find that HATT is an efficacious base learner for online bagging and online boosting ensembles. On UCI and synthetic streams, HATT as a base learner outperforms HT at a 0.05 significance level for the majority of tested ensembles on what we believe is the largest and most comprehensive set of testbenches in the online learning literature. Our results indicate that HATT is a superior alternative to Hoeffding Tree in a large number of ensemble settings.

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Notes

  1. In the prequential setting, training instances arrive in a sequence, and the true target value pertaining to each training instance is made available after the predictor has offered a prediction for a sequence of n instances. The loss function applied is necessarily incremental in nature. Choosing \(n=1\) — that is, evaluating and then updating the predictor after every instance—is an obvious transformation of a periodic evaluation process into an instantaneous one. While not typical of real world application scenarios, prequential accuracy serves as a useful approximation thereto.

  2. There is a common misconception that an individual random variable “changes, taking on a number of values during a process”; in fact, a process is a sequence of events, each of which corresponds to an individual random variable that has taken a particular value (which is fixed and never to change).

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Authors and Affiliations

  1. Monash University, Clayton, Australia

    Chaitanya Manapragada, Mahsa Salehi & Geoffrey I. Webb

  2. University of Waikato, Hamilton, New Zealand

    Heitor M. Gomes & Albert Bifet

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  1. Chaitanya Manapragada
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  2. Heitor M. Gomes
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  3. Mahsa Salehi
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  4. Albert Bifet
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  5. Geoffrey I. Webb
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Correspondence to Chaitanya Manapragada.

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Manapragada, C., Gomes, H.M., Salehi, M. et al. An eager splitting strategy for online decision trees in ensembles. Data Min Knowl Disc 36, 566–619 (2022). https://doi.org/10.1007/s10618-021-00816-x

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