Source-linked AI summary
Extremely Fast Decision Tree
Chaitanya Manapragada, Geoff Webb, Mahsa Salehi
TL;DR
Incremental Hoeffding Tree learning delays useful splits and never revisits them, motivating a more statistically efficient alternative. The paper introduces Hoeffding Anytime Tree and evaluates its EFDT implementation, which generally achieves higher prequential accuracy while converging to the asymptotic batch tree at additional computational cost.
Problem
Hoeffding Tree delays split decisions and never revisits them, limiting its ability to exploit useful information before the best split is identified.
Method
Hoeffding Anytime Tree deploys a useful split as soon as it is sufficiently supported, then replaces it when a better alternative becomes evident.
Results
EFDT achieves significantly lower prequential error than VFDT on most tested benchmark datasets and retains its advantage 100 million examples into a stream.
Takeaways & Limitations
HATT provides a higher-accuracy replacement for Hoeffding Tree in scenarios where incrementally learned trees must make predictions before they are fully learned.
Takeaways & Limitations
HATT can underperform when information gains and their differences are both low, because its low-level adjustments may overfit; deeper trees also increase the chance of wrong splits.
Abstract
from arXiv · showhide
We introduce a novel incremental decision tree learning algorithm, Hoeffding Anytime Tree, that is statistically more efficient than the current state-of-the-art, Hoeffding Tree. We demonstrate that an implementation of Hoeffding Anytime Tree---"Extremely Fast Decision Tree", a minor modification to the MOA implementation of Hoeffding Tree---obtains significantly superior prequential accuracy on most of the largest classification datasets from the UCI repository. Hoeffding Anytime Tree produces the asymptotic batch tree in the limit, is naturally resilient to concept drift, and can be used as a higher accuracy replacement for Hoeffding Tree in most scenarios, at a small additional computational cost.
1 INTRODUCTION
The paper introduces Hoeffding Anytime Tree (HATT), which makes and revisits useful splits earlier than Hoeffding Tree. Its EFDT implementation learns faster and achieves higher prequential accuracy on most tested benchmark datasets, with modest computational overhead.
- 1 INTRODUCTION: EFDT learns concepts quickly across increasing task complexity, while incurring a modest computational overhead relative to VFDT.The comparison varies the number of classes from 2 to 5 and tracks prequential error over the stream.
- 1 INTRODUCTION: HATT improves on Hoeffding Tree by selecting a useful split early and revisiting it when a better split becomes evident.Hoeffding Tree delays splitting until it is confident about the best split and never revisits that decision.
- 1 INTRODUCTION: HATT learns more rapidly from stationary data and eventually converges to the asymptotic batch decision tree.The computationally cheaper Hoeffding Tree instead avoids revisiting split decisions.
- 1 INTRODUCTION: EFDT adjusts for potential overfitting as fresh examples arrive.This follows from its strategy of revisiting and replacing earlier split decisions.
- 1 INTRODUCTION: EFDT achieves significantly lower prequential error than VFDT on most tested benchmark datasets, including after 100 million examples.VFDT slightly outperforms EFDT on the Higgs, SUSY, and Hepmass synthetic physics datasets.
2 BACKGROUND
Hoeffding Tree uses the Hoeffding Bound to choose splits incrementally with a probabilistic guarantee. However, its comparison does not control whether the selected attribute is worse than every other attribute, and it cannot revise the choice.
- 2 BACKGROUND: Hoeffding Tree was introduced as an incremental decision-tree algorithm for high-speed data streams.It became the de facto standard for constructing decision trees from streaming data.
- 2 BACKGROUND: The Hoeffding Bound estimates whether a potential split’s observed information-gain difference is sufficiently reliable.The bound provides a probabilistic guarantee on the difference between an estimated and true mean.
- 2 BACKGROUND: Hoeffding Tree selects the top attribute Xa when the information-gain difference ∆G exceeds the tolerance ϵ.The comparison is between the attributes with the highest and second-highest information gains.
- 2 BACKGROUND: The test controls the risk that Xa is worse than Xb, but not the risk that another attribute Xc is better.As the number of attributes increases, the chance of such an overlooked superior split increases, and the tree cannot revise the decision.
3 HOEFDDING ANYTIME TREE
Hoeffding Anytime Tree (HATT) improves incremental splitting by allowing later corrections to current choices, while converging in probability to the asymptotic batch decision tree. Its EFDT instantiation retains Hoeffding Tree’s node-statistics complexity and is designed to learn faster when useful split information emerges.
- Algorithm: HATT is instantiated as Extremely Fast Decision Tree (EFDT), an incremental decision-tree learner for streaming examples.The algorithm processes an observed sequence of examples and maintains a tree model over time.
- Algorithm: HATT builds structure when the best split exceeds the current split or no-split alternative, then can reevaluate and replace earlier choices as evidence accumulates.This contrasts with Hoeffding Tree’s comparison of the best and second-best candidate attributes before splitting.
- Convergence: At the root, HATT eventually matches the asymptotic batch tree’s split attribute with probability tending to 1.The argument relies on measured information-gain differences converging to their infinite-dataset values while the Hoeffding threshold decreases.
- Convergence: HATT converges in probability to the asymptotic batch tree as the number of examples grows.The proof extends convergence from the root split through successive tree levels under the assumption that no two attributes have identical information gain.
- Complexity: HATT and Hoeffding Tree require equivalent space complexity, with HATT requiring O(dvc) memory for node statistics and O(ndvc) in terms of total nodes.Here d is the number of attributes, v the values per attribute, c the classes, and n the total number of nodes.
4 RELATED WORK
HATT differs from prior Hoeffding Tree adaptations by re-evaluating splits for stationary-stream performance rather than explicitly forgetting data for drift adaptation. Its comparison with CVFDT is complementary, but applying HATT’s split criterion to drifting streams remains outside this paper’s scope.
- Prior adaptations: Prior Hoeffding Tree adaptations change tests or leaf models, whereas HATT changes the learning premise through split re-evaluation.The cited literature substitutes statistical tests or adds Naive Bayes leaves; HATT instead revisits split decisions.
- CVFDT comparison: CVFDT and HATT both re-evaluate splits, but CVFDT targets drifting streams while HATT targets lower prequential error on stationary streams.CVFDT uses a moving window and alternate subtrees; HATT compares the current split or null split without deliberate forgetting.
- CVFDT comparison: HATT and CVFDT differ in replacement strategy: CVFDT builds alternate subtrees, whereas HATT discards a subtree only when a split is replaced.The methods therefore share split re-evaluation but use different objectives and historical-statistics handling.
- Scope boundary: Whether HATT’s comparison with the current or null split improves CVFDT on concept-drifting streams is left for future work.The paper explicitly places this combination beyond its scope.
- Related drift learners: HAT adapts to drift by growing alternate subtrees and replacing the original when recent predictive error favors the alternate.This distinguishes HAT’s error-estimator-based adaptation from HATT’s stationary-stream split re-evaluation.
5 PERFORMANCE
The evaluation compares VFDT and EFDT on large UCI streams, including shuffled and unshuffled orders. EFDT generally achieves higher prequential accuracy, with especially strong gains on ordered data, while its main weakness appears when low-information splits invite later readjustment.
- Evaluation design: EFDT was compared with VFDT on large UCI classification datasets and the WISDM dataset, using shuffled streams to simulate stationary sampling.The implementation modified MOA’s VFDT split evaluations, and the experiments were made reproducible with released code and scripts.
- Overall performance: EFDT attains substantially higher prequential accuracy on most streams, whether shuffled or unshuffled.VFDT wins on three synthetic physics datasets, but those margins are smaller than most EFDT wins.
- Computational cost: EFDT’s runtime usually exceeds VFDT’s but rarely more than doubles, and it can be lower when EFDT learns smaller trees.Leaves were evaluated every 200 timesteps and internal nodes every 2000 timesteps.
- Data ordering: Shuffling can reduce performance for both learners because it removes order-specific structure, as illustrated by the Skin, Poker, and Forest-Covertype results.The unshuffled Skin stream presents all positive examples before all negative examples, whereas shuffling requires learning a more complex boundary.
- Ordered streams: Ordered datasets can favor EFDT because VFDT repeatedly relearns changing concepts, while EFDT discards outdated splits; on Fonts, EFDT reaches around 99.8% accuracy.The Fonts stream is ordered by font name, requiring repeated adaptation at increasingly complex tree leaves.
- Mechanism: HATT is expected to help when VFDT delays splits despite significant information gains, because each delayed level postpones learning deeper splits.The tree’s fragmenting of input space makes delays cascade exponentially with depth.
- Failure mode: EFDT can underperform when both information gains and their differences are low, because an initially chosen split may require extensive readjustment.The paper identifies Higgs, Hepmass, and SUSY as synthetic datasets exhibiting this scenario.
- Long streams: EFDT’s prequential error remains an order of magnitude lower than VFDT’s after a 100 million-example synthetic stream.This result is reported for the MOA tree generator used in the comparison.
6 CONCLUSIONS
Hoeffding Anytime Tree changes incremental tree learning by using useful splits early and replacing them when better alternatives emerge. The strategy performs effectively on benchmark datasets while retaining some tolerance to concept drift, though it is not specifically designed for drift.
- HATT splits when a useful split is identified and replaces it when a better alternative becomes evident.This contrasts with Hoeffding Tree’s strategy of waiting for the best split and never revisiting the decision.
- HATT’s strategy is highly effective on benchmark datasets.
- HATT has some inbuilt tolerance to concept drift but is not specifically designed as a drift learner.The paper suggests building ensemble, forgetting, decay, or subtree replacement approaches upon HATT for drift handling.
- HATT benefits early deployment by using the most useful splits identified to date before the tree is fully learned.Hoeffding Tree delays potential improvements until they are sufficiently unlikely to require revision.