Due to their efficiency and small size, decision trees and random forests are popular machine learning models used for classification on resource-constrained systems. In such systems, the available execution time for inference in a random forest might not be sufficient for a complete model execution. Ideally, the already gained prediction confidence should be retained. An anytime algorithm is designed to be able to be aborted anytime, while giving a result with an increasing quality over time. Previous approaches have realized random forests as anytime algorithms on the granularity of trees, stopping after some but not all trees of a forest have been executed. However, due to the way decision trees subdivide the sample space in every step, an increase in prediction quality is achieved with every additional step in one tree. In this paper, we realize decision trees and random forest as anytime algorithms on the granularity of single steps in trees. This approach opens a design space to define the step order in a forest, which has the potential to optimize the mean accuracy. We propose the Optimal Order, which finds a step order with a maximal mean accuracy in exponential runtime and the polynomial runtime heuristics Forward Squirrel Order and Backward Squirrel Order, which greedily maximize the accuracy for each additional step taken down and up the trees, respectively. Our evaluation shows, that the Backward Squirrel Order performs ∼94% as well as the Optimal Order and ∼99% as well as all other step orders.
Figures & tables
Fig. 1: Example Forest with Marked Samples
Fig. 2: Graph of Example Forest
Fig. 3: Expiry Time vs. Steps - adult (10 Trees, Depth 10)
Fig. 4: Step Order Runtime and Accuracy - adult (Depth 8)
Fig. 5: Steps vs. Accuracy - letter (7 Trees, Depth 7)
Fig. 6: Average Normalized Mean Accuracy - All Data-Sets
Bagging-based ensembles, most notably Adaptive Random Forests, are among the strongest performers for learning from data streams. A common denominator across these methods is their reliance on Hoeffding Trees as base learners, which grow decision trees incrementally by testing whether a candidate split is significantly better than its alternatives using concentration inequalities. Despite their empirical success, existing variants lack valid statistical guarantees. Current analyses rely on fixed-sample concentration bounds, while split decisions are made using data-dependent stopping rules, which invalidates their guarantees and can drive the probabilty of incorrect splits to one. We introduce a principled alternative based on anytime-valid inference. Our method provides: (i) anytime-valid control of false splits under arbitrary data streams, including non-stationary settings; (ii) finite commitment time under a predictive advantage; and (iii) under stationary i.i.d. data, risk is monotone decreasing and strictly improves at every split. Empirically, we evaluate both standalone trees and their use within Adaptive Random Forests on non-stationary streams. Our method improves performance while producing substantially smaller trees.
Optimal decision trees (ODTs) are compact, interpretable machine learning models that globally optimize a given objective, but their scalability remains challenging. While recent work has proposed a variety of search strategies to improve scalability, the precise contribution of each strategy remains unclear. To address this gap, we introduce a general algorithmic framework for ODTs that instantiates previously used search strategies and enables the definition of new ones. This provides a common lens through which to understand and compare different strategies, which we use to empirically investigate the effect of 18 search strategies. Compared to the state of the art, the best strategy in our evaluation achieves significantly better anytime performance for classification, and improves runtime by more than an order of magnitude for regression.
Jacobus G. M. van der Linden, Mim van den Bos, Emir Demirović
The Random Forest model is one of the popular models of Machine learning. We present a quantum algorithm for testing (forecasting) process of the Random Forest machine learning model for the Regression problem. The presented algorithm is more efficient (in terms of query complexity or running time) than the classical counterpart.
Kamil Khadiev, Liliya Safina
Institute of Computational Mathematics and IT, Kazan Federal University, Kazan, Russia · Zavoisky Physical-Technical Institute, FRC Kazan Scientific Center of RAS, Kazan, Russia