Random forests (RF) are one of the most widely used ensemble learning methods in classification and regression tasks. Despite its impressive performance, its theoretical consistency, which would ensure that its result converges to the optimum as the sample size increases, has been left far behind. Several consistent random forest variants have been proposed, yet all with relatively poor performance compared to the original random forests. In this paper, a novel RF framework named multinomial random forests (MRF) is proposed. In the MRF, an impurity-based multinomial distribution is constructed as the basis for the selection of a splitting point. This ensures that a certain degree of randomness is achieved while the overall quality of the trees is not much different from the original random forests. We prove the consistency of the MRF and demonstrate with multiple datasets that it performs similarly as the original random forests and better than existent consistent random forest variants for both classification and regression tasks.
@cite_26: Random forests were introduced as a machine learning tool in Breiman (2001) and have since proven to be very popular and powerful for high-dimensional regression and classification. For regression, random forests give an accurate approximation of the conditional mean of a response variable. It is shown here that random forests provide information about the full conditional distribution of the response variable, not only about the conditional mean. Conditional quantiles can be inferred with quantile regression forests, a generalisation of random forests. Quantile regression forests give a non-parametric and accurate way of estimating conditional quantiles for high-dimensional predictor variables. The algorithm is shown to be consistent. Numerical examples suggest that the algorithm is competitive in terms of predictive power.
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@cite_22: Much of previous attention on decision trees focuses on the splitting criteria and optimization of tree sizes. The dilemma between overfitting and achieving maximum accuracy is seldom resolved. A method to construct a decision tree based classifier is proposed that maintains highest accuracy on training data and improves on generalization accuracy as it grows in complexity. The classifier consists of multiple trees constructed systematically by pseudorandomly selecting subsets of components of the feature vector, that is, trees constructed in randomly chosen subspaces. The subspace method is compared to single-tree classifiers and other forest construction methods by experiments on publicly available datasets, where the method's superiority is demonstrated. We also discuss independence between trees in a forest and relate that to the combined classification accuracy.
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@cite_9: Advanced analysis of data streams is quickly becoming a key area of data mining research as the number of applications demanding such processing increases. Online mining when such data streams evolve over time, that is when concepts drift or change completely, is becoming one of the core issues. When tackling non-stationary concepts, ensembles of classifiers have several advantages over single classifier methods: they are easy to scale and parallelize, they can adapt to change quickly by pruning under-performing parts of the ensemble, and they therefore usually also generate more accurate concept descriptions. This paper proposes a new experimental data stream framework for studying concept drift, and two new variants of Bagging: ADWIN Bagging and Adaptive-Size Hoeffding Tree (ASHT) Bagging. Using the new experimental framework, an evaluation study on synthetic and real-world datasets comprising up to ten million examples shows that the new ensemble methods perform very well compared to several known methods.
@cite_3: Bagging and boosting are methods that generate a diverse ensemble of classifiers by manipulating the training data given to a “base” learning algorithm. Breiman has pointed out that they rely for their effectiveness on the instability of the base learning algorithm. An alternative approach to generating an ensemble is to randomize the internal decisions made by the base algorithm. This general approach has been studied previously by Ali and Pazzani and by Dietterich and Kong. This paper compares the effectiveness of randomization, bagging, and boosting for improving the performance of the decision-tree algorithm C4.5. The experiments show that in situations with little or no classification noise, randomization is competitive with (and perhaps slightly superior to) bagging but not as accurate as boosting. In situations with substantial classification noise, bagging is much better than boosting, and sometimes better than randomization.
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@cite_11: In this paper, we propose gcForest, a decision tree ensemble approach with performance highly competitive to deep neural networks in a broad range of tasks. In contrast to deep neural networks which require great effort in hyper-parameter tuning, gcForest is much easier to train; even when it is applied to different data across different domains in our experiments, excellent performance can be achieved by almost same settings of hyper-parameters. The training process of gcForest is efficient, and users can control training cost according to computational resource available. The efficiency may be further enhanced because gcForest is naturally apt to parallel implementation. Furthermore, in contrast to deep neural networks which require largescale training data, gcForest can work well even when there are only small-scale training data.
Random forest @cite_16 is a distinguished ensemble learning algorithm inspired by the random subspace method @cite_22 and random split selection @cite_3 . In the original method, decision trees are built upon bootstrap datasets from the training set using the CART methodology @cite_4 . Its various variants, such as quantile regression forests @cite_26 and deep forests @cite_11 , have been proposed and used in a wide range of applications @cite_9 @cite_15 @cite_13 @cite_14 for their effective training process and great performance.