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.
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.
@cite_26 @cite_4 @cite_22 @cite_14 @cite_9 @cite_3 @cite_15 @cite_16 @cite_13 @cite_11
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Random Forest is an ensemble supervised machine learning technique. Based on bagging and random feature selection, number of decision trees (base classifiers) is generated and majority voting is taken for classification. For effective learning and classification of Random Forest, there is need for reducing number of trees (Pruning) in Random Forest. We have presented here systematic survey of pruning efforts of Random Forest classifier along with the required theoretical background. Most of the work for pruning takes static approach while recently dynamic pruning is being targeted. We have also generated a Comparison Chart by taking relevant parameters. There is research scope for analyzing behavior of Random forest, generating accurate and diverse base decision trees, truly dynamic pruning algorithm for Random Forest classifier, and generating optimal subset of Random forest. A new classification and regression tool, Random Forest, is introduced and investigated for predicting a compound's quantitative or categorical biological activity based on a quantitative description of the compound's molecular structure. Random Forest is an ensemble of unpruned classification or regression trees created by using bootstrap samples of the training data and random feature selection in tree induction. Prediction is made by aggregating (majority vote or averaging) the predictions of the ensemble. We built predictive models for six cheminformatics data sets. Our analysis demonstrates that Random Forest is a powerful tool capable of delivering performance that is among the most accurate methods to date. We also present three additional features of Random Forest: built-in performance assessment, a measure of relative importance of descriptors, and a measure of compound similarity that is weighted by the relative importance of descriptors. It is the combination of relatively high prediction accu... Breiman (2001a,b) has recently developed an ensemble classification and regression approach that displayed outstanding performance with regard prediction error on a suite of benchmark datasets. As the base constituents of the ensemble are tree-structured predictors, and since each of these is constructed using an injection of randomness, the method is called ‘random forests’. That the exceptional performance is attained with seemingly only a single tuning parameter, to which sensitivity is minimal, makes the methodology all the more remarkable. The individual trees comprising the forest are all grown to maximal depth. While this helps with regard bias, there is the familiar tradeoff with variance. However, these variability concerns were potentially obscured because of an interesting feature of those benchmarking datasets extracted from the UCI machine learning repository for testing: all these datasets are hard to overfit using tree-structured methods. This raises issues about the scope of the repository. With this as motivation, and coupled with experience from boosting methods, we revisit the formulation of random forests and investigate prediction performance on real-world and simulated datasets for which maximally sized trees do overfit. These explorations reveal that gains can be realized by additional tuning to regulate tree size via limiting the number of splits and or the size of nodes for which splitting is allowed. Nonetheless, even in these settings, good performance for random forests can be attained by using larger (than default) primary tuning parameter values. Random forests are a scheme proposed by Leo Breiman in the 2000's for building a predictor ensemble with a set of decision trees that grow in randomly selected subspaces of data. Despite growing interest and practical use, there has been little exploration of the statistical properties of random forests, and little is known about the mathematical forces driving the algorithm. In this paper, we offer an in-depth analysis of a random forests model suggested by Breiman (2004), which is very close to the original algorithm. We show in particular that the procedure is consistent and adapts to sparsity, in the sense that its rate of convergence depends only on the number of strong features and not on how many noise variables are present. Random Forests (RFs) are frequently used in many computer vision and machine learning applications. Their popularity is mainly driven by their high computational efficiency during both training and evaluation while achieving state-of-the-art results. However, in most applications RFs are used off-line. This limits their usability for many practical problems, for instance, when training data arrives sequentially or the underlying distribution is continuously changing. In this paper, we propose a novel on-line random forest algorithm. We combine ideas from on-line bagging, extremely randomized forests and propose an on-line decision tree growing procedure. Additionally, we add a temporal weighting scheme for adaptively discarding some trees based on their out-of-bag-error in given time intervals and consequently growing of new trees. The experiments on common machine learning data sets show that our algorithm converges to the performance of the off-line RF. Additionally, we conduct experiments for visual tracking, where we demonstrate real-time state-of-the-art performance on well-known scenarios and show good performance in case of occlusions and appearance changes where we outperform trackers based on on-line boosting. Finally, we demonstrate the usability of on-line RFs on the task of interactive real-time segmentation. This review presents a unified, efficient model of random decision forests which can be applied to a number of machine learning, computer vision, and medical image analysis tasks. Our model extends existing forest-based techniques as it unifies classification, regression, density estimation, manifold learning, semi-supervised learning, and active learning under the same decision forest framework. This gives us the opportunity to write and optimize the core implementation only once, with application to many diverse tasks. The proposed model may be used both in a discriminative or generative way and may be applied to discrete or continuous, labeled or unlabeled data. The main contributions of this review are: (1) Proposing a unified, probabilistic and efficient model for a variety of learning tasks; (2) Demonstrating margin-maximizing properties of classification forests; (3) Discussing probabilistic regression forests in comparison with other nonlinear regression algorithms; (4) Introducing density forests for estimating probability density functions; (5) Proposing an efficient algorithm for sampling from a density forest; (6) Introducing manifold forests for nonlinear dimensionality reduction; (7) Proposing new algorithms for transductive learning and active learning. Finally, we discuss how alternatives such as random ferns and extremely randomized trees stem from our more general forest model. This document is directed at both students who wish to learn the basics of decision forests, as well as researchers interested in the new contributions. It presents both fundamental and novel concepts in a structured way, with many illustrative examples and real-world applications. Thorough comparisons with state-of-the-art algorithms such as support vector machines, boosting and Gaussian processes are presented and relative advantages and disadvantages discussed. The many synthetic examples and existing commercial applications demonstrate the validity of the proposed model and its flexibility. In this letter, an ensemble learning approach, Rotation Forest, has been applied to hyperspectral remote sensing image classification for the first time. The framework of Rotation Forest is to project the original data into a new feature space using transformation methods for each base classifier (decision tree), then the base classifier can train in different new spaces for the purpose of encouraging both individual accuracy and diversity within the ensemble simultaneously. Principal component analysis (PCA), maximum noise fraction, independent component analysis, and local Fisher discriminant analysis are introduced as feature transformation algorithms in the original Rotation Forest. The performance of Rotation Forest was evaluated based on several criteria: different data sets, sensitivity to the number of training samples, ensemble size and the number of features in a subset. Experimental results revealed that Rotation Forest, especially with PCA transformation, could produce more accurate results than bagging, AdaBoost, and Random Forest. They indicate that Rotation Forests are promising approaches for generating classifier ensemble of hyperspectral remote sensing. Random forests is currently one of the most used machine learning algorithms in the non-streaming (batch) setting. This preference is attributable to its high learning performance and low demands with respect to input preparation and hyper-parameter tuning. However, in the challenging context of evolving data streams, there is no random forests algorithm that can be considered state-of-the-art in comparison to bagging and boosting based algorithms. In this work, we present the adaptive random forest (ARF) algorithm for classification of evolving data streams. In contrast to previous attempts of replicating random forests for data stream learning, ARF includes an effective resampling method and adaptive operators that can cope with different types of concept drifts without complex optimizations for different data sets. We present experiments with a parallel implementation of ARF which has no degradation in terms of classification performance in comparison to a serial implementation, since trees and adaptive operators are independent from one another. Finally, we compare ARF with state-of-the-art algorithms in a traditional test-then-train evaluation and a novel delayed labelling evaluation, and show that ARF is accurate and uses a feasible amount of resources. Random forests (RFs) are recognized as one type of ensemble learning method and are effective for the most classification and regression tasks. Despite their impressive empirical performance, the theory of RFs has yet been fully proved. Several theoretically guaranteed RF variants have been presented, but their poor practical performance has been criticized. In this paper, a novel RF framework is proposed, named Bernoulli RFs (BRFs), with the aim of solving the RF dilemma between theoretical consistency and empirical performance. BRF uses two independent Bernoulli distributions to simplify the tree construction, in contrast to the RFs proposed by Breiman. The two Bernoulli distributions are separately used to control the splitting feature and splitting point selection processes of tree construction. Consequently, theoretical consistency is ensured in BRF, i.e., the convergence of learning performance to optimum will be guaranteed when infinite data are given. Importantly, our proposed BRF is consistent for both classification and regression. The best empirical performance is achieved by BRF when it is compared with state-of-the-art theoretical consistent RFs. This advance in RF research toward closing the gap between theory and practice is verified by the theoretical and experimental studies in this paper. Decision trees and randomized forests are widely used in computer vision and machine learning. Standard algorithms for decision tree induction optimize the split functions one node at a time according to some splitting criteria. This greedy procedure often leads to suboptimal trees. In this paper, we present an algorithm for optimizing the split functions at all levels of the tree jointly with the leaf parameters, based on a global objective. We show that the problem of finding optimal linear-combination (oblique) splits for decision trees is related to structured prediction with latent variables, and we formulate a convex-concave upper bound on the tree's empirical loss. Computing the gradient of the proposed surrogate objective with respect to each training exemplar is O(d2), where d is the tree depth, and thus training deep trees is feasible. The use of stochastic gradient descent for optimization enables effective training with large datasets. Experiments on several classification benchmarks demonstrate that the resulting non-greedy decision trees outperform greedy decision tree baselines.