Label distribution learning (LDL) is a general learning framework, which assigns to an instance a distribution over a set of labels rather than a single label or multiple labels. Current LDL methods have either restricted assumptions on the expression form of the label distribution or limitations in representation learning, e.g., to learn deep features in an end-to-end manner. This paper presents label distribution learning forests (LDLFs) - a novel label distribution learning algorithm based on differentiable decision trees, which have several advantages: 1) Decision trees have the potential to model any general form of label distributions by a mixture of leaf node predictions. 2) The learning of differentiable decision trees can be combined with representation learning. We define a distribution-based loss function for a forest, enabling all the trees to be learned jointly, and show that an update function for leaf node predictions, which guarantees a strict decrease of the loss function, can be derived by variational bounding. The effectiveness of the proposed LDLFs is verified on several LDL tasks and a computer vision application, showing significant improvements to the state-of-the-art LDL methods.
. Random forests or randomized decision trees @cite_3 @cite_5 @cite_17 @cite_20 , are a popular ensemble predictive model suitable for many machine learning tasks. In the past, learning of a decision tree was based on heuristics such as a greedy algorithm where locally-optimal hard decisions are made at each split node @cite_5 , and thus, cannot be integrated into in a deep learning framework, i.e., be combined with representation learning in an end-to-end manner.
@cite_5 @cite_20 @cite_3 @cite_17
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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. 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. 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. 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.