Random forests are a combination of tree predictors such that each tree depends on the values of a random vector sampled independently and with the same distribution for all trees in the forest. The generalization error for forests converges a.s. to a limit as the number of trees in the forest becomes large. The generalization error of a forest of tree classifiers depends on the strength of the individual trees in the forest and the correlation between them. Using a random selection of features to split each node yields error rates that compare favorably to Adaboost (Y. Freund & R. Schapire, Machine Learning: Proceedings of the Thirteenth International conference, aaa, 148–156), but are more robust with respect to noise. Internal estimates monitor error, strength, and correlation and these are used to show the response to increasing the number of features used in the splitting. Internal estimates are also used to measure variable importance. These ideas are also applicable to regression.

Random Forests

Data Mining: Practical Machine Learning Tools and Techniques offers a thorough grounding in machine learning concepts as well as practical advice on applying machine learning tools and techniques in real-world data mining situations. This highly anticipated third edition of the most acclaimed work on data mining and machine learning will teach you everything you need to know about preparing inputs, interpreting outputs, evaluating results, and the algorithmic methods at the heart of successful data mining. Thorough updates reflect the technical changes and modernizations that have taken place in the field since the last edition, including new material on Data Transformations, Ensemble Learning, Massive Data Sets, Multi-instance Learning, plus a new version of the popular Weka machine learning software developed by the authors. Witten, Frank, and Hall include both tried-and-true techniques of today as well as methods at the leading edge of contemporary research. *Provides a thorough grounding in machine learning concepts as well as practical advice on applying the tools and techniques to your data mining projects *Offers concrete tips and techniques for performance improvement that work by transforming the input or output in machine learning methods *Includes downloadable Weka software toolkit, a collection of machine learning algorithms for data mining tasks-in an updated, interactive interface. Algorithms in toolkit cover: data pre-processing, classification, regression, clustering, association rules, visualization

Data Mining: Practical Machine Learning Tools and Techniques

This paper describes a machine learning approach for visual object detection which is capable of processing images extremely rapidly and achieving high detection rates. This work is distinguished by three key contributions. The first is the introduction of a new image representation called the "integral image" which allows the features used by our detector to be computed very quickly. The second is a learning algorithm, based on AdaBoost, which selects a small number of critical visual features from a larger set and yields extremely efficient classifiers. The third contribution is a method for combining increasingly more complex classifiers in a "cascade" which allows background regions of the image to be quickly discarded while spending more computation on promising object-like regions. The cascade can be viewed as an object specific focus-of-attention mechanism which unlike previous approaches provides statistical guarantees that discarded regions are unlikely to contain the object of interest. In the domain of face detection the system yields detection rates comparable to the best previous systems. Used in real-time applications, the detector runs at 15 frames per second without resorting to image differencing or skin color detection.

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Rapid object detection using a boosted cascade of simple features

Recently there has been a lot of interest in “ensemble learning” — methods that generate many classifiers and aggregate their results. Two well-known methods are boosting (see, e.g., Shapire et al., 1998) and bagging Breiman (1996) of classification trees. In boosting, successive trees give extra weight to points incorrectly predicted by earlier predictors. In the end, a weighted vote is taken for prediction. In bagging, successive trees do not depend on earlier trees — each is independently constructed using a bootstrap sample of the data set. In the end, a simple majority vote is taken for prediction. Breiman (2001) proposed random forests, which add an additional layer of randomness to bagging. In addition to constructing each tree using a different bootstrap sample of the data, random forests change how the classification or regression trees are constructed. In standard trees, each node is split using the best split among all variables. In a random forest, each node is split using the best among a subset of predictors randomly chosen at that node. This somewhat counterintuitive strategy turns out to perform very well compared to many other classifiers, including discriminant analysis, support vector machines and neural networks, and is robust against overfitting (Breiman, 2001). In addition, it is very user-friendly in the sense that it has only two parameters (the number of variables in the random subset at each node and the number of trees in the forest), and is usually not very sensitive to their values. The randomForest package provides an R interface to the Fortran programs by Breiman and Cutler (available at http://www.stat.berkeley.edu/ users/breiman/). This article provides a brief introduction to the usage and features of the R functions.

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Classification and Regression by randomForest

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

One of the surprising recurring phenomena observed in experiments with boosting is that the test error of the generated classifier usually does not increase as its size becomes very large, and often is observed to decrease even after the training error reaches zero. In this paper, we show that this phenomenon is related to the distribution of margins of the training examples with respect to the generated voting classification rule, where the margin of an example is simply the difference between the number of correct votes and the maximum number of votes received by any incorrect label. We show that techniques used in the analysis of Vapnik's support vector classifiers and of neural networks with small weights can be applied to voting methods to relate the margin distribution to the test error. We also show theoretically and experimentally that boosting is especially effective at increasing the margins of the training examples. Finally, we compare our explanation to those based on the bias-variance

/pdf/boosting-the-margin-a-new-explanation-for-the-effectiveness-ck9ah7g8d8.pdf

Boosting the margin: A new explanation for the effectiveness of voting methods

One of the surprising recurring phenomena observed in experiments with boosting is that the test error of the generated classifier usually does not increase as its size becomes very large, and often is observed to decrease even after the training error reaches zero. In this paper, we show that this phenomenon is related to the distribution of margins of the training examples with respect to the generated voting classification rule, where the margin of an example is simply the difference between the number of correct votes and the maximum number of votes received by any incorrect label. We show that techniques used in the analysis of Vapnik's support vector classifiers and of neural networks with small weights can be applied to voting methods to relate the margin distribution to the test error. We also show theoretically and experimentally that boosting is especially effective at increasing the margins of the training examples. Finally, we compare our explanation to those based on the bias-variance decomposition.

/pdf/boosting-the-margin-a-new-explanation-for-the-effectiveness-prb9baf13x.pdf

Boosting the margin: a new explanation for the effectiveness of voting methods

IN Proc. Robotics: Science & Systems, 2008 Abstract—Motion planning in uncertain and dynamic environ- ments is an essential capability for autonomous robots. Partially observable Markov decision processes (POMDPs) provide a principled mathematical framework for solving such problems, but they are often avoided in robotics due to high computational complexity. Our goal is to create practical POMDP algorithms and software for common robotic tasks. To this end, we have developed a new point-based POMDP algorithm that exploits the notion of optimally reachable belief spaces to improve com- putational efficiency. In simulation, we successfully applied the algorithm to a set of common robotic tasks, including instances of coastal navigation, grasping, mobile robot exploration, and target tracking, all modeled as POMDPs with a large number of states. In most of the instances studied, our algorithm substantially outperformed one of the fastest existing point-based algorithms. A software package implementing our algorithm will soon be released at http://motion.comp.nus.edu.sg/ projects/pomdp/pomdp.html.

http://www.roboticsproceedings.org/rss04/p9.pdf

SARSOP: Efficient Point-Based POMDP Planning by Approximating Optimally Reachable Belief Spaces

We study the problem of building text classifiers using positive and unlabeled examples. The key feature of this problem is that there is no negative example for learning. Recently, a few techniques for solving this problem were proposed in the literature. These techniques are based on the same idea, which builds a classifier in two steps. Each existing technique uses a different method for each step. We first introduce some new methods for the two steps, and perform a comprehensive evaluation of all possible combinations of methods of the two steps. We then propose a more principled approach to solving the problem based on a biased formulation of SVM, and show experimentally that it is more accurate than the existing techniques.

/pdf/building-text-classifiers-using-positive-and-unlabeled-21s5ex7sdx.pdf

Building text classifiers using positive and unlabeled examples

Question classification is very important for question answering. This paper presents our research work on automatic question classification through machine learning approaches. We have experimented with five machine learning algorithms: Nearest Neighbors (NN), Naive Bayes (NB), Decision Tree (DT), Sparse Network of Winnows (SNoW), and Support Vector Machines (SVM) using two kinds of features: bag-of-words and bag-of-ngrams. The experiment results show that with only surface text features the SVM outperforms the other four methods for this task. Further, we propose to use a special kernel function called the tree kernel to enable the SVM to take advantage of the syntactic structures of questions. We describe how the tree kernel can be computed efficiently by dynamic programming. The performance of our approach is promising, when tested on the questions from the TREC QA track.

/pdf/question-classification-using-support-vector-machines-1elj6oqrvw.pdf

Wee Sun Lee

Papers

Boosting the margin: A new explanation for the effectiveness of voting methods

Boosting the margin: a new explanation for the effectiveness of voting methods

SARSOP: Efficient Point-Based POMDP Planning by Approximating Optimally Reachable Belief Spaces

Building text classifiers using positive and unlabeled examples

Question classification using support vector machines