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

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

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Combining Pattern Classifiers

Character recognition (CR) has been extensively studied in the last half century and has progressed to a level that is sufficient to produce technology-driven applications. Now, rapidly growing computational power is enabling the implementation of the present CR methodologies and is creating an increasing demand in many emerging application domains which require more advanced methodologies. This paper serves as a guide and update for readers working in the CR area. First, the historical evolution of CR systems is presented. Then, the available CR techniques, with their superiorities and weaknesses, are reviewed. Finally, the current status of CR is discussed and directions for future research are suggested. Special attention is given to off-line handwriting recognition, since this area requires more research in order to reach the ultimate goal of machine simulation of human reading.

An overview of character recognition focused on off-line handwriting

General regression and classification models are constructed as linear combinations of simple rules derived from the data. Each rule consists of a conjunction of a small number of simple statements concerning the values of individual input variables. These rule ensembles are shown to produce predictive accuracy comparable to the best methods. However, their principal advantage lies in interpretation. Because of its simple form, each rule is easy to understand, as is its influence on individual predictions, selected subsets of predictions, or globally over the entire space of joint input variable values. Similarly, the degree of relevance of the respective input variables can be assessed globally, locally in different regions of the input space, or at individual prediction points. Techniques are presented for automatically identifying those variables that are involved in interactions with other variables, the strength and degree of those interactions, as well as the identities of the other variables with which they interact. Graphical representations are used to visualize both main and interaction effects.

Predictive learning via rule ensembles

Stochastic discrimination is a general methodology for constructing classifiers appropriate for pattern recognition. It is based on combining arbitrary numbers of very weak components, which are usually generated by some pseudorandom process, and it has the property that the very complex and accurate classifiers produced in this way retain the ability, characteristic of their weak component pieces, to generalize to new data. In fact, it is often observed, in practice, that classifier performance on test sets continues to rise as more weak components are added, even after performance on training sets seems to have reached a maximum. This is predicted by the underlying theory, for even though the formal error rate on the training set may have reached a minimum, more sophisticated measures intrinsic to this method indicate that classifier performance on both training and test sets continues to improve as complexity increases. We begin with a review of the method of stochastic discrimination as applied to pattern recognition. Through a progression of examples keyed to various theoretical issues, we discuss considerations involved with its algorithmic implementation. We then take such an algorithmic implementation and compare its performance, on a large set of standardized pattern recognition problems from the University of California Irvine, and Statlog collections, to many other techniques reported on in the literature, including boosting and bagging. In doing these studies, we compare our results to those reported in the literature by the various authors for the other methods, using the same data and study paradigms used by them. Included in the paper is an outline of the underlying mathematical theory of stochastic discrimination and a remark concerning boosting, which provides a theoretical justification for properties of that method observed in practice, including its ability to generalize.

On the algorithmic implementation of stochastic discrimination

In this paper, we describe a system for rapid verification of unconstrained off-line handwritten phrases using perceptual holistic features of the handwritten phrase image. The system is used to verify handwritten street names automatically extracted from live US mail against recognition results of analytical classifiers. Presented with a binary image of a street name and an ASCII street name, holistic features (reference lines, large gaps and local contour extrema) of the street name hypothesis are "predicted" from the expected features of the constituent characters using heuristic rules. A dynamic programming algorithm is used to match the predicted features with the extracted image features. Classes of holistic features are matched sequentially in increasing order of cost, allowing an ACCEPT/REJECT decision to be arrived at in a time-efficient manner. The system rejects errors with 98 percent accuracy at the 30 percent accept level, while consuming approximately 20/msec per image on the average on a 150 MHz SPARC 10.

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Holistic verification of handwritten phrases

The authors describe ongoing research on a system for rapid verification of unconstrained off-line handwritten phrases using perceptual holistic features of the handwritten phrase image. The system is used to verify handwritten street names automatically extracted from live US mail against recognition results of analytical classifiers. The system rejects errors with 98% accuracy at the 30% accept level, while consuming approximately 20 msec per image on the average on a 150 MHz SPARC 10.

The HOVER system for rapid holistic verification of off-line handwritten phrases

A central task in the interpretation of handwritten US postal addresses is the off-line recognition of the street name. A lexicon of candidate street names may be extracted from a database of postal delivery points (DPF) by first locating and recognizing numeric fields such as the ZIP code and strewet number. The off-line handwritten word recognition (HWR) task is made difficult by the unconstrained, omni-scriptor nature of the input, and incomplete lexicons resulting from errors in processing numeric fields and intrinsic deficiencies in the DPF. In this paper, we describe an empirical approach to the design of a multi-classifier HWR Thresholding/Control module which forms part of a real-time handwritten address interpretation (HWAI) system. The decisions of two word classifiers are combined in a hierarchical manner to improve recognition and error-rejection performance, while meeting real-time requirements. The design employs logistic regression and agreement for evidence combination, and lexicon reduction for improved throughput as well as performance. The paper concludes with experimental results and directions for future research.

E. Kleinberg

Papers

On the algorithmic implementation of stochastic discrimination

Holistic verification of handwritten phrases

The HOVER system for rapid holistic verification of off-line handwritten phrases

Empirical Design of a Multi-Classifier Thresholding/Control Strategy for Recognition of Handwritten Street Names

HOVER system for rapid holistic verification of off-line handwritten phrases