Research in machine learning, statistics and related fields has produced a wide variety of algorithms for classification. However, most of these algorithms assume that all errors have the same cost, which is seldom the case in KDD prob- lems. Individually making each classification learner costsensitive is laborious, and often non-trivial. In this paper we propose a principled method for making an arbitrary classifier cost-sensitive by wrapping a cost-minimizing procedure around it. This procedure, called MetaCost, treats the underlying classifier as a black box, requiring no knowledge of its functioning or change to it. Unlike stratification, MetaCost is applicable to any number of classes and to arbitrary cost matrices. Empirical trials on a large suite of benchmark databases show that MetaCost almost always produces large cost reductions compared to the cost-blind classifier used (C4.5RULES) and to two forms of stratification. Further tests identify the key components of MetaCost and those that can be varied without substantial loss. Experiments on a larger database indicate that MetaCost scales well.

Tree induction is one of the most effective and widely used methods for building classification models. However, many applications require cases to be ranked by the probability of class membership. Probability estimation trees (PETs) have the same attractive features as classification trees (e.g., comprehensibility, accuracy and efficiency in high dimensions and on large data sets). Unfortunately, decision trees have been found to provide poor probability estimates. Several techniques have been proposed to build more accurate PETs, but, to our knowledge, there has not been a systematic experimental analysis of which techniques actually improve the probability-based rankings, and by how much. In this paper we first discuss why the decision-tree representation is not intrinsically inadequate for probability estimation. Inaccurate probabilities are partially the result of decision-tree induction algorithms that focus on maximizing classification accuracy and minimizing tree size (for example via reduced-error pruning). Larger trees can be better for probability estimation, even if the extra size is superfluous for accuracy maximization. We then present the results of a comprehensive set of experiments, testing some straghtforward methods for improving probability-based rankings. We show that using a simple, common smoothing method--the Laplace correction--uniformly improves probability-based rankings. In addition, bagging substantioJly improves the rankings, and is even more effective for this purpose than for improving accuracy. We conclude that PETs, with these simple modifications, should be considered when rankings based on class-membership probability are required.

1 INTRODUCTION The AdaBoost algorithm [7, 16] has recently proved to be an important component in practical learning algorithms. Two of the most successful combinations have been boosting decision trees and boosting stumps [6, 1, 13, 8]. Stumps are the simplest special case of decision trees which consist of a single decision node and two prediction leaves. Boosting decision trees learning algorithms, such as CART [2] and C4.5 [14], yields very good classifiers.

. One of the defining challenges for the KDD research community is to enable inductive learning algorithms to mine very large databases. This paper summarizes, categorizes, and compares existing work on scaling up inductive algorithms. We concentrate on algorithms that build decision trees and rule sets, in order to provide focus and specific details; the issues and techniques generalize to other types of data mining. We begin with a discussion of important issues related to scaling up. We highlight similarities among scaling techniques by categorizing them into three main approaches. For each approach, we then describe, compare, and contrast the different constituent techniques, drawing on specific examples from published papers. Finally, we use the preceding analysis to suggest how to proceed when dealing with a large problem, and where to focus future research. Keywords: scaling up, inductive learning, decision trees, rule learning 1. Introduction The knowledge discovery and data...

Abstract: This chapter discusses the use of evolutionary algorithms, particularly genetic algorithms and genetic programming, in data mining and knowledge discovery. We focus on the data mining task of classification. In addition, we discuss some preprocessing and postprocessing steps of the knowledge discovery process, focusing on attribute selection and pruning of an ensemble of classifiers. We show how the requirements of data mining and knowledge discovery influence the design of evolutionary algorithms. In particular, we discuss how individual representation, genetic operators and fitness functions have to be adapted for extracting high-level knowledge from data. 1.

Abstract. Many KDD systems incorporate an implicit or explicit preference for simpler models, but this use of “Occam’s razor ” has been strongly criticized by several authors (e.g., Schaffer, 1993; Webb, 1996). This controversy arises partly because Occam’s razor has been interpreted in two quite different ways. The first interpretation (simplicity is a goal in itself) is essentially correct, but is at heart a preference for more comprehensible models. The second interpretation (simplicity leads to greater accuracy) is much more problematic. A critical review of the theoretical arguments for and against it shows that it is unfounded as a universal principle, and demonstrably false. A review of empirical evidence shows that it also fails as a practical heuristic. This article argues that its continued use in KDD risks causing significant opportunities to be missed, and should therefore be restricted to the comparatively few applications where it is appropriate. The article proposes and reviews the use of domain constraints as an alternative for avoiding overfitting, and examines possible methods for handling the accuracy–comprehensibility trade-off.

This paper motivates and precisely formulates the problem of learning from distributed data; describes a general strategy for transforming traditional machine learning algorithms into algorithms for learning from distributed data; demonstrates the application of this strategy to devise algorithms for decision tree induction from distributed data; and identifies the conditions under which the algorithms in the distributed setting are superior to their centralized counterparts in terms of time and communication complexity; The resulting algorithms are provably exact in that the decision tree constructed from distributed data is identical to that obtained in the centralized setting. Some natural extensions leading to algorithms for learning from heterogeneous distributed data and learning under privacy constraints are outlined.

Decision trees are one of the most effective and widely used classification methods. However, many applications require class probability estimates, and probability estimation trees (PETs) have the same attractive features as classification trees (e.g., comprehensibility, accuracy and efficiency in high dimensions and on large data sets). Unfortunately, decision trees have been found to provide poor probability estimates. Several techniques have been proposed to build more accurate PETs, but, to our knowledge, there has not been a systematic experimental analysis of which techniques actually improve the probability estimates, and by how much. In this paper we first discuss why the decision-tree representation is not intrinsically inadequate for probability estimation. Inaccurate probabilities are partially the result of decision-tree induction algorithms that focus on maximizing classification accuracy and minimizing tree size (for example via reduced-error pruning). Larger tree...

The error rate of decision-tree and other classification learners can often be much reduced by bagging: learning multiple models from bootstrap samples of the database, and combining them by uniform voting. In this paper we empirically test two alternative explanations for this, both based on Bayesian learning theory: (1) bagging works because it is an approximation to the optimal procedure of Bayesian model averaging, with an appropriate implicit prior; (2) bagging works because it effectively shifts the prior to a more appropriate region of model space. All the experimental evidence contradicts the first hypothesis, and confirms the second. Bagging Bagging (Breiman 1996a) is a simple and effective way to reduce the error rate of many classification learning algorithms. For example, in the empirical study described below, it reduces the error of a decision-tree learner in 19 of 26 databases, by 4% on average. In the bagging procedure, given a training set of size s, a "bootstrap" re...

We propose to use AdaBoost to efficiently learn classifiers over very large and possibly distributed data sets that cannot fit into main memory, as well as on-line learning where new data become available periodically. We propose two new ways to apply AdaBoost. The first allows the use of a small sample of the weighted training set to compute a weak hypothesis. The second approach involves using AdaBoost as a means to re-weight classifiers in an ensemble, and thus to reuse previously computed classifiers along with new classifier computed on a new increment of data. These two techniques of using AdaBoost provide scalable, distributed and on-line learning. We discuss these methods and their implementation in JAM, an agent-based learning system. Empirical studies on four real world and artifical data sets have shown results that are either comparable to or better than learning classifiers over the complete training set and, in some cases, are comparable to boosting on the complete data set. However, our algorithms use much smaller samples of the training set and require much less memory.