An approach to the construction of classifiers from imbalanced datasets is described. A dataset is imbalanced if the classification categories are not approximately equally represented. Often real-world data sets are predominately composed of ``normal'' examples with only a small percentage of ``abnormal'' or ``interesting'' examples. It is also the case that the cost of misclassifying an abnormal (interesting) example as a normal example is often much higher than the cost of the reverse error. Under-sampling of the majority (normal) class has been proposed as a good means of increasing the sensitivity of a classifier to the minority class. This paper shows that a combination of our method of over-sampling the minority (abnormal) class and under-sampling the majority (normal) class can achieve better classifier performance (in ROC space) than only under-sampling the majority class. This paper also shows that a combination of our method of over-sampling the minority class and under-sampling the majority class can achieve better classifier performance (in ROC space) than varying the loss ratios in Ripper or class priors in Naive Bayes. Our method of over-sampling the minority class involves creating synthetic minority class examples. Experiments are performed using C4.5, Ripper and a Naive Bayes classifier. The method is evaluated using the area under the Receiver Operating Characteristic curve (AUC) and the ROC convex hull strategy.

In real-world environments it is usually difficult to specify target operating conditions precisely. This uncertainty makes building robust classification systems problematic. We present a method for the comparison of classifier performance that is robust to imprecise class distributions and misclassification costs. The ROC convex hull method combines techniques from ROC analysis, decision analysis and computational geometry, and adapts them to the particulars of analyzing learned classifiers. The method is efficient and incremental, minimizes the management of classifier performance data, and allows for clear visual comparisons and sensitivity analyses. We then show that it is possible to build a hybrid classifier that will perform at least as well as the best available classifier for any target conditions. This robust performance extends across a wide variety of comparison frameworks, including the optimization of metrics such as accuracy, expected cost, lift, precision, recall, and ...

Receiver Operating Characteristics (ROC) graphs are a useful technique for organizing classifiers and visualizing their performance. ROC graphs are commonly used in medical decision making, and in recent years have been increasingly adopted in the machine learning and data mining research communities. Although ROC graphs are apparently simple, there are some common misconceptions and pitfalls when using them in practice. This article serves both as a tutorial introduction to ROC graphs and as a practical guide for using them in research.

Receiver Operating Characteristics (ROC) graphs are a useful technique for organizing classifiers and visualizing their performance. ROC graphs are commonly used in medical decision making, and in recent years have been increasingly adopted in the machine learning and data mining research communities. Although ROC graphs are apparently simple, there are some common misconceptions and pitfalls when using them in practice. This article serves both as a tutorial introduction to ROC graphs and as a practical guide for using them in research. Keywords: 1

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.

This paper addresses the repeated acquisition of labels for data items when the labeling is imperfect. We examine the improvement (or lack thereof) in data quality via repeated labeling, and focus especially on the improvement of training labels for supervised induction. With the outsourcing of small tasks becoming easier, for example via Rent-A-Coder or Amazon’s Mechanical Turk, it often is possible to obtain less-than-expert labeling at low cost. With low-cost labeling, preparing the unlabeled part of the data can become considerably more expensive than labeling. We present repeated-labeling strategies of increasing complexity, and show several main results. (i) Repeated-labeling can improve label quality and model quality, but not always. (ii) When labels are noisy, repeated labeling can be preferable to single labeling even in the traditional setting where labels are not particularly cheap. (iii) As soon as the cost of processing the unlabeled data is not free, even the simple strategy of labeling everything multiple times can give considerable advantage. (iv) Repeatedly labeling a carefully chosen set of points is generally preferable, and we present a robust technique that combines different notions of uncertainty to select data points for which quality should be improved. The bottom line: the results show clearly that when labeling is not perfect, selective acquisition of multiple labels is a strategy that data miners should have in their repertoire; for certain label-quality/cost regimes, the benefit is substantial.

We propose and evaluate a family of methods for converting classifier learning algorithms and classification theory into cost-sensitive algorithms and theory. The proposed conversion is based on cost-proportionate weighting of the training examples, which can be realized either by feeding the weights to the classification algorithm (as often done in boosting), or by careful subsampling. We give some theoretical performance guarantees on the proposed methods, as well as empirical evidence that they are practical alternatives to existing approaches. In particular, we propose costing, a method based on cost-proportionate rejection sampling and ensemble aggregation, which achieves excellent predictive performance on two publicly available datasets, while drastically reducing the computation required by other methods.

Accurate, well-calibrated estimates of class membership probabilities are needed in many supervised learning applications, in particular when a cost-sensitive decision must be made about examples with example-dependent costs. This paper presents simple but successful methods for obtaining calibrated probability estimates from decision tree and naive Bayesian classifiers. Using the large and challenging KDD'98 contest dataset as a testbed, we report the results of a detailed experimental comparison of ten methods, according to four evaluation measures. We conclude that binning succeeds in significantly improving naive Bayesian probability estimates, while for improving decision tree probability estimates, we recommend smoothing by -estimation and a new variant of pruning that we call curtailment.

The class imbalance problem is one of the (relatively) new problems that emerged when machine learning matured from an embryonic science to an applied technology, amply used in the worlds of business, industry and scientific research.

Essentially all data mining algorithms assume that the datagenerating process is independent of the data miner's activities. However, in many domains, including spam detection, intrusion detection, fraud detection, surveillance and counter-terrorism, this is far from the case: the data is actively manipulated by an adversary seeking to make the classifier produce false negatives. In these domains, the performance of a classifier can degrade rapidly after it is deployed, as the adversary learns to defeat it. Currently the only solution to this is repeated, manual, ad hoc reconstruction of the classifier. In this paper we develop a formal framework and algorithms for this problem. We view classification as a game between the classifier and the adversary, and produce a classifier that is optimal given the adversary's optimal strategy. Experiments in a spam detection domain show that this approach can greatly outperform a classifier learned in the standard way, and (within the parameters of the problem) automatically adapt the classifier to the adversary's evolving manipulations.