Johannes Fürnkranz

Separate-and-Conquer Rule Learning

This paper is a survey of inductive rule learning algorithms that use a separate-and-conquer strategy. This strategy can be traced back to the AQ learning system and still enjoys popularity as can be seen from its frequent use in inductive logic programming systems. We will put this wide variety of algorithms into a single framework and analyze them along three different dimensions, namely their search, language and overfitting avoidance biases.

Multilabel classification via calibrated label ranking

Label ranking studies the problem of learning a mapping from instances to rankings over a predefined set of labels. Hitherto existing approaches to label ranking implicitly operate on an underlying (utility) scale which is not calibrated in the sense that it lacks a natural zero point. We propose a suitable extension of label ranking that incorporates the calibrated scenario and substantially extends the expressive power of these approaches. In particular, our extension suggests a conceptually novel technique for extending the common learning by pairwise comparison approach to the multilabel scenario, a setting previously not being amenable to the pairwise decomposition technique. The key idea of the approach is to introduce an artificial calibration label that, in each example, separates the relevant from the irrelevant labels. We show that this technique can be viewed as a combination of pairwise preference learning and the conventional relevance classification technique, where a separate classifier is trained to predict whether a label is relevant or not. Empirical results in the area of text categorization, image classification and gene analysis underscore the merits of the calibrated model in comparison to state-of-the-art multilabel learning methods.

Round robin classification

In this paper, we discuss round robin classification (aka pairwise classification), a technique for handling multi-class problems with binary classifiers by learning one classifier for each pair of classes. We present an empirical evaluation of the method, implemented as a wrapper around the Ripper rule learning algorithm, on 20 multi-class datasets from the UCI database repository. Our results show that the technique is very likely to improve Rippers classification accuracy without having a high risk of decreasing it. More importantly, we give a general theoretical analysis of the complexity of the approach and show that its run-time complexity is below that of the commonly used one-against-all technique. These theoretical results are not restricted to rule learning but are also of interest to other communities where pairwise classification has recently received some attention. Furthermore, we investigate its properties as a general ensemble technique and show that round robin classification with C5.0 may improve C5.0s performance on multi-class problems. However, this improvement does not reach the performance increase of boosting, and a combination of boosting and round robin classification does not produce any gain over conventional boosting. Finally, we show that the performance of round robin classification can be further improved by a straight-forward integration with bagging.

Label ranking by learning pairwise preferences

Preference learning is an emerging topic that appears in different guises in the recent literature. This work focuses on a particular learning scenario called label ranking, where the problem is to learn a mapping from instances to rankings over a finite number of labels. Our approach for learning such a mapping, called ranking by pairwise comparison (RPC), first induces a binary preference relation from suitable training data using a natural extension of pairwise classification. A ranking is then derived from the preference relation thus obtained by means of a ranking procedure, whereby different ranking methods can be used for minimizing different loss functions. In particular, we show that a simple (weighted) voting strategy minimizes risk with respect to the well-known Spearman rank correlation. We compare RPC to existing label ranking methods, which are based on scoring individual labels instead of comparing pairs of labels. Both empirically and theoretically, it is shown that RPC is superior in terms of computational efficiency, and at least competitive in terms of accuracy.

ROC 'n' rule learning: towards a better understanding of covering algorithms

This paper provides an analysis of the behavior of separate-and-conquer or covering rule learning algorithms by visualizing their evaluation metrics and their dynamics in coverage space, a variant of ROC space. Our results show that most commonly used metrics, including accuracy, weighted relative accuracy, entropy, and Gini index, are equivalent to one of two fundamental prototypes: precision, which tries to optimize the area under the ROC curve for unknown costs, and a cost-weighted difference between covered positive and negative examples, which tries to find the optimal point under known or assumed costs. We also show that a straightforward generalization of the m-estimate trades off these two prototypes. Furthermore, our results show that stopping and filtering criteria like CN2’s significance test focus on identifying significant deviations from random classification, which does not necessarily avoid overfitting. We also identify a problem with Foil’s MDL-based encoding length restriction, which proves to be largely equivalent to a variable threshold on the recall of the rule. In general, we interpret these results as evidence that, contrary to common conception, pre-pruning heuristics are not very well understood and deserve more investigation.

Pairwise preference learning and ranking

We consider supervised learning of a ranking function, which is a mapping from instances to total orders over a set of labels (options). The training information consists of examples with partial (and possibly inconsistent) information about their associated rankings. From these, we induce a ranking function by reducing the original problem to a number of binary classification problems, one for each pair of labels. The main objective of this work is to investigate the trade-off between the quality of the induced ranking function and the computational complexity of the algorithm, both depending on the amount of preference information given for each example. To this end, we present theoretical results on the complexity of pairwise preference learning, and experimentally investigate the predictive performance of our method for different types of preference information, such as top-ranked labels and complete rankings. The domain of this study is the prediction of a rational agents ranking of actions in an uncertain environment.

Exploiting Structural Information for Text Classification on the WWW

In this paper, we report on a set of experiments that explore the utility of making use of the structural information of WWW documents. Our working hypothesis is that it is often easier to classify a hypertext page using information provided on pages that point to it instead of using information that is provided on the page itself. We present experimental evidence that confirms this hypothesis on a set of Web-pages that relate to Computer Science Departments.

Pruning Algorithms for Rule Learning

Pre-pruning and Post-pruning are two standard techniques for handling noise in decision tree learning. Pre-pruning deals with noise during learning, while post-pruning addresses this problem after an overfitting theory has been learned. We first review several adaptations of pre- and post-pruning techniques for separate-and-conquer rule learning algorithms and discuss some fundamental problems. The primary goal of this paper is to show how to solve these problems with two new algorithms that combine and integrate pre- and post-pruning.

Efficient Pairwise Multilabel Classification for Large-Scale Problems in the Legal Domain

In this paper we applied multilabel classification algorithms to the EUR-Lex database of legal documents of the European Union. On this document collection, we studied three different multilabel classification problems, the largest being the categorization into the EUROVOC concept hierarchy with almost 4000 classes. We evaluated three algorithms: (i) the binary relevance approach which independently trains one classifier per label; (ii) the multiclass multilabel perceptron algorithm, which respects dependencies between the base classifiers; and (iii) the multilabel pairwise perceptron algorithm, which trains one classifier for each pair of labels. All algorithms use the simple but very efficient perceptron algorithm as the underlying classifier, which makes them very suitable for large-scale multilabel classification problems. The main challenge we had to face was that the almost 8,000,000 perceptrons that had to be trained in the pairwise setting could no longer be stored in memory. We solve this problem by resorting to the dual representation of the perceptron, which makes the pairwise approach feasible for problems of this size. The results on the EUR-Lex database confirm the good predictive performance of the pairwise approach and demonstrates the feasibility of this approach for large-scale tasks.

Efficient Pairwise Classification

Pairwise classification is a class binarization procedure that converts a multi-class problem into a series of two-class problems, one problem for each pair of classes. While it can be shown that for training, this procedure is more efficient than the more commonly used one-against-all approach, it still has to evaluate a quadratic number of classifiers when computing the predicted class for a given example. In this paper, we propose a method that allows a faster computation of the predicted class when weighted or unweighted voting are used for combining the predictions of the individual classifiers. While its worst-case complexity is still quadratic in the number of classes, we show that even in the case of completely random base classifiers, our method still outperforms the conventional pairwise classifier. For the more practical case of well-trained base classifiers, its asymptotic computational complexity seems to be almost linear.