We discuss the problem of ranking k instances with the use of a "large margin" principle. We introduce two main approaches: the first is the "fixed margin" policy in which the margin of the closest neighboring classes is being maximized - which turns out to be a direct generalization of SVM to ranking learning. The second approach allows for k - 1 different margins where the sum of margins is maximized. This approach is shown to reduce to lI-SVM when the number of classes k 2. Both approaches are optimal in size of 21 where I is the total number of training examples. Experiments performed on visual classification and "collaborative filtering" show that both approaches outperform existing ordinal regression algorithms applied for ranking and multi-class SVM applied to general multi-class classification.

We introduce a new learning algorithm for decision lists to allow features that are constructed from the data and to allow a tradeoff between accuracy and complexity. We bound its generalization error in terms of the number of errors and the size of the classifier it finds on the training data. We also compare its performance on some natural data sets with the set covering machine and the support vector machine.

In this paper, we study a special kind of learning problem in which each training instance is given a set of (or distribution over) candidate class labels and only one of the candidate labels is the correct one. Such a problem can occur, e.g., in an information retrieval setting where a set of words is associated with an image, or if classes labels are organized hierarchically. We propose a novel discriminative approach for handling the ambiguity of class labels in the training examples. The experiments with the proposed approach over five different UCI datasets show that our approach is able to find the correct label among the set of candidate labels and actually achieve performance close to the case when each training instance is given a single correct label. In contrast, naIve methods degrade rapidly as more ambiguity is introduced into the labels. 1 Introduction Supervised and unsupervised learning problems have been extensively studied in the machine learning literature. In supervised classification each training instance is associated with a single class label, while in unsupervised classification (i.e.

One of the first semi-supervised algorithms [1] was applied to web page classification. This is a typical example where the number of unlabeled examples can be made as large as possible since there are billions of web page, but labeling is expensive since it requires human intervention. Since then, there has been a lot of interest for this paradigm in the machine learning community; an extensive review of existing techniques can be found in [10]. It has been shown experimentally that under certain conditions, the decision function can be estimated more accurately, yielding lower generalization error [1, 4, 6]. However, in a discriminative framework, it is not obvious to determine how unlabeled data or even the perfect knowledge of the input distribution P(x) can help in the estimation of the decision function.

One of the first semi-supervised algorithms [1] was applied to web page classification. This is a typical example where the number of unlabeled examples can be made as large as possible since there are billions of web page, but labeling is expensive since it requires human intervention. Since then, there has been a lot of interest for this paradigm in the machine learning community; an extensive review of existing techniques can be found in [10]. It has been shown experimentally that under certain conditions, the decision function canbe estimated more accurately, yielding lower generalization error [1, 4, 6] . However, in a discriminative framework, it is not obvious to determine how unlabeled dataor even the perfect knowledge of the input distribution P(x) can help in the estimation of the decision function.

We introduce a new learning algorithm for decision lists to allow features that are constructed from the data and to allow a tradeoff betweenaccuracy and complexity. We bound its generalization error in terms of the number of errors and the size of the classifier it finds on the training data. We also compare its performance on some natural data sets with the set covering machine and the support vector machine.

In this paper, we study a special kind of learning problem in which each training instance is given a set of (or distribution over) candidate class labels and only one of the candidate labels is the correct one. Such a problem can occur, e.g., in an information retrieval setting where a set of words is associated with an image, or if classes labels are organized hierarchically. We propose a novel discriminative approach for handling the ambiguity of class labels in the training examples. The experiments with the proposed approach over five different UCI datasets show that our approach is able to find the correct label among the set of candidate labels and actually achieve performance close to the case when each training instance is given a single correct label. In contrast, naIve methods degrade rapidly as more ambiguity is introduced into the labels. 1 Introduction Supervised and unsupervised learning problems have been extensively studied in the machine learning literature. In supervised classification each training instance is associated with a single class label, while in unsupervised classification (i.e.

We discuss the problem of ranking k instances with the use of a "large margin" principle. We introduce two main approaches: the first is the "fixed margin" policy in which the margin of the closest neighboring classes is being maximized - which turns out to be a direct generalization ofSVM to ranking learning. The second approach allows for k - 1 different margins where the sum of margins is maximized. This approach is shown to reduce to lI-SVM when the number of classes k 2. Both approaches are optimal in size of 21 where I is the total number of training examples. Experiments performed on visual classification and "collaborative filtering"show that both approaches outperform existing ordinal regression algorithms applied for ranking and multi-class SVM applied to general multi-class classification. 1 Introduction In this paper we investigate the problem of inductive learning from the point of view of predicting variables of ordinal scale [3, 7,5], a setting referred to as ranking learning or ordinal regression. We consider the problem of applying the large margin principle used in Support Vector methods [12, 1] to the ordinal regression problem while maintaining an (optimal) problem size linear in the number of training examples.

For large, real-world inductive learning problems, the number of training examples often must be limited due to the costs associated with procuring, preparing, and storing the training examples and/or the computational costs associated with learning from them. In such circumstances, one question of practical importance is: if only n training examples can be selected, in what proportion should the classes be represented? In this article we help to answer this question by analyzing, for a fixed training-set size, the relationship between the class distribution of the training data and the performance of classification trees induced from these data. We study twenty-six data sets and, for each, determine the best class distribution for learning. The naturally occurring class distribution is shown to generally perform well when classifier performance is evaluated using undifferentiated error rate (0/1 loss). However, when the area under the ROC curve is used to evaluate classifier performance, a balanced distribution is shown to perform well. Since neither of these choices for class distribution always generates the best-performing classifier, we introduce a "budget-sensitive" progressive sampling algorithm for selecting training examples based on the class associated with each example. An empirical analysis of this algorithm shows that the class distribution of the resulting training set yields classifiers with good (nearly-optimal) classification performance.

The article introduces the reader to a large interdisciplinary research project whose goal is to use AI to gain new insight into a complex artistic phenomenon. We study fundamental principles of expressive music performance by measuring performance aspects in large numbers of recordings by highly skilled musicians (concert pianists) and analyzing the data with state-of-the-art methods from areas such as machine learning, data mining, and data visualization. The article first introduces the general research questions that guide the project and then summarizes some of the most important results achieved to date, with an emphasis on the most recent and still rather speculative work. A broad view of the discovery process is given, from data acquisition through data visualization to inductive model building and pattern discovery, and it turns out that AI plays an important role in all stages of such an ambitious enterprise. Our current results show that it is possible for machines to make novel and interesting discoveries even in a domain such as music and that even if we might never find the "Horowitz Factor," AI can give us completely new insights into complex artistic behavior.