We consider the problem of using a large unlabeled sample to boost performance of a learning algorithm when only a small set of labeled examples is available. In particular, we consider a setting in which the description of each example can be partitioned into two distinct views, motivated by the task of learning to classify web pages. For example, the description of a web page can be partitioned into the words occurring on that page, and the words occurring in hyperlinks that point to that page. We assume that either view of the example would be su cient for learning if we had enough labeled data, but our goal is to use both views together to allow inexpensive unlabeled data to augment a m uch smaller set of labeled examples. Speci cally, the presence of two distinct views of each example suggests strategies in which t wo learning algorithms are trained separately on each view, and then each algorithm's predictions on new unlabeled examples are used to enlarge the training set of the other. Our goal in this paper is to provide a PAC-style analysis for this setting, and, more broadly, a P AC-style framework for the general problem of learning from both labeled and unlabeled data. We also provide empirical results on real web-page data indicating that this use of unlabeled examples can lead to signi cant improvement o f h ypotheses in practice. As part of our analysis, we p r o vide new reThis is an extended version of a paper that appeared in the

In this survey, we review work in machine learning on methods for handling data sets containing large amounts of irrelevant information. We focus on two k ey issues: the problem of selecting relevant features, and the problem of selecting relevant examples. We describe the advances that have been made on these topics in both empirical and theoretical work in machine learning, and we present a general framework that we use to compare di erent methods. We close with some challenges for future work in this area.

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We demonstrate that, ignoring computational constraints, it is possible to release privacy-preserving databases that are useful for all queries over a discretized domain from any given concept class with polynomial VC-dimension. We show a new lower bound for releasing databases that are useful for halfspace queries over a continuous domain. Despite this, we give a privacy-preserving polynomial time algorithm that releases information useful for all halfspace queries, for a slightly relaxed definition of usefulness. Inspired by learning theory, we introduce a new notion of data privacy, which we call distributional privacy, and show that it is strictly stronger than the prevailing privacy notion, differential privacy.