We abstract out the core search problem of active learning schemes, to better understand the extent to which adaptive labeling can improve sample complexity. We give various upper and lower bounds on the number of labels which need to be queried, and we prove that a popular greedy active learning rule is approximately as good as any other strategy for minimizing this number of labels.

We prove generalization error bounds for predicting entries in a partially observed matrix by approximating the observed entries with a low-rank matrix. To do so, we bound the number of sign configurations of lowrank matrices using a result about realizable oriented matroids.

In this paper we discuss the Recommendz recommender system. This domain-independent system combines the advantages of collaborative and content-based filtering in a novel way. By allowing users to provide feedback not only about an item as a whole, but also properties of an item that motivated their opinion, increased performance seems to be achieved. The features used to describe items are specified by the users of the system rather than predetermined using manual knowledge-engineering. We describe a method for combining descriptive features and simple ratings, and provide a performance analysis.

We introduce a new combinatorial dimension that characterizes the number of queries needed to learn, no matter what set of queries is used. This new dimension generalizes previous dimensions providing upper and lower bounds on the query complexity for all sorts of queries, and not for just example-based queries as in previous works. Moreover, the new characterization is not only valid for exact learning but also for approximate learning. We present several Results from sections 4 and 5 were presented at COLT/EUROCOLT 2001 [4]; results from sections 7 and 8 were presented at ALT 2002 [24].

The goal of one type of recommenders is to minimize the number of clicks users need to reach the information they are looking for. Recommenders typically estimate the probability that pages contain the user’s target information and provide the user with links to the most promising pages. In this paper we show that this greedy strategy can lead to recommendations that are suboptimal in terms of the number of clicks. We present a recommendation method which aims at gathering information about the user’s targets rather than guessing the target immediately. This method uses recommendations as questions and clicks on links as answers. Evaluation shows that this strategy leads to significantly shorter user sessions than the greedy strategy. 1

In this paper we present an overview of a recommender system that attempts to predict user preferences based on several sources including prior choices and selected user-defined features. By using a combination of collaborative filtering and semantic features, we hope to provide performance superior to either alone. Further, our set of semantic features is acquired and updated using a learning-based procedure that avoids the need for manual knowledgeengineering. Our system is implemented in a web-based application server environment and can be used with arbitrary domains, although the test data reported here is restricted to recommendations of movies. I.

We introduce a new combinatorial dimension that characterizes the number of queries needed to learn, no matter what set of queries is used. This new dimension generalizes previous dimensions providing upper and lower bounds on the query complexity for all sorts of queries, and not for just example-based queries as in previous works. Moreover, the new characterization is not only valid for exact learning but also for approximate learning. We present several

We study simultaneous learning and covering problems: submodular set cover problems that depend on the solution to an active (query) learning problem. The goal is to jointly minimize the cost of both learning and covering. We extend recent work in this setting to allow for a limited amount of adversarial noise. Certain noisy query learning problems are a special case of our problem. Crucial to our analysis is a lemma showing the logical OR of two submodular cover constraints can be reduced to a single submodular set cover constraint. Combined with known results, this new lemma allows for arbitrary monotone circuits of submodular cover constraints to be reduced to a single constraint. As an example practical application, we present a movie recommendation website that minimizes the total cost of learning what the user wants to watch and recommending a set of movies. 1. Background Consider a movie recommendation problem where we want to recommend to a user a small set of movies to watch. Assume first that we already have some model of the user’s taste in movies (for example learned from the user’s ratings history or stated genre preferences). In this case, we can pose the recommendation problem as an optimization problem: using the model, we can design an objective function F (S) which measures the quality of a set of movie recommendations S ⊆ V. Our goal is then to maximize F (S) subject to a constraint on the size or cost of S (e.g. |S | ≤ k). Alternatively