Conjunctions of Unate DNF Formulas: Learning and Structure

AbstractA central topic in query learning is to determine which classes of Boolean formulas are efficiently learnable with membership and equivalence queries. We consider the class Rkconsisting of conjunctions ofkunate DNF formulas. This class generalizes the class ofk-clause CNF formulas and the class of unate DNF formulas, both of which are known to be learnable in polynomial time with membership and equivalence queries. We prove that R2can be properly learned with a polynomial number of polynomial-size membership and equivalence queries, but can be properly learned in polynomial time with such queries if and only if P=NP. Thus the barrier to properly learning R2with membership and equivalence queries is computational rather than informational. Few results of this type are known. In our proofs, we use recent results of Hellersteinet al.(1997,J. Assoc. Comput. Mach.43(5), 840–862), characterizing the classes that are polynomial-query learnable, together with work of Bshouty on the monotone dimension of Boolean functions. We extend some of our results to Rkand pose open questions on learning DNF formulas of small monotone dimension. We also prove structural results for Rk. We construct, for any fixedk⩾2, a class of functionsfthat cannot be represented by any formula in Rk, but which cannot be “easily” shown to have this property. More precisely, for any functionfonnvariables in the class, the value offon any polynomial-size set of points in its domain is not a witness thatfcannot be represented by a formula in Rk. Our construction is based on BCH codes

Active Learning with Multiple Views

Active learners alleviate the burden of labeling large amounts of data by detecting and asking the user to label only the most informative examples in the domain. We focus here on active learning for multi-view domains, in which there are several disjoint subsets of features (views), each of which is sufficient to learn the target concept. In this paper we make several contributions. First, we introduce Co-Testing, which is the first approach to multi-view active learning. Second, we extend the multi-view learning framework by also exploiting weak views, which are adequate only for learning a concept that is more general/specific than the target concept. Finally, we empirically show that Co-Testing outperforms existing active learners on a variety of real world domains such as wrapper induction, Web page classification, advertisement removal, and discourse tree parsing

Learning to Reason

We introduce a new framework for the study of reasoning. The Learning (in order) to Reason approach developed here combines the interfaces to the world used by known learning models with the reasoning task and a performance criterion suitable for it. In this framework the intelligent agent is given access to her favorite learning interface, and is also given a grace period in which she can interact with this interface and construct her representation KB of the world W. Her reasoning performance is measured only after this period, when she is presented with queries a from some query language, relevant to the world, and has to answer whether W implies a. The approach is meant to overcome the main computational difficulties in the traditional treatment of reasoning which stem from its separation from the "world". First, by allowing the reasoning task to interface the world (as in the known learning models), we avoid the rigid syntactic restriction on the intermediate knowledge representation. Second, we make explicit the dependence of the reasoning performance on the input from the environment. This is possible only because the agent interacts with the world when constructing her knowledge representation. We show how previous results from learning theory and reasoning illustrate the usefulness of the Learning to Reason approach by exhibiting new results that are not possible in the traditional setting. First, we give a Learning to Reason algorithm for a class of propositional languages for which there are no efficient reasoning algorithms, when represented as a traditional (formula-based) knowledge base. Second, we exhibit a Learning to Reason Algorithm for a class of propositional languages that is not known to be learnable in the traditional sense.Engineering and Applied Science