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OPUS is a branch and bound search algorithm that enables efficient admissible search through spaces for which the order of search operator application is not significant. The algorithm's search efficiency is demonstrated with respect to very large machine learning search spaces. The use of admissible search is of potential value to the machine learning community as it means that the exact learning biases to be employed for complex learning tasks can be precisely specified and manipulated. OPUS also has potential for application in other areas of artificial intelligence, notably, truth maintenance.

Characteristic models are an alternative, model based, representation for Horn expressions. It has been shown that these two representations are incomparable and each has its advantages over the other. It is therefore natural to ask what is the cost of translating, back and forth, between these representations. Interestingly, the same translation questions arise in database theory, where it has applications to the design of relational databases. This paper studies the computational complexity of these problems. Our main result is that the two translation problems are equivalent under polynomial reductions, and that they are equivalent to the corresponding decision problem. Namely, translating is equivalent to deciding whether a given set of models is the set of characteristic models for a given Horn expression. We also relate these problems to the hypergraph transversal problem, a well known problem which is related to other applications in AI and for which no polynomial time algorithm is known. It is shown that in general our translation problems are at least as hard as the hypergraph transversal problem, and in a special case they are equivalent to it.

We describe a machine learning method for predicting the value of a real-valued function, given the values of multiple input variables. The method induces solutions from samples in the form of ordered disjunctive normal form (DNF) decision rules. A central objective of the method and representation is the induction of compact, easily interpretable solutions. This rule-based decision model can be extended to search efficiently for similar cases prior to approximating function values. Experimental results on real-world data demonstrate that the new techniques are competitive with existing machine learning and statistical methods and can sometimes yield superior regression performance.

We present a definition of cause and effect in terms of decision-theoretic primitives and thereby provide a principled foundation for causal reasoning. Our definition departs from the traditional view of causation in that causal assertions may vary with the set of decisions available. We argue that this approach provides added clarity to the notion of cause. Also in this paper, we examine the encoding of causal relationships in directed acyclic graphs. We describe a special class of influence diagrams, those in canonical form, and show its relationship to Pearl's representation of cause and effect. Finally, we show how canonical form facilitates counterfactual reasoning.

This article describes an application of three well-known statistical methods in the field of game-tree search: using a large number of classified Othello positions, feature weights for evaluation functions with a game-phase-independent meaning are estimated by means of logistic regression, Fisher's linear discriminant, and the quadratic discriminant function for normally distributed features. Thereafter, the playing strengths are compared by means of tournaments between the resulting versions of a world-class Othello program. In this application, logistic regression - which is used here for the first time in the context of game playing - leads to better results than the other approaches.

In the area of inductive learning, generalization is a main operation, and the usual definition of induction is based on logical implication. Recently there has been a rising interest in clausal representation of knowledge in machine learning. Almost all inductive learning systems that perform generalization of clauses use the relation theta-subsumption instead of implication. The main reason is that there is a well-known and simple technique to compute least general generalizations under theta-subsumption, but not under implication. However generalization under theta-subsumption is inappropriate for learning recursive clauses, which is a crucial problem since recursion is the basic program structure of logic programs. We note that implication between clauses is undecidable, and we therefore introduce a stronger form of implication, called T-implication, which is decidable between clauses. We show that for every finite set of clauses there exists a least general generalization under T-implication. We describe a technique to reduce generalizations under implication of a clause to generalizations under theta-subsumption of what we call an expansion of the original clause. Moreover we show that for every non-tautological clause there exists a T-complete expansion, which means that every generalization under T-implication of the clause is reduced to a generalization under theta-subsumption of the expansion.

This paper presents an approach to learning from situated, interactive tutorial instruction within an ongoing agent. Tutorial instruction is a flexible (and thus powerful) paradigm for teaching tasks because it allows an instructor to communicate whatever types of knowledge an agent might need in whatever situations might arise. To support this flexibility, however, the agent must be able to learn multiple kinds of knowledge from a broad range of instructional interactions. Our approach, called situated explanation, achieves such learning through a combination of analytic and inductive techniques. It combines a form of explanation-based learning that is situated for each instruction with a full suite of contextually guided responses to incomplete explanations. The approach is implemented in an agent called Instructo-Soar that learns hierarchies of new tasks and other domain knowledge from interactive natural language instructions. Instructo-Soar meets three key requirements of flexible instructability that distinguish it from previous systems: (1) it can take known or unknown commands at any instruction point; (2) it can handle instructions that apply to either its current situation or to a hypothetical situation specified in language (as in, for instance, conditional instructions); and (3) it can learn, from instructions, each class of knowledge it uses to perform tasks.

Functionality-based recognition systems recognize objects at the category level by reasoning about how well the objects support the expected function. Such systems naturally associate a ``measure of goodness'' or ``membership value'' with a recognized object. This measure of goodness is the result of combining individual measures, or membership values, from potentially many primitive evaluations of different properties of the object's shape. A membership function is used to compute the membership value when evaluating a primitive of a particular physical property of an object. In previous versions of a recognition system known as Gruff, the membership function for each of the primitive evaluations was hand-crafted by the system designer. In this paper, we provide a learning component for the Gruff system, called Omlet, that automatically learns membership functions given a set of example objects labeled with their desired category measure. The learning algorithm is generally applicable to any problem in which low-level membership values are combined through an and-or tree structure to give a final overall membership value.

Symmetric networks designed for energy minimization such as Boltzman machines and Hopfield nets are frequently investigated for use in optimization, constraint satisfaction and approximation of NP-hard problems. Nevertheless, finding a global solution (i.e., a global minimum for the energy function) is not guaranteed and even a local solution may take an exponential number of steps. We propose an improvement to the standard local activation function used for such networks. The improved algorithm guarantees that a global minimum is found in linear time for tree-like subnetworks. The algorithm, called activate, is uniform and does not assume that the network is tree-like. It can identify tree-like subnetworks even in cyclic topologies (arbitrary networks) and avoid local minima along these trees. For acyclic networks, the algorithm is guaranteed to converge to a global minimum from any initial state of the system (self-stabilization) and remains correct under various types of schedulers. On the negative side, we show that in the presence of cycles, no uniform algorithm exists that guarantees optimality even under a sequential asynchronous scheduler. An asynchronous scheduler can activate only one unit at a time while a synchronous scheduler can activate any number of units in a single time step. In addition, no uniform algorithm exists to optimize even acyclic networks when the scheduler is synchronous. Finally, we show how the algorithm can be improved using the cycle-cutset scheme. The general algorithm, called activate-with-cutset, improves over activate and has some performance guarantees that are related to the size of the network's cycle-cutset.