Categorizing numeric information for generalization

Learning programs that generalize from real-world examples will have to deal with many different kinds of data. Continuous numeric data can cause problems for algorithms that search for examples with identical property values. These problems can be surmounted by categorizing the numeric data. However, this process has problems of its own. In this paper, we look at the need for categorizing numeric data and several methods for doing so. We concentrate on the use of generalization-based memory, a memory organization where actual examples are stored along with generalizations, which leads to a generalization-based categorization algorithm. We also consider how to use a number heuristic, looking for gaps. These methods have been implemented in the UNIMEM computer system. Examples are presented of these algorithms categorizing data about the states of the United States.     

Learning to search: From weak methods to domain-specific heuristics

Learning from experience involves three distinct components—generating behavior, assigning credit, and modifying behavior. We discuss these components in the context of learning search heuristics, along with the types of learning that can occur. We then focus on SAGE, a system that improves its search strategies with practice. The program is implemented as a production system, and learns by creating and strengthening rules for proposing moves. SAGE incorporates five different heuristics for assigning credit and blame, and employs a discrimination process to direct its search through the space of rules. The system has shown its generality by learning heuristics for directing search in six different task domains. In addition to improving its search behavior on practice problems, SAGE is able to transfer its expertise to scaled-up versions of a task, and in one case, transfers its acquired search strategy to problems with different initial and goal states.     

An evolutionary approach to support decision making with linear decision models

In this paper we consider decision problems that can be described as linear decision models. These models have been traditionally solved using linear programming, fuzzy linear programming, multiple-objective linear programming or ‘what-if’ analysis. Using these approaches, one encounters a number of difficulties. We propose an ‘evolutionary approach’ to overcome these difficulties. In the proposed approach the decision maker does not have to precisely specify the model (i.e. the objective functions, the RHS values, etc.) at the beginning of the solution procedure. In fact, the model evolves as the solution procedure proceeds.     

Planning and acting

A new theory of problem solving is presented, which embeds problem solving in the theory of action; in this theory, a problem is just a difficult action. Making this work requires a sophisticated language for-talking about plans and their execution. This language allows a broad range of types of action, and can also be used to express rules for choosing and scheduling plans. To ensure flexibility, the problem solver consists of an interpreter driven by a theorem prover which actually manipulates formulas of the language. Many examples of the use of the system six given. including an extended treatment of the world of blocks. Limitations and extensions of the system are discussed at length. It is concluded that a rule-based problem solver is necessary and feasible, but that much more work remains to be done on the underlying theory of planning and acting.     

An attempt to understand students' understanding of basic algebra

This paper reports the results obtained with a group of 24 14-year-old students when presented with a set of algebra tasks by the Leeds Modelling System, LMS. These same students were given a comparable paper-and-pencil test and detailed interviews some four months later. The latter studies uncovered several kinds of student misunderstandings that LMS had not detected. Some students had profound misunderstandings of algebraic notation: Others used strategies such as substituting numbers for variables until the equation balanced. Additionally, it appears that the student errors fall into several distinct classes: namely, manipulative, parsing, clerical, and “random.” LMS and its rule database have been enhanced as the result of this experiment, and LMS is now able to diagnose the majority of the errors encountered in this experiment. Finally, the paper gives a process-oriented explanation for student errors, and re-examines related work in cognitive modelling in the light of the types of student errors reported in this experiment. Misgeneralization is a mechanism suggested to explain some of the mal-rules noted in this study.     

Rules and topics in conversation

Rules of conversation are given that specify what can follow what. A system for deciding what makes a reasonable subject for a conversation is shown. Topics are discussed and rules for topic shift are presented.     

A learning algorithm for boltzmann machines

The computational power of massively parallel networks of simple processing elements resides in the communication bandwidth provided by the hardware connections between elements. These connections can allow a significant fraction of the knowledge of the system to be applied to an instance of a problem in a very short time. One kind of computation for which massively parallel networks appear to be well suited is large constraint satisfaction searches, but to use the connections efficiently two conditions must be met: First, a search technique that is suitable for parallel networks must be found. Second, there must be some way of choosing internal representations which allow the preexisting hardware connections to be used efficiently for encoding the constraints in the domain being searched. We describe a general parallel search method, based on statistical mechanics, and we show how it leads to a general learning rule for modifying the connection strengths so as to incorporate knowledge about a task domain in an efficient way. We describe some simple examples in which the learning algorithm creates internal representations that are demonstrably the most efficient way of using the preexisting connectivity structure.