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Authors: Phan, Thong Huy
Keywords: Computer Science
Issue Date: 1-Jun-1994
Abstract: This thesis describes the design and implementation of a system that infers real-valued functions of one argument from example data points. The system, LINUS, can identify a wide range of functions: rational functions, quadratic relations, and many transcendental functions: rational functions, quadratic relations, and many transcendental functions, as well as expressions that can be transformed to rational functions by combinations of differentiation, logarithm and function inverse operations. As a result of its representation of functions and the flexibility of the underlying model, LINUS's ability exceeds that of previous discovery systems. The idea of transforming from one function to another forms the basis of both the search operation and the structural representation of functions, an idea pioneered by an earlier system called "FFD". Augmenting this with on-demand data selection, automatic error analysis, data splitting and solution merging, aggregated transformations, and local approximations, results in a practical discovery method that is shown to be theoretically sound. LINUS is tested on several tasks to evaluate both the expressiveness of its representation and the practicality of its discovery method in the domain of real-valued functions. From the design of LINUS, formal properties are identified that are critical to the data transformation method. First, all transformations must be numerically reversible. Second, for any transformation sequence it must be possible to select examples that satisfy a certain accuracy requirement for that sequence. Third, it must be possible to enumerate all sequences, though the transformations themselves may contain parameters that are not enumerable. Based on these properties, a discovery model is developed that can be applied within more general domains.
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