FUNCTION DISCOVERY USING DATA TRANSFORMATION
Date
1994-06-01
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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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Computer Science