Download e-book for iPad: Incremental Version-Space Merging: A General Framework for by Haym Hirsh

By Haym Hirsh

ISBN-10: 1461288347

ISBN-13: 9781461288343

ISBN-10: 1461315573

ISBN-13: 9781461315575

One of the main relaxing stories in technology is listening to an easy yet novel inspiration which immediately jewelry precise, and whose effects then start to spread in unexpected instructions. For me, this booklet offers such an concept and a number of other of its ramifications. This publication is anxious with laptop studying. It specializes in a ques­ tion that's principal to knowing how pcs may well study: "how can a working laptop or computer collect the definition of a few basic idea by means of abstracting from particular education cases of the concept?" even if this query of the way to immediately generalize from examples has been thought of via many researchers over numerous many years, it is still in simple terms partially responded. The strategy built during this booklet, in response to Haym Hirsh's Ph.D. dis­ sertation, results in an set of rules which successfully and exhaustively searches an area of hypotheses (possible generalizations of the knowledge) to discover all maxi­ mally constant hypotheses, even within the presence of specific sorts of incon­ sistencies within the facts. extra ordinarily, it presents a framework for integrat­ ing types of constraints (e.g., education examples, past wisdom) which enable the learner to lessen the set of hypotheses less than consideration.

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Extra info for Incremental Version-Space Merging: A General Framework for Concept Learning

Example text

Haussler, 1988» has developed techniques for analyzing how the quality of results is influenced by the amount of data used in learning. This section gives such an analysis for learning from data with bounded inconsistency. To do this a number of definitions are necessary. 1: Neighbors(z) = {y I yisnearz}. Furthermore, since data may have bounded inconsistency, it is necessary to redefine what it means for a concept definition to be consistent with an instance. 2: An instance z is said to be consistent with a concept C (written Consistent( z, C)) if, when z is positive, 3p E Neighbors( z) with p E C, and when z is negative, 3n E Neighbors(z) with n ¢ C (where pEe means C would have classified p as positive, and n ¢ C means C would have classified n as negative).

Note that this merely instantiates the general incremental version-space merging algorithm specified in Chapter 2, specifying how individual version spaces are fonned in Step 1. 1 will again be used. The initial version space has boundary sets S={0} and G={[any-size, any-shape]} (where 0 represents the empty concept that says nothing is an example of the target concept). The version space for the first positive instance, a small cube, has the boundary sets S={[small, cube]} and G={[any-size, any-shape]} (Step I of the incremental version-space merging algorithm), and when merged with the initial version space simply returns the instance version space (Step 2).

PolyhedronIT G {[any-size. any-shape]} {[any-size. polynearon]} {[any-size. cube]; [small. polyhedron]} {[small. 1. Learning Example. 3 Candidate-Elimination Algorithm Emulation The preceding section gives an example of the use of the original candidateelimination algorithm. This section describes how the functionality of the candidate-elimination algorithm can be emulat¢ by incremental versionspace merging. The simple idea is that. as eadh new training instance is obtained, the set of concept definitions that correctly classify the single instance is formed.

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Incremental Version-Space Merging: A General Framework for Concept Learning by Haym Hirsh

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