Grammar induction

Grammatical induction, also known as grammatical inference or syntactic pattern recognition, refers to the process in machine learning of inducing a formal grammar (usually in the form of re-write rules or productions) from a set of observations, thus constructing a model which accounts for the characteristics of the observed objects. Grammatical inference is distinguished from traditional decision rules and other such methods principally by the nature of the resulting model, which in the case of grammatical inference relies heavily on hierarchical substitutions. Whereas a traditional decision rule set is geared toward assessing object classification, a grammatical rule set is geared toward the generation of examples. In this sense, the grammatical induction problem can be said to seek a generative model, while the decision rule problem seeks a descriptive model.

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Methodologies

There are a wide variety of methods for grammatical inference. Two of the classic sources are Fu (1977) and Fu (1982). Duda, Hart & Stork (2001) also devote a brief section to the problem, and cite a number of references. The basic trial-and-error method they present is discussed below.

Grammatical inference by trial-and-error

The method proposed in Section 8.7 of Duda, Hart & Stork (2001) suggests successively guessing grammar rules (productions) and testing them against positive and negative observations. The rule set is expanded so as to be able to generate each positive example, but if a given rule set also generates a negative example, it must be discarded. This particular approach can be characterized as "hypothesis testing" and bears some similarity to Mitchel's version space algorithm. The Duda, Hart & Stork (2001) text provide a simple example which nicely illustrates the process, but the feasibility of such an unguided trial-and-error approach for more substantial problems is dubious. An evolutionary approach, such as that described below, is likely to yield much better results.

Grammatical inference by genetic algorithms

Grammatical Induction using evolutionary algorithms is the process of evolving a representation of the grammar of a target language through some evolutionary process. Formal grammars can easily be represented as a tree structure of production rules that can be subjected to evolutionary operators. Algorithms of this sort stem from the genetic programming paradigm pioneered by John Koza.^{[citation needed]} Other early work on simple formal languages used the binary string representation of genetic algorithms, but the inherently hierarchical structure of grammars couched in the EBNF language made trees a more flexible approach.

Koza represented Lisp programs as trees. He was able to find analogues to the genetic operators within the standard set of tree operators. For example, swapping sub-trees is equivalent to the corresponding process of genetic crossover, where sub-strings of a genetic code are transplanted into an individual of the next generation. Fitness is measured by scoring the output from the functions of the lisp code. Similar analogues between the tree structured lisp representation and the represenation of grammars as trees, made the application of genetic programming techniques possible for grammar induction.

In the case of Grammar Induction, the transplantation of sub-trees corresponds to the swapping of production rules that enable the parsing of phrases from some language. The fitness operator for the grammar is based upon some measure of how well it performed in parsing some group of sentences from the target language. In a tree representation of a grammar, a terminal symbol (e.g. a noun or verb or some other part of speech) of a production rule corresponds to a leaf node of the tree. Its parent nodes corresponds to a non-terminal symbol (e.g. a noun phrase or a verb phrase) in the rule set. Ultimately, the root node might correspond to a sentence non-terminal.

Applications

The principle of grammar induction has been applied to other aspects of natural language processing, and have been applied (among many other problems) to morpheme analysis, and even place name derivations.

See also

• Syntactic pattern recognition
• Inductive inference

References

• Duda, Richard O.; Peter E. Hart & David G. Stork (2001), written at New York, (2 ed.), John Wiley & Sons,

• Fu, King Sun (1982), written at Englewood Cliffs, NJ, , Prentice-Hall

• Fu, King Sun (1977), written at Berlin, , Springer-Verlag