||This article needs attention from an expert in Computer science or Robotics. (February 2009)|
Grammatical induction, also known as grammatical inference or syntactic pattern recognition, refers to the process in machine learning of learning 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.
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.
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. 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 representation 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 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.
Grammatical inference by greedy algorithms 
Like all greedy algorithms, greedy grammar inference algorithms make, in iterative manner, decisions that seem to be the best at that stage. These made decisions deal usually with things like the making of a new or the removing of the existing rules, the choosing of the applied rule or the merging of some existing rules. Because there are several ways to define 'the stage' and 'the best', there are also several greedy grammar inference algorithms.
These context-free grammar generating algorithms make the decision after every read symbol:
- Lempel-Ziv-Welch algorithm creates a context-free grammar in a deterministic way such that it is necessary to store only the start rule of the generated grammar.
- Sequitur and its modifications.
These context-free grammar generating algorithms first read the whole given symbol-sequence and then start to make decisions:
- Byte pair encoding and its optimizations.
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. Grammar induction has also been used for lossless data compression and statistical inference via MML and MDL principles.
See also 
- Artificial grammar learning
- Syntactic pattern recognition
- Inductive inference
- Straight-line grammar
- Kolmogorov complexity
- Automatic distillation of structure
- Duda, Richard O.; Hart, Peter E.; Stork, David G. (2001), Pattern Classification, New York: John Wiley & Sons Unknown parameter
- Fu, King Sun (1982), Syntactic Pattern Recognition and Applications, Englewood Cliffs, NJ: Prentice-Hall
- Fu, King Sun (1977), Syntactic Pattern Recognition, Applications, Berlin: Springer-Verlag
- Horning, James Jay (1969), A Study of Grammatical Inference (Ph.D. Thesis ed.), Stanford: Stanford University Computer Science Department
- Gold, E Mark (1967), Language Identification in the Limit, Information and Control