3,599 research outputs found
Learning context-free grammars from structural data in polynomial time
AbstractWe consider the problem of learning a context-free grammar from its structural descriptions. Structural descriptions of a context-free grammar are unlabelled derivation trees of the grammar. We present an efficient algorithm for learning context-free grammars using two types of queries: structural equivalence queries and structural membership queries. The learning protocol is based on what is called āminimally adequate teacherā, and it is shown that a grammar learned by the algorithm is not only a correct grammar, i.e. equivalent to the unknown grammar but also structurally equivalent to it. Furthermore, the algorithm runs in time polynomial in the number of states of the minimum frontier-to-root tree automaton for the set of structural descriptions of the unknown grammar and the maximum size of any counter-example returned by a structural equivalence query
Learning cover context-free grammars from structural data
We consider the problem of learning an unknown context-free grammar when the
only knowledge available and of interest to the learner is about its structural
descriptions with depth at most The goal is to learn a cover
context-free grammar (CCFG) with respect to , that is, a CFG whose
structural descriptions with depth at most agree with those of the
unknown CFG. We propose an algorithm, called , that efficiently learns
a CCFG using two types of queries: structural equivalence and structural
membership. We show that runs in time polynomial in the number of
states of a minimal deterministic finite cover tree automaton (DCTA) with
respect to . This number is often much smaller than the number of states
of a minimum deterministic finite tree automaton for the structural
descriptions of the unknown grammar
Empirical Risk Minimization for Probabilistic Grammars: Sample Complexity and Hardness of Learning
Probabilistic grammars are generative statistical models that are useful for compositional and sequential structures. They are used ubiquitously in computational linguistics. We present a framework, reminiscent of structural risk minimization, for empirical risk minimization of probabilistic grammars using the log-loss. We derive sample complexity bounds in this framework that apply both to the supervised setting and the unsupervised setting. By making assumptions about the underlying distribution that are appropriate for natural language scenarios, we are able to derive distribution-dependent sample complexity bounds for probabilistic grammars. We also give simple algorithms for carrying out empirical risk minimization using this framework in both the supervised and unsupervised settings. In the unsupervised case, we show that the problem of minimizing empirical risk is NP-hard. We therefore suggest an approximate algorithm, similar to expectation-maximization, to minimize the empirical risk. Learning from data is central to contemporary computational linguistics. It is in common in such learning to estimate a model in a parametric family using the maximum likelihood principle. This principle applies in the supervised case (i.e., using annotate
Synthesizing Program Input Grammars
We present an algorithm for synthesizing a context-free grammar encoding the
language of valid program inputs from a set of input examples and blackbox
access to the program. Our algorithm addresses shortcomings of existing grammar
inference algorithms, which both severely overgeneralize and are prohibitively
slow. Our implementation, GLADE, leverages the grammar synthesized by our
algorithm to fuzz test programs with structured inputs. We show that GLADE
substantially increases the incremental coverage on valid inputs compared to
two baseline fuzzers
Inducing Probabilistic Grammars by Bayesian Model Merging
We describe a framework for inducing probabilistic grammars from corpora of
positive samples. First, samples are {\em incorporated} by adding ad-hoc rules
to a working grammar; subsequently, elements of the model (such as states or
nonterminals) are {\em merged} to achieve generalization and a more compact
representation. The choice of what to merge and when to stop is governed by the
Bayesian posterior probability of the grammar given the data, which formalizes
a trade-off between a close fit to the data and a default preference for
simpler models (`Occam's Razor'). The general scheme is illustrated using three
types of probabilistic grammars: Hidden Markov models, class-based -grams,
and stochastic context-free grammars.Comment: To appear in Grammatical Inference and Applications, Second
International Colloquium on Grammatical Inference; Springer Verlag, 1994. 13
page
Data-Oriented Language Processing. An Overview
During the last few years, a new approach to language processing has started
to emerge, which has become known under various labels such as "data-oriented
parsing", "corpus-based interpretation", and "tree-bank grammar" (cf. van den
Berg et al. 1994; Bod 1992-96; Bod et al. 1996a/b; Bonnema 1996; Charniak
1996a/b; Goodman 1996; Kaplan 1996; Rajman 1995a/b; Scha 1990-92; Sekine &
Grishman 1995; Sima'an et al. 1994; Sima'an 1995-96; Tugwell 1995). This
approach, which we will call "data-oriented processing" or "DOP", embodies the
assumption that human language perception and production works with
representations of concrete past language experiences, rather than with
abstract linguistic rules. The models that instantiate this approach therefore
maintain large corpora of linguistic representations of previously occurring
utterances. When processing a new input utterance, analyses of this utterance
are constructed by combining fragments from the corpus; the
occurrence-frequencies of the fragments are used to estimate which analysis is
the most probable one.
In this paper we give an in-depth discussion of a data-oriented processing
model which employs a corpus of labelled phrase-structure trees. Then we review
some other models that instantiate the DOP approach. Many of these models also
employ labelled phrase-structure trees, but use different criteria for
extracting fragments from the corpus or employ different disambiguation
strategies (Bod 1996b; Charniak 1996a/b; Goodman 1996; Rajman 1995a/b; Sekine &
Grishman 1995; Sima'an 1995-96); other models use richer formalisms for their
corpus annotations (van den Berg et al. 1994; Bod et al., 1996a/b; Bonnema
1996; Kaplan 1996; Tugwell 1995).Comment: 34 pages, Postscrip
Efficient learning of context-free grammars from positive structural examples
AbstractIn this paper, we introduce a new normal form for context-free grammars, called reversible context-free grammars, for the problem of learning context-free grammars from positive-only examples. A context-free grammar G = (N, Ī£, P, S) is said to be reversible if (1) A ā Ī± and B ā Ī± in P implies A = B and (2) A ā Ī±BĪ² and A ā Ī±CĪ² in P implies B = C. We show that the class of reversible context-free grammars can be identified in the limit from positive samples of structural descriptions and there exists an efficient algorithm to identify them from positive samples of structural descriptions, where a structural description of a context-free grammar is an unlabelled derivation tree of the grammar. This implies that if positive structural examples of a reversible context-free grammar for the target language are available to the learning algorithm, the full class of context-free languages can be learned efficiently from positive samples
On the learning of vague languages for syntactic pattern recognition
The method of the learning of vague languages which represent distorted/ambiguous patterns is proposed in the paper. The goal of the method is to infer the quasi-context-sensitive string grammar which is used in our model as the generator of patterns. The method is an important component of the multi-derivational model of the parsing of vague languages used for syntactic pattern recognition
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