## Stochastic Inference of Regular Tree Languages (1999)

Venue: | Machine Learning |

Citations: | 40 - 11 self |

### BibTeX

@INPROCEEDINGS{Carrasco99stochasticinference,

author = {Rafael C. Carrasco and Jose Oncina and Jorge Calera-rubio},

title = {Stochastic Inference of Regular Tree Languages},

booktitle = {Machine Learning},

year = {1999},

pages = {185--197}

}

### Years of Citing Articles

### OpenURL

### Abstract

this paper, we introduce a modi cation of the last algorithm that can be trained with positive samples generated according to a probabilistic production scheme. The construction follows the same guidelines as the algorithm for string languages in Carrasco and Oncina (1998). A dierent approach (Sakakibara et al., 1994) generalizes the

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Citation Context ...) : (10) ml.tex; 15/09/1999; 13:03; p.4 5 If p(V T $ tjT ) = 0, the quotient (10) is undened and in such case, we will write by convention T=t = ;. The Myhill-Nerode's theorem for regular languages (H=-=opcroft and Ullman, 19-=-80) can be generalized for regular tree languages (Gecseg and Steinby, 1984) as well as for stochastic languages (Carrasco and Oncina, 1998). If T is a stochastic RTL, the number of dierent sets T=t i... |

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Citation Context ...n , where n is the number of dierent subtrees in S n . Then, the probability p n that equiv T (x; y) 6= comp n (x; y) is smaller than 2 n n . If P n p n issnite then, the Borel-Cantelli lemma (Felle=-=r, 1-=-950) guarantees that, with probability one, only asnite number of mistakes take place. The expected number of dierent subtrees n grows at most linearly with n and then, P 1 n=1 n ns1 is a sucient con... |

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Citation Context ...1998). Given a probability distribution p(tjA 0 ) over V T that approximates the true one p(tjA), the magnitude G(A; A 0 ) = X t2V T p(tjA) log 2 p(tjA 0 ) (19) bounds, within a deviation of one bit (=-=Cover and Thomas, 199-=-1), the average length of the string needed to code a tree in V T provided that the information contained in A 0 and an optimal coding scheme are used. The dierence H(A;A 0 ) = G(A; A 0 ) G(A; A) give... |

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Citation Context ... samples is possible if rather general assumption about the probability distribution are made. Some algorithms for learning string regular languages from stochastic samples have been proposed before (=-=Stolcke and Omohundro, 199-=-3; Carrasco and Oncina, 1998). The last one has the interesting property that identication in the limit of the structure of the deterministic automaton (DFA) is guaranteed. Learning context-free langu... |

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Citation Context ...r general assumption about the probability distribution are made. Some algorithms for learning string regular languages from stochastic samples have been proposed before (Stolcke and Omohundro, 1993; =-=Carrasco and Oncina, 19-=-98). The last one has the interesting property that identication in the limit of the structure of the deterministic automaton (DFA) is guaranteed. Learning context-free languages is harder, but identi... |

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Citation Context ...amples generated according to a probabilistic production scheme. The construction follows the same guidelines as the algorithm for string languages in Carrasco and Oncina (1998). A dierent approach (S=-=akakibara et al., 199-=-4) generalizes the Work partially supported by the Spanish CICYT under grant TIC97-0941. cs1999 Kluwer Academic Publishers. Printed in the Netherlands. ml.tex; 15/09/1999; 13:03; p.1 2 forward-backwa... |

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Citation Context ...(j) (20) where j ij , defined as j ij = X t2L ij ��(t); (21) represents the probability that a node of type i 2 Q expands as a subtree t such that ffi 0 (t) = j. It is not difficult to show (Caler=-=a & Carrasco 1998-=-) that all j ij can be easily obtained by means of an iterative procedure: j [t+1] ij = n X k=0 X f2V X i 1 ;i 2 ;:::;i k 2Q: ffi k (f;i 1 ;i 2 ;:::;i k )=i X j1 ;j 2 ;:::;j k 2Q 0 : ffi 0 k (f;j1 ;j ... |

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Citation Context ...omaton A 0 = (Q 0 ; V;s0 ; p 0 ; r 0 ) is given by the product of two dierent factors, and then log 2 p(tjA 0 ) = log 2 r 0 ( 0 (t)) + log 2 0 (t). The contribution to G(A;A 0 ) of the r-terms is (Ca=-=lera-Rubio and Carrasco, 19-=-98) G r (A; A 0 ) = X i2Q j2Q 0 r(i) ij log 2 r 0 (j) (20) where ij represents the probability that a node of type i 2 Q expands as a subtree t such thats0 (t) = j and can be easily obtained by means... |

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Citation Context ...) 2 Fg. By convention, undened transitions lead to absorption states, i.e., to nonacceptable trees. DTA are closely connected to context-free grammars. For instance, given a backwards-deterministic (A=-=ho and Ullman-=-, 1972) grammar G = (N; ; P; S), the acceptor Q = N [ V = fg [ s0 (a) = a 8a 2 sk (; X 1 ; :::; X k ) = A if A ! X 1 :::X k 2 P (3) recognizes the set of skeletal derivation trees of G. 3. Stochastic... |

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Citation Context ...xperimental settings involve random or noisy examples. Some algorithms for learning regular (string) languages from stochastic samples have been proposed before (Stolcke & Omohundro, 1993; Carrasco & =-=Oncina, 1994-=-). The last one has the interesting property that identification in the limit of the structure of the deterministic automaton (DFA) is guaranteed. Learning context-free languages is harder, but identi... |

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