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Keywords
(1)
Finite State Automata
Related Publications
(4)
On the learnability and usage of acyclic probabilistic finite automata
Crytographic limitations on learning Boolean formulae and finite automata
On the Computational Complexity of Approximating Distributions by Probabilistic Automata
On the learnability of discrete distributions
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Probabilistic finite state automatapart I
Probabilistic finite state automatapart I,IEEE Transactions on Pattern Analysis and Machine Intelligence,E. Vidal,F. Thollard,C. De La Higuera,F. Cas
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Probabilistic finite state automatapart I
(
Citations: 7
)
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E. Vidal
,
F. Thollard
,
C. De La Higuera
,
F. Casacuberta
,
R. C. Carrasco
Journal:
IEEE Transactions on Pattern Analysis and Machine Intelligence  PAMI
, 2004
Cumulative
Annual
Citation Context
(6)
...This approach aims at avoiding the problem by imposing a different bias: the data come from a distribution, itself represented by a stochastic automaton [
16
]...
Frédéric Tantini
,
et al.
Identification in the Limit of SystematicNoisy Languages
...Alternatively one can define distances between distributions; a survey can be found in [
19
]...
Colin De La Higuera
.
Ten Open Problems in Grammatical Inference
... As we will prove in the second part of our paper [
40
],...
...Part II [
40
] of the paper will be devoted to the comparison with other types of models, learning issues, and the presentation of some of the extensions of the probabilistic automata...
...The cases that do not fit in this definition will be analyzed in the second part of our paper [
40
]...
...All this will be done in Part II of this paper [
40
]...
Enrique Vidal
,
et al.
Probabilistic FiniteState MachinesPart I
...N the first part [
1
] of this survey, we introduced probabilistic finitestate automata (PFA), their deterministic counterparts (DPFA), and the properties of the distributions these objects can generate...
...Among the models proposed so far, some are based on acyclic automata [
1
], [16], [17], [18], [19]...
...This distribution (which is similar to that used in Part I [
1
] to prove that the mean of two deterministic distributions may not be deterministic) is exactly generated by the PFA shown in Fig. 3 (left)...
...Maximizing the likelihood is equivalent to minimizing the empirical cross entropy ^ X S;DAÞ (see Section 6 of [
1
])...
...The parameter updating is based on the forward and backward dynamic programming recurrences to compute the probability of a string discussed in Section 3 of [
1
]...
...Using the optimal path (Viterbi) approximation rather than the true (forward) probability (see [
1
], Section 3.2, and Section 3.1, respectively) in the function to be optimized (8), a simpler algorithm is obtained, called the Viterbi reestimation algorithm...
...1. We studied in the section concerning topology of part I [
1
] the questions of computing the distances between two distributions represented by PFA .I n the case where the PFA are DPFA the computation of the L2 distance and of the KullbackLeibler divergence can take polynomial time, but what about the L1, L1, and logarithmic distances? 2. In the same trend, it is reasonably clear that, if at least one of the distributions is represented ...
...5. We have provided a number of results on distances in the section concerning distances of part I [
1
]...
...Proof. By Proposition 11 of [
1
], D can be generated by a PFA with a single initial state...
...which, according to (1) in Section 2.6 of [
1
] (and noting that, in our PFA, Iðq0 Þ¼ 1), is the probability of the path for x in A y is associated with...
...Finally, following (2) in Section 2.6 of [
1
] (that gives the probability of generating a string),...
...For each path in M, there is one and only one path in A 0 . Moreover, by construction, Iðs1 Þ¼ Iðs1Þ and P ðq; a; q 0 Þ¼ Eðq; a Þ� Tðq; q 0 Þ; therefore, DA0 ¼D M. Finally, by Proposition 11 of [
1
], we can build a PFA A, with at most jQ j¼ n states, such that DA0 ¼D A. t...
Enrique Vidal
,
et al.
Probabilistic finitestate machines  part II
...A number of ideas have been developed in the literature to deal with these problems [DA00,
Tho01
]...
...Smoothing techniques [
Tho01
] are developed in order to cope with parsing failures by an Sdfa...
Colin De La Higuera
,
et al.
Learning Stochastic Finite Automata for Musical Style Recognition
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Citations
(7)
Identification in the Limit of SystematicNoisy Languages
(
Citations: 4
)
Frédéric Tantini
,
Colin De La Higuera
,
Jeanchristophe Janodet
Conference:
International Colloquium on Grammatical Inference  ICGI
, pp. 1931, 2006
Ten Open Problems in Grammatical Inference
(
Citations: 4
)
Colin De La Higuera
Conference:
International Colloquium on Grammatical Inference  ICGI
, pp. 3244, 2006
Probabilistic FiniteState MachinesPart I
(
Citations: 71
)
Enrique Vidal
,
Franck Thollard
,
Colin De La Higuera
,
Francisco Casacuberta
,
Rafael C. Carrasco
Journal:
IEEE Transactions on Pattern Analysis and Machine Intelligence  PAMI
, vol. 27, no. 7, pp. 10131025, 2005
Probabilistic finitestate machines  part II
(
Citations: 13
)
Enrique Vidal
,
Frank Thollard
,
C. de la Higuera
,
F. Casacuberta
,
R. C. Carrasco
Journal:
IEEE Transactions on Pattern Analysis and Machine Intelligence  PAMI
, vol. 27, no. 7, pp. 10261039, 2005
Learning Stochastic Finite Automata for Musical Style Recognition
(
Citations: 3
)
Colin De La Higuera
,
Frédéric Piat
,
Frédéric Tantini
Conference:
Workshop on Implementing Automata/Conference on Implementation and Application of Automata  CIAA(WIA)
, pp. 345346, 2005