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PAClearnability of Probabilistic Deterministic Finite State Automata
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2004
"... We study the learnability of Probabilistic Deterministic Finite State Automata under a modified PAClearning criterion. We argue that it is necessary to add additional parameters to the sample complexity polynomial, namely a bound on the expected length of strings generated from any state, and a ..."
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Cited by 25 (7 self)
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We study the learnability of Probabilistic Deterministic Finite State Automata under a modified PAClearning criterion. We argue that it is necessary to add additional parameters to the sample complexity polynomial, namely a bound on the expected length of strings generated from any state, and a bound on the distinguishability between states. With this, we demonstrate that the class of PDFAs is PAClearnable using a variant of a standard statemerging algorithm and the KullbackLeibler divergence as error function.
Probabilistic FiniteState Machines  Part I
"... Probabilistic finitestate machines are used today in a variety of areas in pattern recognition, or in fields to which pattern recognition is linked: computational linguistics, machine learning, time series analysis, circuit testing, computational biology, speech recognition and machine translatio ..."
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Cited by 15 (1 self)
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Probabilistic finitestate machines are used today in a variety of areas in pattern recognition, or in fields to which pattern recognition is linked: computational linguistics, machine learning, time series analysis, circuit testing, computational biology, speech recognition and machine translation are some of them. In part I of this paper we survey these generative objects and study their definitions and properties. In part II, we will study the relation of probabilistic finitestate automata with other well known devices that generate strings as hidden Markov models and ngrams, and provide theorems, algorithms and properties that represent a current state of the art of these objects.
Towards Feasible PACLearning of Probabilistic Deterministic Finite Automata
, 2008
"... We present an improvement of an algorithm due to Clark and ..."
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Cited by 7 (5 self)
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We present an improvement of an algorithm due to Clark and
Improvement of the State Merging Rule on Noisy Data in Probabilistic Grammatical Inference
 10th European Conference on Machine Learning. Number 2837 in LNAI, SpringerVerlag (2003) 169–1180
, 2003
"... In this paper we study the influence of noise in probabilistic grammatical inference. We paradoxically bring out the idea that specialized automata deal better with noisy data than more general ones. We propose then to replace the statistical test of the Alergia algorithm by a more restrictive m ..."
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Cited by 4 (1 self)
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In this paper we study the influence of noise in probabilistic grammatical inference. We paradoxically bring out the idea that specialized automata deal better with noisy data than more general ones. We propose then to replace the statistical test of the Alergia algorithm by a more restrictive merging rule based on a test of proportion comparison.
Learning Hidden Markov Models to Fit LongTerm Dependencies
, 2005
"... this report a novel approach to the induction of the structure of Hidden Markov Models (HMMs). The notion of partially observable Markov models (POMMs) is introduced. POMMs form a particular case of HMMs where any state emits a single letter with probability one, but several states can emit the ..."
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Cited by 2 (2 self)
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this report a novel approach to the induction of the structure of Hidden Markov Models (HMMs). The notion of partially observable Markov models (POMMs) is introduced. POMMs form a particular case of HMMs where any state emits a single letter with probability one, but several states can emit the same letter. It is shown that any HMM can be represented by an equivalent POMM. The proposed induction algorithm aims at finding a POMM fitting the dynamics of the target machine, that is to best approximate the stationary distribution and the mean first passage times observed in the sample. The induction relies on nonlinear optimization and iterative state splitting from an initial order one Markov chain. Experimental results illustrate the advantages of the proposed approach as compared to BaumWelch HMM estimation or backo# smoothed Ngrams equivalent to variable order Markov chains
in Language Learning
"... We present a computational model of language learning via a sequence of interactions between a teacher and a learner. The utterances of the teacher and learner refer to shared situations, and the learner uses crosssituational correspondences to learn to comprehend the teacher’s utterances and produ ..."
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We present a computational model of language learning via a sequence of interactions between a teacher and a learner. The utterances of the teacher and learner refer to shared situations, and the learner uses crosssituational correspondences to learn to comprehend the teacher’s utterances and produce appropriate utterances of its own. We show that in this model the teacher and learner come to be able to understand each other’s meanings. Moreover, the teacher is able to produce meaningpreserving corrections of the learner’s utterances, and the learner is able to detect them. We test our model with limited sublanguages of several natural languages in a common domain of situations. The results show that learning to a high level of performance occurs after a reasonable number of interactions. Moreover, even if the learner does not treat corrections specially, in several cases a high level of performance is achieved significantly sooner by a learner interacting with a correcting teacher than by a learner interacting with a noncorrecting teacher. Demonstrating the benefit of semantics to the learner, we compare the number of interactions to reach a high level of performance in our system with the number of similarly generated utterances (with no semantics) required by the ALERGIA algorithm to achieve the same level of performance. We also define and analyze a simplified model of a probabilistic process of collecting corrections to help understand the possibilities and limitations of corrections in our setting. 1
Efficient Pruning of Probabilistic Automata 1 Franck Thollard and Baptiste Jeudy
"... Abstract. Applications of probabilistic grammatical inference are limited due to time and space consuming constraints. In statistical language modeling, for example, large corpora are now available and lead to managing automata with millions of states. We propose in this article a method for pruning ..."
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Abstract. Applications of probabilistic grammatical inference are limited due to time and space consuming constraints. In statistical language modeling, for example, large corpora are now available and lead to managing automata with millions of states. We propose in this article a method for pruning automata (when restricted to tree based structures) which is not only efficient (subquadratic) but that allows to dramatically reduce the size of the automaton with a small impact on the underlying distribution. Results are evaluated on a language modeling task. 1
Grammatical Inference by ngram Modeling of Convex Groups: Representation of Visual Random Polytopes ∗
"... In this paper, a joint solution to the problem of finding appropriate abstract representations for visual polytopes is given. By using support from convex and stochastic geometry, collecting information of views from different viewpoints, perceptual grouping of 3D pointcloud image points into halfp ..."
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In this paper, a joint solution to the problem of finding appropriate abstract representations for visual polytopes is given. By using support from convex and stochastic geometry, collecting information of views from different viewpoints, perceptual grouping of 3D pointcloud image points into halfplanes with probabilistic robust fitting and the segmentation of edges and corners by intersecting halfplanes yields an aggregation of visual primitives into object prototypes by Bayes ’ belief networks. In order to build object prototypes, a ngram model is trained by edge and corner primitives, derived from MonteCarlo simulations and processing of real 3D pointclouds. Finally, we use perplexity to find out the best performing network and define a Dirichlet distribution model of the ngrams.
Correction of Uniformly Noisy Distributions to Improve Probabilistic Grammatical Inference Algorithms ∗
, 2009
"... In this paper, we aim at correcting distributions of noisy samples in order to improve the inference of probabilistic automata. Rather than definitively removing corrupted examples before the learning process, we propose a technique, based on statistical estimates and linear regression, for correcti ..."
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In this paper, we aim at correcting distributions of noisy samples in order to improve the inference of probabilistic automata. Rather than definitively removing corrupted examples before the learning process, we propose a technique, based on statistical estimates and linear regression, for correcting the probabilistic prefix tree automaton (PPTA). It requires a human expertise to correct only a small sample of data, selected in order to estimate the noise level. This statistical information permits us to automatically correct the whole PPTA and then to infer better models from a generalization point of view. After a theoretical analysis of the noise impact, we present a large experimental study on several datasets.