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PAC-Learnability of Probabilistic Deterministic Finite State Automata in Terms of Variation Distance [chapter]

Nick Palmer, Paul W. Goldberg
2005 Lecture Notes in Computer Science  
We consider the problem of PAC-learning distributions over strings, represented by probabilistic deterministic finite automata (PDFAs).  ...  PDFAs are a probabilistic model for the generation of strings of symbols, that have been used in the context of speech and handwriting recognition, and bioinformatics.  ...  Introduction A probabilistic deterministic finite automaton (PDFA) is a deterministic finite automaton that has, for each state, a probability distribution over the transitions going out from that state  ... 
doi:10.1007/11564089_14 fatcat:elftebjq3bdxnngqqiidyfktum

PAC-learnability of probabilistic deterministic finite state automata in terms of variation distance

Nick Palmer, Paul W. Goldberg
2007 Theoretical Computer Science  
We consider the problem of PAC-learning distributions over strings, represented by probabilistic deterministic finite automata (PDFAs).  ...  PDFAs are a probabilistic model for the generation of strings of symbols, that have been used in the context of speech and handwriting recognition, and bioinformatics.  ...  Introduction A probabilistic deterministic finite automaton (PDFA) is a deterministic finite automaton that has, for each state, a probability distribution over the transitions going out from that state  ... 
doi:10.1016/j.tcs.2007.07.023 fatcat:dsegekwgcfddbljrt4lzqb6zoe

Page 3464 of Mathematical Reviews Vol. , Issue 99e [page]

1999 Mathematical Reviews  
probabilistic finite automata.  ...  Summary: “We show that deterministic finite automata (DFAs) with n states and input alphabet © can efficiently be learned from fewer than |Z|n? smallest counterexamples.  ... 

Some Classes of Regular Languages Identifiable in the Limit from Positive Data [chapter]

François Denis, Aurélien Lemay, Alain Terlutte
2002 Lecture Notes in Computer Science  
from Positive Data p. 63 Learning Probabilistic Residual Finite State Automata p. 77 Fragmentation: Enhancing Identifiability p. 92 On Limit Points for Some Variants of Rigid Lambek Grammars  ...  Attribute Grammars with Structured Data for Natural Language Processing p. 237 A PAC Learnability of Simple Deterministic Languages p. 249 On the Learnability of Hidden Markov Models p. 261 Shallow  ... 
doi:10.1007/3-540-45790-9_6 fatcat:nmlknwqoyfbybhb6rpomqrn7qy

Learnability of Probabilistic Automata via Oracles [chapter]

Omri Guttman, S. V. N. Vishwanathan, Robert C. Williamson
2005 Lecture Notes in Computer Science  
Efficient learnability using the state merging algorithm is known for a subclass of probabilistic automata termed µ-distinguishable.  ...  By combining new results from property testing with the state merging algorithm we obtain KL-PAC learnability of the new automata class.  ...  and the ICT Center of Excellence program.  ... 
doi:10.1007/11564089_15 fatcat:pmy6zlcgnvfodd76z5gyqtpcci

Links between probabilistic automata and hidden Markov models: probability distributions, learning models and induction algorithms

P. Dupont, F. Denis, Y. Esposito
2005 Pattern Recognition  
It is proved that probabilistic deterministic automata (PDFA) form a proper subclass of probabilistic non-deterministic automata (PNFA). Two families of equivalent models are described next.  ...  On the other hand, HMMs with final probabilities and probabilistic automata generate distributions over strings of finite length.  ...  The distinction between probabilistic deterministic automata (PDFA) and probabilistic non-deterministic automata (PNFA) is introduced.  ... 
doi:10.1016/j.patcog.2004.03.020 fatcat:uytkvkyfpfbj3lhibry6cfwue4

Identifiability of Model Properties in Over-Parameterized Model Classes [chapter]

Manfred Jaeger
2013 Lecture Notes in Computer Science  
We exemplify the use of the framework in three different applications: the identification of temporal logic properties of probabilistic automata learned from sequence data, the identification of causal  ...  dependencies in probabilistic graphical models, and the transfer of probabilistic relational models to new domains.  ...  (Non-identifiability of PCTL) Let M nd be the class of non-deterministic probabilistic finite automata, and let D (n) = (Σ * ) n .  ... 
doi:10.1007/978-3-642-40994-3_8 fatcat:7mqtsmxjqnhqleh5b2kb2ifctu

Learning Stochastic Finite Automata [chapter]

Colin de la Higuera, Jose Oncina
2004 Lecture Notes in Computer Science  
Stochastic deterministic finite automata have been introduced and are used in a variety of settings. We report here a number of results concerning the learnability of these finite state machines.  ...  In the setting of identification in the limit with probability one, we prove that stochastic deterministic finite automata cannot be identified from only a polynomial quantity of data.  ...  Introduction Probabilistic finite state automata [Paz71] have been introduced to describe distributions over strings.  ... 
doi:10.1007/978-3-540-30195-0_16 fatcat:4mlmcctfsvcnnbqnso5v4b6w34

Guest Editors' foreword

Marcus Hutter, Frank Stephan, Vladimir Vovk, Thomas Zeugmann
2013 Theoretical Computer Science  
Moreover, the difficulty of learning distributions generated by probabilistic deterministic finite automata using statistical queries depends on a parameter µ which is quite frequently studied in the literature  ...  Learning Theory, 21st International Conference, Gavaldà distinguishes between algorithms that learn probabilistic deterministic finite automata from (a) independent and identically distributed samples  ... 
doi:10.1016/j.tcs.2012.10.007 fatcat:ciit7zasgzgytfxx66tzb5onku

A bibliographical study of grammatical inference

Colin de la Higuera
2005 Pattern Recognition  
The goal of this paper is to introduce a certain number of papers related with grammatical inference.  ...  The field of grammatical inference (also known as grammar induction) is transversal to a number of research areas including machine learning, formal language theory, syntactic and structural pattern recognition  ...  These are deterministic finite automata with outputs both on the edges and the final states.  ... 
doi:10.1016/j.patcog.2005.01.003 fatcat:62qwskiqcvddjobakbdshwebqq

Learning PDFA with Asynchronous Transitions [chapter]

Borja Balle, Jorge Castro, Ricard Gavaldà
2010 Lecture Notes in Computer Science  
Our model is rather the finite-state and deterministic restriction of so-called semi-Markov processes; a widely-studied particular case of the latter are continuous-time Markov chains, in which times between  ...  The problem has also been studied in variants of the PAC model.  ...  In particular, the definition of probabilistic deterministic finite automaton (PDFA) and associated notation used here are from [2] .  ... 
doi:10.1007/978-3-642-15488-1_24 fatcat:mm26lwwm5vbzrdqn3arggxbfle

On the Learnability of Hidden Markov Models [chapter]

Sebastiaan A. Terwijn
2002 Lecture Notes in Computer Science  
A simple result is presented that links the learning of hidden Markov models to results in complexity theory about nonlearnability of finite automata under certain cryptographic assumptions.  ...  Rather than considering all probability distributions, or even just certain specific ones, the learning of a hidden Markov model takes place under a distribution induced by the model itself.  ...  polynomial size finite automata is not efficiently pac-learnable.  ... 
doi:10.1007/3-540-45790-9_21 fatcat:7wt7t4gsczc37dxqchsuk6jtz4

Learning Probability Distributions Generated by Finite-State Machines [chapter]

Jorge Castro, Ricard Gavaldà
2016 Topics in Grammatical Inference  
The methods we review are state merging and state splitting methods for probabilistic deterministic automata and the recently developed spectral method for nondeterministic probabilistic automata.  ...  We review methods for inference of probability distributions generated by probabilistic automata and related models for sequence generation.  ...  We thank the chairs of ICGI 2012 for the invitation to present a preliminary version of this work as tutorial. We particularly thank the reviewer of this version for a thorough and useful work.  ... 
doi:10.1007/978-3-662-48395-4_5 fatcat:u4cepbpghjcv7ct6zoqrgir2cy

Editors' Introduction [chapter]

Sanjay Jain, Rémi Munos, Frank Stephan, Thomas Zeugmann
2013 Lecture Notes in Computer Science  
state automata.  ...  using a polynomial amount of data and processing time, provided that the distributions of the samples are restricted to be generated by one of a large family of related probabilistic deterministic finite  ...  These distributions are generated by probabilistic deterministic finite automata (PDFA).  ... 
doi:10.1007/978-3-642-40935-6_1 fatcat:pchrsvhjezfbvh6dfplqhxhgcy

Learning probabilistic automata and Markov chains via queries

Wen-Guey Tzeng
1992 Machine Learning  
Probabilistic automata and Markov chains are probabilistic extensions of finite state ,automata and have similar structures.  ...  We investigate the problem of learning probabilistic automata and Markov chains via queries in the teacher-student learning model.  ...  Part of this paper appeared in the extended abstract "The equivalence and learning of probabilistic automata." Proceedings of the Thirtieth Annual Symposium on Foundations of Computer Science (1989).  ... 
doi:10.1007/bf00992862 fatcat:d3wq5mnhmza7hfeyav34atd5ey
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