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A Lower Bound for Learning Distributions Generated by Probabilistic Automata [chapter]

Borja Balle, Jorge Castro, Ricard Gavaldà
2010 Lecture Notes in Computer Science  
Finally, we show a lower bound: every algorithm to learn PDFA using queries with a resonable tolerance needs a number of queries larger than (1/µ) c for every c < 1.  ...  We show that the dependence on µ is necessary for every algorithm whose structure resembles existing ones. As a technical tool, a new variant of Statistical Queries termed L∞-queries is defined.  ...  A problem that was shown to be NP-hard for the case of distributions generated by probabilistic automata in [14] .  ... 
doi:10.1007/978-3-642-16108-7_17 fatcat:xknfxptpsfhvra7udyy4dn47mu

Improvement of the State Merging Rule on Noisy Data in Probabilistic Grammatical Inference [chapter]

Amaury Habrard, Marc Bernard, Marc Sebban
2003 Lecture Notes in Computer Science  
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.  ...  We also want to thank Thierry Murgue for his help and for his experience in the evaluation of PFSA.  ... 
doi:10.1007/978-3-540-39857-8_17 fatcat:s7ajqxsfn5cslfa2lxopf2sxi4

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

1999 Mathematical Reviews  
For this purpose, we present a general lower bound on the number of smailest counterexamples (required by any learning algorithm).  ...  Summary: “We propose and analyze a distribution learning al- gorithm for a subclass of acyclic probabilistic finite automata (APFA).  ... 

Compositional Verification of Probabilistic Systems Using Learning

Lu Feng, Marta Kwiatkowska, David Parker
2010 2010 Seventh International Conference on the Quantitative Evaluation of Systems  
To overcome this, we propose a novel learning technique based on the L* algorithm, which automatically generates probabilistic assumptions using the results of queries executed by a probabilistic model  ...  Our approach builds upon a recently proposed assume-guarantee framework for probabilistic automata, in which assumptions and guarantees are probabilistic safety properties, represented using finite automata  ...  ACKNOWLEDGEMENTS The authors are supported in part by EPSRC projects EP/D07956X and EP/F001096, EU FP7 project CONNECT and ERC Advanced Grant VERIWARE.  ... 
doi:10.1109/qest.2010.24 dblp:conf/qest/FengKP10 fatcat:kretrqvlcjcwnmrdraan42rni4

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

P. Dupont, F. Denis, Y. Esposito
2005 Pattern Recognition  
The first part of this work concentrates on probability distributions generated by these models. Necessary and sufficient conditions for an automaton to define a probabilistic language are detailed.  ...  On the other hand, HMMs with final probabilities and probabilistic automata generate distributions over strings of finite length.  ...  A PAC learning model for probabilistic automata The PAC 7 learning model was introduced by Valiant [35] .  ... 
doi:10.1016/j.patcog.2004.03.020 fatcat:uytkvkyfpfbj3lhibry6cfwue4

Human in the Loop: Interactive Passive Automata Learning via Evidence-Driven State-Merging Algorithms [article]

Christian A. Hammerschmidt, Radu State, Sicco Verwer
2017 arXiv   pre-print
Learning these automata often amounts to recovering or reverse engineering the model generating the data despite noisy, incomplete, or imperfectly sampled data sources rather than optimizing a purely numeric  ...  We present an interactive version of an evidence-driven state-merging (EDSM) algorithm for learning variants of finite state automata.  ...  Acknowledgements I would like to thank my collages for the valuable discussions and the feedback.  ... 
arXiv:1707.09430v1 fatcat:rd3vmzlivngf7ixlrngs7zr2qy

Learning PDFA with Asynchronous Transitions [chapter]

Borja Balle, Jorge Castro, Ricard Gavaldà
2010 Lecture Notes in Computer Science  
In this paper we extend the PAC learning algorithm due to Clark and Thollard for learning distributions generated by PDFA to automata whose transitions may take varying time lengths, governed by exponential  ...  Motivation The problem of learning (distributions generated by) probabilistic automata and related models has been intensely studied by the grammatical inference community; see [4, 12, 13] and references  ...  Carrasco's formula was used in [3] to bound the KL divergence between a target PDFA and an hypothesis produced by a learning algorithm.  ... 
doi:10.1007/978-3-642-15488-1_24 fatcat:mm26lwwm5vbzrdqn3arggxbfle

Learnability of Probabilistic Automata via Oracles [chapter]

Omri Guttman, S. V. N. Vishwanathan, Robert C. Williamson
2005 Lecture Notes in Computer Science  
Using an analog of the Myhill-Nerode theorem for probabilistic automata, we analyze µ-distinguishability and generalize it to µp-distinguishability.  ...  Efficient learnability using the state merging algorithm is known for a subclass of probabilistic automata termed µ-distinguishable.  ...  Acknowledgements We thank Alex Smola for insightful discussions.  ... 
doi:10.1007/11564089_15 fatcat:pmy6zlcgnvfodd76z5gyqtpcci

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  ...  For each strategy an explicit lower bound on the payoff achieved by that strategy is provided.  ... 
doi:10.1016/j.tcs.2012.10.007 fatcat:ciit7zasgzgytfxx66tzb5onku

ON THE COMPUTATION OF THE RELATIVE ENTROPY OF PROBABILISTIC AUTOMATA

CORINNA CORTES, MEHRYAR MOHRI, ASHISH RASTOGI, MICHAEL RILEY
2008 International Journal of Foundations of Computer Science  
by using a monoid morphism.  ...  The relative entropy is used in a variety of machine learning algorithms and applications to measure the discrepancy of two distributions.  ...  This project was also sponsored in part by the Department of the Army Award Number W23RYX-3275-N605. The U.S.  ... 
doi:10.1142/s0129054108005644 fatcat:3ti32le7vbeavg7p6owl7pd36u

Random DFAs are Efficiently PAC Learnable [article]

Leonid Aryeh Kontorovich
2009 arXiv   pre-print
This paper has been withdrawn due to an error found by Dana Angluin and Lev Reyzin.  ...  This work is supported in part by the Israel Science Foundation.  ...  Acknowledgements Many thanks to Dana Angluin, Boaz Nadler and Lev Reyzin for the many fruitful discussions, to Mark Rudelson for the anti-concentration lemma and to Gideon Schechtman for the hosting and  ... 
arXiv:0907.0453v2 fatcat:oz3vy4dfond33g7xxyct53wuuq

Generalized Stochastic Tree Automata for Multi-relational Data Mining [chapter]

Amaury Habrard, Marc Bernard, François Jacquenet
2002 Lecture Notes in Computer Science  
This paper addresses the problem of learning a statistical distribution of data in a relational database.  ...  We propose two extensions of this algorithm: use of sorts and generalization of the infered automaton according to a local criterion.  ...  The upper bound is the rule containing only variables and the lower bounds are the rules of R f,q .  ... 
doi:10.1007/3-540-45790-9_10 fatcat:vgktyjpxcbe2rlct5cjrwlh5ly

Assume-Guarantee Verification for Probabilistic Systems [chapter]

Marta Kwiatkowska, Gethin Norman, David Parker, Hongyang Qu
2010 Lecture Notes in Computer Science  
We present a compositional verification technique for systems that exhibit both probabilistic and nondeterministic behaviour.  ...  We present asymmetric and circular assume-guarantee rules, and show how they can be adapted to form quantitative queries, yielding lower and upper bounds on the actual probabilities that a property is  ...  The authors are supported in part by EPSRC grants EP/D07956X and EP/D076625 and European Commission FP 7 project CON-NECT (IST Project Number 231167).  ... 
doi:10.1007/978-3-642-12002-2_3 fatcat:kzcdr7obtjf2fexu66vrlpfp3y

PAutomaC: a probabilistic automata and hidden Markov models learning competition

Sicco Verwer, Rémi Eyraud, Colin de la Higuera
2013 Machine Learning  
Approximating distributions over strings is a hard learning problem.  ...  The Probabilistic Automata learning Competition (PAutomaC), run in 2012, was the first grammatical inference challenge that allowed the comparison between these methods and algorithms.  ...  Acknowledgements We are very thankful to the members of the scientific committee for their help in designing this competition.  ... 
doi:10.1007/s10994-013-5409-9 fatcat:ey3ghvxqxzbevmpzxmv5tytvay

Compositional Stochastic Model Checking Probabilistic Automata via Assume-guarantee Reasoning

Yang Liu, Rui Li
2020 International Journal of Networked and Distributed Computing (IJNDC)  
For each conjectured assumption, we have a lower bound lb(A, P) and an upper bound ub(A, P) on the probabilistic safety property P. through multi-objective model checking [18, 33] .  ...  Here, the conjectured assumption A M1 is the one derived after i iterations of learning, similarly for j. PA M1 is the lower bound of the interval I A1 , similarly for PA M2 .  ... 
doi:10.2991/ijndc.k.190918.001 fatcat:55ee6cvpp5btfdox3qg7qezyci
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