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Exploring learnability between exact and PAC

Nader H. Bshouty, Jeffrey C. Jackson, Christino Tamon
2005 Journal of computer and system sciences (Print)  
We also introduce a model of probably almost exactly correct (PAExact) learning that requires a hypothesis with negligible error and thus lies between the PExact and PAC models.  ...  Unlike the Exact and PExact models, PAExact learning is applicable to classes of functions defined over infinite instance spaces. We obtain a number of separation results between these models.  ...  Acknowledgments The two referees of the journal version of this paper provided numerous helpful questions and comments that resulted in significant improvements.  ... 
doi:10.1016/j.jcss.2004.10.002 fatcat:7zkdo2wtzbckbjusbrbbkwuhcq

Learning Shuffle Ideals Under Restricted Distributions

Dongqu Chen
2014 Neural Information Processing Systems  
In this paper, we study the PAC learnability of shuffle ideals and present positive results on this learning problem under element-wise independent and identical distributions and Markovian distributions  ...  Experiments demonstrate the advantage for both efficiency and accuracy of our algorithm.  ...  Acknowledgments We give our sincere gratitude to Professor Dana Angluin of Yale University for valuable discussions and comments on the learning problem and the proofs.  ... 
dblp:conf/nips/Chen14 fatcat:63ki4ev35be6pfytjaqs6vrq6e

On the learnability of majority rule

Yuval Salant
2007 Journal of Economic Theory  
The committee uses majority rule to choose between pairs of alternatives. Each member's vote is derived from a linear ordering over all the alternatives.  ...  See Kalai [6] for a discussion on PAC-learnability and describability.  ...  , both are PAC-learnable from O(N) examples.  ... 
doi:10.1016/j.jet.2006.03.012 fatcat:mieuc3mt2nbcjkyok6ph2v4xeu

Learning schema mappings

Balder ten Cate, Víctor Dalmau, Phokion G. Kolaitis
2012 Proceedings of the 15th International Conference on Database Theory - ICDT '12  
A schema mapping is a high-level specification of the relationship between a source schema and a target schema.  ...  We also obtain results concerning the learnability of schema mappings in the context of Valiant's well known PAC (Probably-Approximately-Correct) learning model.  ...  PAC learnability. In [5] , Angluin showed that, in many cases, exact learnability with equivalence queries implies PAC learnability.  ... 
doi:10.1145/2274576.2274596 dblp:conf/icdt/CateDK12 fatcat:oozqpfl6hrbgxdcw24p5s5ywta

Blending Autonomous Exploration and Apprenticeship Learning

Thomas J. Walsh, Daniel Hewlett, Clayton T. Morrison
2011 Neural Information Processing Systems  
Our approach modifies an existing apprenticeship learning framework that relies on teacher demonstrations and does not necessarily explore the environment.  ...  We present theoretical and empirical results for a framework that combines the benefits of apprenticeship and autonomous reinforcement learning.  ...  Acknowledgments We thank Michael Littman and Lihong Li for discussions and DARPA-27001328 for funding.  ... 
dblp:conf/nips/WalshHM11 fatcat:s5fbir432bhnhdtmjooplm2udy

Learnable: Theory vs Applications [article]

Marina Sapir
2018 arXiv   pre-print
I show that, under some conditions, the theory of PAC Learnable provides a way to solve the Applied learning problem.  ...  Two different views on machine learning problem: Applied learning (machine learning with business applications) and Agnostic PAC learning are formalized and compared here.  ...  One path to reformulate the problem is explored in PAC learnable theory.  ... 
arXiv:1807.10681v1 fatcat:fb4m7eoohnh4lpri4kkzqrlmii

Learning from a Consistently Ignorant Teacher

Michael Frazier, Sally Goldman, Nina Mishra, Leonard Pitt
1996 Journal of computer and system sciences (Print)  
Both learnability and non-learnability results are presented. \Consistency requires you to be as ignorant today as you were a y e ar ago." { Bernard Berenson (1865-1959  ...  We i n vestigate the learnability o f a v ariety of concept classes in this model, including monomials, monotone DNF formulas, Horn sentences, decision trees, DFAs, and axis-parallel boxes in Euclidean  ...  Acknowledgements We thank Dana Angluin and Haym Hirsh for helpful conversations regarding this work.  ... 
doi:10.1006/jcss.1996.0035 fatcat:ci4lb5mtvrgxrooglbqwc6i6lq

Learning orthogonal F-Horn formulas [chapter]

Akira Miyashiro, Eiji Takimoto, Yoshifumi Sakai, Akira Maruoka
1995 Lecture Notes in Computer Science  
In the PAC-learning, or the query learning model, it has been an important open problem to decide whether the class of DNF and CNF formulas is learnable.  ...  It is shown that under a condition on F, the class of orthogonal F-Horn formulas is learnable with membership, equivalence and subset queries.  ...  These results suggest the significance of exploring the learnability of k-quasi Horn formulas.  ... 
doi:10.1007/3-540-60454-5_32 fatcat:q2zcwpqbmvaxxescccklqdssqu

Learning orthogonal F-Horn formulas

Eiji Takimoto, Akira Miyashiro, Akira Maruoka, Yoshifumi Sakai
1997 Theoretical Computer Science  
In the PAC-learning, or the query learning model, it has been an important open problem to decide whether the class of DNF and CNF formulas is learnable.  ...  It is shown that under a condition on F, the class of orthogonal F-Horn formulas is learnable with membership, equivalence and subset queries.  ...  These results suggest the significance of exploring the learnability of k-quasi Horn formulas.  ... 
doi:10.1016/s0304-3975(97)00020-0 fatcat:o6hmxyj5rbhqlm6csuxbvvpj3a

Sample Complexity Bounds for Robustly Learning Decision Lists against Evasion Attacks [article]

Pascale Gourdeau, Varun Kanade, Marta Kwiatkowska, James Worrell
2022 arXiv   pre-print
In this paper we address this issue within the framework of PAC learning, focusing on the class of decision lists.  ...  Our first main result is a sample-complexity lower bound: the class of monotone conjunctions (essentially the simplest non-trivial hypothesis class on the Boolean hypercube) and any superclass has sample  ...  Acknowledgments MK and PG received funding from the ERC under the European Union's Horizon 2020 research and innovation programme (FUN2MODEL, grant agreement No. 834115).  ... 
arXiv:2205.06127v1 fatcat:xsjjf6awwrgifihhwc6dekgttm

Sample Complexity of Learning Parametric Quantum Circuits [article]

Haoyuan Cai, Qi Ye, Dong-Ling Deng
2022 arXiv   pre-print
Here, we prove that physical quantum circuits are PAC (probably approximately correct) learnable on a quantum computer via empirical risk minimization: to learn a parametric quantum circuit with at most  ...  Our results provide a valuable guide for quantum machine learning in both theory and practice.  ...  Appendix B: Appendix: PAC learnability of F The following lemma shows that any finite hypothesis space F satisfies the PAC learnability. Our circuit F consists of R x (θ), H, and CNOT gates.  ... 
arXiv:2107.09078v2 fatcat:w34x5ig4tfgwzos5rg7ru4bb24

Page 6621 of Mathematical Reviews Vol. , Issue 2001I [page]

2001 Mathematical Reviews  
Jackson and Christino Tamon, Uniform-distribution attribute noise learnability (75-80 (electronic)); Nader H. Bshouty and David K.  ...  Kobourov, Polylogarithmic-overhead piecemeal graph exploration (280-286 (elecronic)); Leslie G.  ... 

Stabiliser states are efficiently PAC-learnable [article]

Andrea Rocchetto
2018 arXiv   pre-print
A, 2088, (2007)] and propose learning theory as a tool for exploring the power of quantum computation.  ...  In this model, quantum states have been shown to be Probably Approximately Correct (PAC)-learnable with sample complexity linear in the number of qubits.  ...  , Varun Kanade, Ying Li, Simon Perdrix, Fabio Sciarrino, Simone Severini and two anonymous reviewers for helpful comments and suggestions.  ... 
arXiv:1705.00345v2 fatcat:wz6p2xrubzfqvms42zsvpax3um

On Exact Learning from Random Walk [chapter]

Nader H. Bshouty, Iddo Bentov
2006 Lecture Notes in Computer Science  
We investigate the learnability of common concept classes via random walk, and give positive and negative separation results as to whether exact learning in the random walk models is easier than in less  ...  We consider exact learning models based on random walk, and thus having in effect a more restricted teacher compared to both the adversarial and the uniform exact learning models.  ...  However, it is also unknown whether non-exact learning of O(log n)-juntas is possible in the uniform PAC model, and UROnline learnability indeed implies uniform PAC learnability.  ... 
doi:10.1007/11894841_17 fatcat:v3hz4hs5tfawjjydlikivw33be

Learning Description Logic Ontologies: Five Approaches. Where Do They Stand?

Ana Ozaki
2020 Künstliche Intelligenz  
We provide an overview of each approach and how it has been adapted for dealing with DL ontologies. Finally, we discuss the benefits and limitations of each of them for learning DL ontologies.  ...  These are based on association rule mining, formal concept analysis, inductive logic programming, computational learning theory, and neural networks.  ...  as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.  ... 
doi:10.1007/s13218-020-00656-9 fatcat:styfgvgsjbb5vl3vfo6kn3drzu
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