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Learning Monotone DNF from a Teacher That Almost Does Not Answer Membership Queries [chapter]

Nader H. Bshouty, Nadav Eiron
2001 Lecture Notes in Computer Science  
We present results concerning the learning of Monotone DNF (MDNF) from Incomplete Membership Queries and Equivalence Queries.  ...  In a sense this is the best possible, as learning with p = 1 − 1/ω(poly(n, t)) would imply learning MDNF, and thus also DNF, from equivalence queries alone. 1  ...  Part of this research was done while the second author was a graduate student at the Department of Computer Science, Technion -Israel Institute of Technology, Haifa, Israel.  ... 
doi:10.1007/3-540-44581-1_36 fatcat:plvz5cini5adxduuw4h6rfvpp4

A Model of Interactive Teaching

H.David Mathias
1997 Journal of computer and system sciences (Print)  
An important concept class that is not known to be learnable is DNF formulas. We demonstrate the power of our approach by providing a deterministic teacher and learner for the class of DNF formulas.  ...  Previous teaching models in the learning theory community have been batch models. That is, in these models the teacher has generated a single set of helpful examples to present to the learner.  ...  Our learner is almost identical to Bshouty's learning algorithm with unknown monotone basis.  ... 
doi:10.1006/jcss.1997.1491 fatcat:7dp7hsez3zhaxgcujby3dqj5pa

Learning the Boundary of Inductive Invariants [article]

Yotam M. Y. Feldman and Mooly Sagiv and Sharon Shoham and James R. Wilcox
2020 arXiv   pre-print
We further harness Bshouty's seminal result in concept learning to efficiently infer invariants of a larger syntactic class of invariants beyond monotone DNF.  ...  We define a condition on invariants and their geometry, called the fence condition, which permits applying theoretical results from exact concept learning to answer open problems in invariant inference  ...  Learning with errors in queries. Exact learning has also been studied in models where the teacher might not respond "unknown" or answer incorrectly; see [Bshouty 2018] for a short survey.  ... 
arXiv:2008.09909v2 fatcat:ccdrf54d4jf7lmjpc7bz2q27su

Learning orthogonal F-Horn formulas [chapter]

Akira Miyashiro, Eiji Takimoto, Yoshifumi Sakai, Akira Maruoka
1995 Lecture Notes in Computer Science  
Recently, it was pointed out that the problem of PAC-learning for these classes with membership queries can be reduced to that of learning for the class of k-quasi Horn formulas with membership and equivalence  ...  It is shown that under a condition on F, the class of orthogonal F-Horn formulas is learnable with membership, equivalence and subset queries.  ...  In the query learning model, a teacher of the learning algorithm is assumed to exist and give partial information about a formula f to be learned when a query arises from the algorithm.  ... 
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  
Recently, it was pointed out that the problem of PAC-learning for these classes with membership queries can be reduced to that of learning for the class of k-quasi Horn formulas with membership and equivalence  ...  It is shown that under a condition on F, the class of orthogonal F-Horn formulas is learnable with membership, equivalence and subset queries.  ...  In the query learning model, a teacher of the learning algorithm is assumed to exist and give partial information about a formula f to be learned when a query arises from the algorithm.  ... 
doi:10.1016/s0304-3975(97)00020-0 fatcat:o6hmxyj5rbhqlm6csuxbvvpj3a

Exact Learning from an Honest Teacher That Answers Membership Queries [article]

Nader H. Bshouty
2017 arXiv   pre-print
Given a teacher that holds a function f:X→ R from some class of functions C.  ...  The teacher can receive from the learner an element d in the domain X (a query) and returns the value of the function in d, f(d)∈ R.  ...  A hardness result in learning a class C from equivalent and membership queries does not imply hardness in learning C from membership queries only.  ... 
arXiv:1706.03935v1 fatcat:r4qihzswkvhwdpv76vb54w4dp4

Learning the boundary of inductive invariants

Yotam M. Y. Feldman, Mooly Sagiv, Sharon Shoham, James R. Wilcox
2021 Proceedings of the ACM on Programming Languages (PACMPL)  
We further harness Bshouty's seminal result in concept learning to efficiently infer invariants of a larger syntactic class of invariants beyond monotone DNF.  ...  We define a condition on invariants and their geometry, called the fence condition, which permits applying theoretical results from exact concept learning to answer open problems in invariant inference  ...  Learning with errors in queries. Exact learning has also been studied in models where the teacher might not respond łunknownž or answer incorrectly; see [Bshouty 2018] for a short survey.  ... 
doi:10.1145/3434296 fatcat:jwuskhwavrffbj7liolbg5mcoy

On Exact Learning Monotone DNF from Membership Queries [chapter]

Hasan Abasi, Nader H. Bshouty, Hanna Mazzawi
2014 Lecture Notes in Computer Science  
In this paper, we study the problem of learning a monotone DNF with at most s terms of size (number of variables in each term) at most r (s term r-MDNF) from membership queries.  ...  We first present new lower bounds for this problem and then present deterministic and randomized adaptive algorithms with query complexities that are almost optimal.  ...  Learning Model Consider a teacher (or a black box) that has a target function f : {0, 1} n → {0, 1} that is s-term r-MDNF. The teacher can answer membership queries.  ... 
doi:10.1007/978-3-319-11662-4_9 fatcat:hmiohwutenf4noqqgv3vdqj5bm

On Exact Learning Monotone DNF from Membership Queries [article]

Hasan Abasi and Nader H. Bshouty and Hanna Mazzawi
2014 arXiv   pre-print
In this paper, we study the problem of learning a monotone DNF with at most s terms of size (number of variables in each term) at most r (s term r-MDNF) from membership queries.  ...  We first present new lower bounds for this problem and then present deterministic and randomized adaptive algorithms with query complexities that are almost optimal.  ...  Learning Model Consider a teacher (or a black box) that has a target function f : {0, 1} n → {0, 1} that is s-term r-MDNF. The teacher can answer membership queries.  ... 
arXiv:1405.0792v1 fatcat:bfk7obiq55eoxnuo7crekuszom

Asking Questions to Minimize Errors

Nader H. Bshouty, Sally A. Goldman, Thomas R. Hancock, Sleiman Matar
1996 Journal of computer and system sciences (Print)  
A number of efficient learning algorithms achieve exact identification of an unknown function from some class using membership and equivalence queries.  ...  Using a standard transformation such algorithms can easily be converted to on-line learning algorithms that use membership queries.  ...  E (Monotone DNF n, m ) m&% \ log m+log n log n&log log m+ . FIG 4 . 4 An algorithm to learn monotone DNF with m&k equivalence queries and O(k(nÂk) k +mn) 2 membership queries.  ... 
doi:10.1006/jcss.1996.0021 fatcat:hoes3bhwcnddddhh65rbkfpi2m

Learning with errors in answers to membership queries

Laurence Bisht, Nader H. Bshouty, Lawrance Khoury
2008 Journal of computer and system sciences (Print)  
Turán, Malicious omissions and errors in answering to membership queries, Machine Learning 28 (2-3) (1997) 211-255]: Learning with equivalence and limited membership queries and learning with equivalence  ...  We show that if a class of concepts that is closed under projection is learnable in polynomial time using equivalence and (standard) membership queries then it is learnable in polynomial time in the above  ...  Except for classes that can be learned from equivalence queries only, almost nothing is known to be learnable in the exact learning model where the teacher lies on answering membership queries with a constant  ... 
doi:10.1016/j.jcss.2007.04.010 fatcat:zv5sqa3adreexdznasdyeoztam

Non-Adaptive Learning a Hidden Hipergraph [article]

Hasan Abasi and Nader H. Bshouty and Hanna Mazzawi
2015 arXiv   pre-print
We give a new deterministic algorithm that non-adaptively learns a hidden hypergraph from edge-detecting queries.  ...  We give the first polynomial time non-adaptive learning algorithm for learning hypergraph that asks almost optimal number of queries.  ...  Learning from Membership Queries Consider a teacher that has a target function f : {0, 1} n → {0, 1} that is s-term r-MDNF. The teacher can answer membership queries.  ... 
arXiv:1502.04137v1 fatcat:kpwq3vof3nfq7fit7wmxihof6u

Separating models of learning with faulty teachers

Vitaly Feldman, Shrenik Shah
2009 Theoretical Computer Science  
Eiron, Learning monotone DNF from a teacher that almost does not answer membership queries, Journal of Machine Learning Research 3 (2002) 49-57].  ...  Slonim, Randomly fallible teachers: Learning monotone DNF with an incomplete membership oracle, Machine Learning 14 (1) (1994) 7-26].  ...  Part of the first author's work was done while the author was at Harvard University supported by grants from the National Science Foundation NSF 0432037 and NSF 0427129.  ... 
doi:10.1016/j.tcs.2009.01.017 fatcat:mojru55gsjeoxdkxh5z22tnuk4

Page 508 of Mathematical Reviews Vol. , Issue 2004a [page]

2004 Mathematical Reviews  
(IL-TECH-C; Haifa) ; Eiron, Naday (1-IBM2; San Jose, CA) Learning monotone DNF from a teacher that almost does not answer membership queries. (English summary) J. Mach. Learn.  ...  Summary: “We present results concerning the learning of mono- tone DNF (MDNF) from incomplete membership queries and equivalence queries.  ... 

Separating Models of Learning with Faulty Teachers [chapter]

Vitaly Feldman, Shrenik Shah, Neal Wadhwa
2007 Lecture Notes in Computer Science  
In this model, the answers to a random subset of the learner's membership queries are flipped.  ...  In this model, the answers to a random subset of the learner's membership queries may be missing.  ...  This result was improved by Bshouty and Eiron who gave an algorithm that can learn monotone DNF even when only an inverse polynomial fraction of membership queries is answered [8] .  ... 
doi:10.1007/978-3-540-75225-7_11 fatcat:ak4o5c6cevd5riazvzzr5p2eiq
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