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Learning Boolean Halfspaces with Small Weights from Membership Queries
[article]

2014
*
arXiv
*
pre-print

We consider the problem of proper

arXiv:1405.1535v1
fatcat:wmj3uolzlbdbrjbsdud4imekni
*learning*a*Boolean**Halfspace**with*integer*weights*{0,1,...,t}*from**membership**queries*only. ...*with**Small**Weights*Using*Membership**Queries*. ... In [4] Abboud et. al. showed that in order to*learn**boolean**Halfspace*functions*with**weights*W = {−1, 0, 1}, we need at least O(2 n−o(n) )*membership**queries*. ...##
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Learning Functions of Halfspaces using Prefix Covers

2012
*
Journal of machine learning research
*

To prove this result, we identify a new structural property of

dblp:journals/jmlr/GopalanKM12
fatcat:pzwe6l34bnad3at5fkhwzwb5om
*Boolean*functions that yields learnability*with**queries*: that of having a*small*prefix cover. ... We present a simple*query*-algorithm for*learning*arbitrary functions of k*halfspaces*under any product distribution on the*Boolean*hypercube. ... Theorem 1 (*Learning*Functions of*Halfspaces*) The concept class of arbitrary*Boolean*functions of k*halfspaces*can be PAC*learned**with**membership**queries*under the uniform distribution {0, 1} n to accuracy ...##
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Learning intersections and thresholds of halfspaces

2004
*
Journal of computer and system sciences (Print)
*

Finally, we also observe that any function of a constant number of polynomial-

doi:10.1016/s0022-0000(03)00181-8
fatcat:iijhmzczcveebbwu2banbmykva
*weight**halfspaces*can be*learned*in polynomial time in the model of exact*learning**from**membership*and equivalence*queries*. ... We also give the first quasipolynomial time algorithm for*learning*any*Boolean*function of a polylog number of polynomial-*weight**halfspaces*under any distribution on the*Boolean*hypercube. ...*Learning*in the exact model We also give results for*learning*an intersection of k*weight*-w*halfspaces*in the model of exact*learning**from**membership*and equivalence*queries*[4] . ...##
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Learning intersections and thresholds of halfspaces

2004
*
Journal of computer and system sciences (Print)
*

Finally, we also observe that any function of a constant number of polynomial-

doi:10.1016/j.jcss.2003.11.002
fatcat:le4ezu5pwjdkveehqwpncmxgje
*weight**halfspaces*can be*learned*in polynomial time in the model of exact*learning**from**membership*and equivalence*queries*. ... We also give the first quasipolynomial time algorithm for*learning*any*Boolean*function of a polylog number of polynomial-*weight**halfspaces*under any distribution on the*Boolean*hypercube. ...*Learning*in the exact model We also give results for*learning*an intersection of k*weight*-w*halfspaces*in the model of exact*learning**from**membership*and equivalence*queries*[4] . ...##
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Near-Optimal Statistical Query Lower Bounds for Agnostically Learning Intersections of Halfspaces with Gaussian Marginals
[article]

2022
*
arXiv
*
pre-print

We prove two variants of our lower bound, each of which combines ingredients

arXiv:2202.05096v1
fatcat:jpmmq7m6qnacvj3gf7zqyafhpi
*from*Diakonikolas et al. (2021)*with*(an extension of) a different earlier approach for agnostic SQ lower bounds for the*Boolean*... We consider the well-studied problem of*learning*intersections of*halfspaces*under the Gaussian distribution in the challenging agnostic*learning*model. ...*small*low-degree Hermite*weight*. ...##
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Page 5022 of Mathematical Reviews Vol. , Issue 96h
[page]

1996
*
Mathematical Reviews
*

Summary: “We study the learnability of

*Boolean*functions*from**membership*and equivalence*queries*. ... Summary: “An algorithm is a weak*learning*algorithm if*with*some*small*probability it outputs a hypothesis*with*error slightly below 50%. ...##
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Unconditional lower bounds for learning intersections of halfspaces

2007
*
Machine Learning
*

Our main result is that any statistical-

doi:10.1007/s10994-007-5010-1
fatcat:y554mbcivjf6xdikd224bpujdq
*query*algorithm for*learning*the intersection of √ n*halfspaces*in n dimensions must make 2 Ω( √ n)*queries*. ... We also show that the intersection of two majorities (low-*weight**halfspaces*) cannot be computed by a polynomial threshold function (PTF)*with*fewer than n Ω(log n/ log log n) monomials. ... We note here that intersections of a constant number of*halfspaces*are learnable*with**membership*and equivalence*queries*in polynomial time via Angluin's algorithm for*learning*finite automata. ...##
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Cryptographic Hardness for Learning Intersections of Halfspaces

2006
*
2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)
*

We also prove that PAC

doi:10.1109/focs.2006.24
dblp:conf/focs/KlivansS06
fatcat:ua2vzd3oczhtramz34sdjvpmjq
*learning*intersections of n ε low-*weight**halfspaces*would yield a polynomial-time quantum solution toÕ(n 1.5 )-SVP andÕ(n 1.5 )-SIVP (shortest vector problem and shortest independent ... We give the first representation-independent hardness results for PAC*learning*intersections of*halfspaces*, a central concept class in computational*learning*theory. ... If, in addition to*membership**queries*, the learner can make equivalence*queries*, Klivans and Shpilka [16] have shown how to exactly*learn*restricted types of depth-3 arithmetic circuits via multiplicity ...##
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On PAC Learning Algorithms for Rich Boolean Function Classes
[chapter]

2006
*
Lecture Notes in Computer Science
*

We give an overview of the fastest known algorithms for

doi:10.1007/11750321_42
fatcat:iqkiulnpd5at7a7enenxwxxjgy
*learning*various expressive classes of*Boolean*functions in the Probably Approximately Correct (PAC)*learning*model. ... In addition to surveying previously known results, we use existing techniques to give the first known subexponential-time algorithms for PAC*learning*two natural and expressive classes of*Boolean*functions ... to the target function, which are often known as*membership**queries*. ...##
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On PAC learning algorithms for rich Boolean function classes

2007
*
Theoretical Computer Science
*

We give an overview of the fastest known algorithms for

doi:10.1016/j.tcs.2007.05.018
fatcat:cfpv3cqkrvbu3ndw7x2vk6j5he
*learning*various expressive classes of*Boolean*functions in the Probably Approximately Correct (PAC)*learning*model. ... In addition to surveying previously known results, we use existing techniques to give the first known subexponential-time algorithms for PAC*learning*two natural and expressive classes of*Boolean*functions ... to the target function, which are often known as*membership**queries*. ...##
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Cryptographic hardness for learning intersections of halfspaces

2009
*
Journal of computer and system sciences (Print)
*

We also prove that PAC

doi:10.1016/j.jcss.2008.07.008
fatcat:emanuf7fevdahh5ty6gbmxar6e
*learning*intersections of n low-*weight**halfspaces*would yield a polynomial-time quantum solution toÕ (n 1.5 )-SVP andÕ (n 1.5 )-SIVP (shortest vector problem and shortest independent ... We give the first representation-independent hardness results for PAC*learning*intersections of*halfspaces*, a central concept class in computational*learning*theory. ... If, in addition to*membership**queries*, the learner can make equivalence*queries*, Klivans and Shpilka [16] have shown how to exactly*learn*restricted types of depth-3 arithmetic circuits via multiplicity ...##
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Computational learning theory

1992
*
Proceedings of the twenty-fourth annual ACM symposium on Theory of computing - STOC '92
*

Hence,
predicting
3p-

doi:10.1145/129712.129746
dblp:conf/stoc/Angluin92
fatcat:7aw3cnd745bellyhu7phywpul4
*boolean*formulas or finite unions of dfas or two-way dfas*with**membership**queries*is as hard as predicting*boolean*formulas*with**membership**queries*. 12.3 Implications of ... Such a*query*is called a*membership**query*. In this setting we may define PAC-*learning**with**membership**queries*in the obvious way. ...##
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Optimal bounds for sign-representing the intersection of two halfspaces by polynomials
[article]

2010
*
arXiv
*
pre-print

*learning*DNF formulas and read-once

*Boolean*formulas. ... Our result shows that the intersection of two

*halfspaces*on 0,1^n only admits a trivial 2^Theta(n)-time

*learning*algorithm based on sign-representation by polynomials, unlike the advances achieved in PAC ... Furthermore, if

*membership*

*queries*are allowed, DNF formulas are known to be learnable in polynomial time

*with*respect to the uniform distribution on the hypercube [12] . Our Techniques. ...

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Noise-Tolerant Parallel Learning of Geometric Concepts

1998
*
Information and Computation
*

noise-tolerant parallel algorithm to PAClearn the class of geometric concepts defined by a polynomial number of (d&1)-dimensional hyperplanes against an arbitrary distribution where each hyperplane has a slope

doi:10.1006/inco.1998.2737
fatcat:vp4f6ufyizbyhh4oukdpwudfqa
*from*... We present several efficient parallel algorithms for PAC-*learning*geometric concepts in a constant-dimensional space. ... that has*small**weight*outside. ...##
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Optimal bounds for sign-representing the intersection of two halfspaces by polynomials

2013
*
Combinatorica
*

Furthermore, if

doi:10.1007/s00493-013-2759-7
fatcat:76pzqyhbtfhcbnsw2xha2a7mwm
*membership**queries*are allowed, DNF formulas are known to be learnable in polynomial time*with*respect to the uniform distribution on the hypercube [12] . Our Techniques. ... As a result, f can be PAC*learned*in time polynomial in N; using any of a variety of*halfspace**learning*algorithms. ... degree into*Boolean*functions*with*high threshold density, due to Krause and Pudlák [21, Prop. 2.1] . ...
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