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Learning Boolean Halfspaces with Small Weights from Membership Queries
[article]
2014
arXiv
pre-print
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We consider the problem of proper 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. ...
arXiv:1405.1535v1
fatcat:wmj3uolzlbdbrjbsdud4imekni
Learning Functions of Halfspaces using Prefix Covers
2012
Journal of machine learning research
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To prove this result, we identify a new structural property of 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 ...
dblp:journals/jmlr/GopalanKM12
fatcat:pzwe6l34bnad3at5fkhwzwb5om
Learning intersections and thresholds of halfspaces
2004
Journal of computer and system sciences (Print)
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Finally, we also observe that any function of a constant number of polynomial-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] . ...
doi:10.1016/s0022-0000(03)00181-8
fatcat:iijhmzczcveebbwu2banbmykva
Learning intersections and thresholds of halfspaces
2004
Journal of computer and system sciences (Print)
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Finally, we also observe that any function of a constant number of polynomial-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] . ...
doi:10.1016/j.jcss.2003.11.002
fatcat:le4ezu5pwjdkveehqwpncmxgje
Near-Optimal Statistical Query Lower Bounds for Agnostically Learning Intersections of Halfspaces with Gaussian Marginals
[article]
2022
arXiv
pre-print
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We prove two variants of our lower bound, each of which combines ingredients 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. ...
arXiv:2202.05096v1
fatcat:jpmmq7m6qnacvj3gf7zqyafhpi
Page 5022 of Mathematical Reviews Vol. , Issue 96h
[page]
1996
Mathematical Reviews
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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%. ...
Unconditional lower bounds for learning intersections of halfspaces
2007
Machine Learning
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Our main result is that any statistical-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. ...
doi:10.1007/s10994-007-5010-1
fatcat:y554mbcivjf6xdikd224bpujdq
Cryptographic Hardness for Learning Intersections of Halfspaces
2006
2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)
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We also prove that PAC 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 ...
doi:10.1109/focs.2006.24
dblp:conf/focs/KlivansS06
fatcat:ua2vzd3oczhtramz34sdjvpmjq
On PAC Learning Algorithms for Rich Boolean Function Classes
[chapter]
2006
Lecture Notes in Computer Science
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We give an overview of the fastest known algorithms for 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. ...
doi:10.1007/11750321_42
fatcat:iqkiulnpd5at7a7enenxwxxjgy
On PAC learning algorithms for rich Boolean function classes
2007
Theoretical Computer Science
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We give an overview of the fastest known algorithms for 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. ...
doi:10.1016/j.tcs.2007.05.018
fatcat:cfpv3cqkrvbu3ndw7x2vk6j5he
Cryptographic hardness for learning intersections of halfspaces
2009
Journal of computer and system sciences (Print)
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We also prove that PAC 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 ...
doi:10.1016/j.jcss.2008.07.008
fatcat:emanuf7fevdahh5ty6gbmxar6e
Computational learning theory
1992
Proceedings of the twenty-fourth annual ACM symposium on Theory of computing - STOC '92
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Hence,
predicting
3p-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. ...
doi:10.1145/129712.129746
dblp:conf/stoc/Angluin92
fatcat:7aw3cnd745bellyhu7phywpul4
Optimal bounds for sign-representing the intersection of two halfspaces by polynomials
[article]
2010
arXiv
pre-print
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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. ...
arXiv:0910.4224v2
fatcat:rde5ogkzbrdsbla22ezfa5r6em
Noise-Tolerant Parallel Learning of Geometric Concepts
1998
Information and Computation
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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 from ...
We present several efficient parallel algorithms for PAC-learning geometric concepts in a constant-dimensional space. ...
that has small weight outside. ...
doi:10.1006/inco.1998.2737
fatcat:vp4f6ufyizbyhh4oukdpwudfqa
Optimal bounds for sign-representing the intersection of two halfspaces by polynomials
2013
Combinatorica
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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. ...
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] . ...
doi:10.1007/s00493-013-2759-7
fatcat:76pzqyhbtfhcbnsw2xha2a7mwm
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