Journal ArticleDOI
Computational limitations on learning from examples
Leonard Pitt,Leslie G. Valiant +1 more
TLDR
It is shown for various classes of concept representations that these cannot be learned feasibly in a distribution-free sense unless R = NP, and relationships between learning of heuristics and finding approximate solutions to NP-hard optimization problems are given.Abstract:
The computational complexity of learning Boolean concepts from examples is investigated. It is shown for various classes of concept representations that these cannot be learned feasibly in a distribution-free sense unless R = NP. These classes include (a) disjunctions of two monomials, (b) Boolean threshold functions, and (c) Boolean formulas in which each variable occurs at most once. Relationships between learning of heuristics and finding approximate solutions to NP-hard optimization problems are given.read more
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Book
Understanding Machine Learning: From Theory To Algorithms
TL;DR: The aim of this textbook is to introduce machine learning, and the algorithmic paradigms it offers, in a principled way in an advanced undergraduate or beginning graduate course.
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The Strength of Weak Learnability
TL;DR: In this paper, a method is described for converting a weak learning algorithm into one that achieves arbitrarily high accuracy, and it is shown that these two notions of learnability are equivalent.
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Learnability and the Vapnik-Chervonenkis dimension
TL;DR: This paper shows that the essential condition for distribution-free learnability is finiteness of the Vapnik-Chervonenkis dimension, a simple combinatorial parameter of the class of concepts to be learned.
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Queries and Concept Learning
TL;DR: This work considers the problem of using queries to learn an unknown concept, and several types of queries are described and studied: membership, equivalence, subset, superset, disjointness, and exhaustiveness queries.
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Property testing and its connection to learning and approximation
TL;DR: This paper considers the question of determining whether a function f has property P or is ε-far from any function with property P, and devise algorithms to test whether the underlying graph has properties such as being bipartite, k-Colorable, or having a clique of density p-Clique with respect to the vertex set.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Proceedings ArticleDOI
A theory of the learnable
TL;DR: This paper regards learning as the phenomenon of knowledge acquisition in the absence of explicit programming, and gives a precise methodology for studying this phenomenon from a computational viewpoint.
Journal ArticleDOI
A Greedy Heuristic for the Set-Covering Problem
TL;DR: It turns out that the ratio between the two grows at most logarithmically in the largest column sum of A when all the components of cT are the same, which reduces to a theorem established previously by Johnson and Lovasz.