Kearns, M.J. (1990). The Computational Complexity of Machine Learning. Cambridge, MA, London, MIT Press.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....learning problem is how hard is the problem But although our theoretical understanding of computational learning has increased rapidly in the last decade, there is still no generic way to evaluate the difficulty of an arbitrary learning problem. Recent results in computational learning theory [6] extend earlier work by Valiant on PAC learning [7, 8] and rely in particular on the concept of VC dimension [9] Work in this area has tended to concentrate on distribution free (i.e. problem independent) analysis although some recent work has given attention to distribution specific analysis ....

Kearns, M. (1990). The Computational Complexity of Machine Learning. The MIT Press.

....This general model allows for both the measurements and the class labels to be subject to noise. There are many other possible models for classi cation whichwe do not consider here. These include models which assume that there exists a target function belonging to a particular class of functions [41, 66], relax the assumption of independently generated examples [1, 7] allow for drift in the generating distribution [4, 8, 33] and relax the assumption that there is a xed relationship between measurements and class labels [6, 12, 39] Typically, the measurement space X is taken to be some subset ....

M. Kearns. The Computational Complexity of Machine Learning. MIT Press, 1990.

....(a) I i (f) nI 1 (f) 13 To get a bound on I 1 (MAJ) note that I 1 (MAJ) 2 Gamman n , for some constant c. Thus n jaj This implies that f (a) 2 We now use the Vapnik Chernovenkis dimension to find lower bounds on the sample size. Kearns [K] had also observed that the VC dimension can be used to prove negative learning results for monotone Boolean functions. Recall that if C is a class of Boolean functions then C shatters A f0; 1g if for every Boolean function g : A f0; 1g there exists a Boolean function f 2 C such that f j A ....

Michael Kearns. The Computational Complexity of Machine Learning. MIT Press, 1990.

....each element is in exactly two sets. Both these problems are NP hard and polynomial time approximation algorithms for both are well studied. For set cover see [12, 26, 29] For vertex cover see [6, 7, 13, 21, 22, 30] In this paper we study the generalization of covering to partial covering [27, 31]. Specifically, in k set cover, we wish to find a minimum number (or, in the weighted version, a minimum weight collection) of sets that cover at least k elements. When k is the total number of elements, we obtain the regular set cover problem; similarly for k vertex cover. We sometimes refer to ....

M. Kearns. The computational complexity of machine learning. M.I.T. Press, 1990.

....ARO grant N00014 89 J 1988, and the Siemens Corporation. email address: rivest theory.lcs.mit.edu published by Morgan Kaufmann) for many interesting papers. The ACM STOC and the IEEE FOCS conference proceedings also contain many key theoretical papers from both areas. The Ph.D. thesis of Kearns [21] is one of the first major works to explore the relationship between cryptography and machine learning, and is also an excellent introduction to many of the key concepts and results. 2 Initial Comparison Machine learning and cryptanalysis can be viewed as sister fields, since they share many ....

....to show that finding an approximately minimum size DFA consistent with such a set of examples is impossible to do e#ciently. These representation dependent results depend on the assumption that P #= NP . In order to obtain hardness results that are representation independent, Kearns and Valiant [22, 21] turned to cryptographic assumptions (namely, the di#culty of inverting RSA, the di#culty of recognizing quadratic residues modulo a Blum integer, and the di#culty of factoring Blum integers) Of course, they also need to explain how learning could be hard in a representation independent manner, ....

Michael Kearns. The Computational Complexity of Machine Learning. PhD thesis, Harvard University Center for Research in Computing Technology, May 1989. Technical Report TR-13-89. Also published by MIT Press as an ACM Distinguished Dissertation.

....1g m , including the concept false . If C is a bizarre class like ff j if a 37 2 R f , then f is a disjunction, else f is a conjunctiong, then C(m) is the class of all conjunctions and disjunctions over f0; 1g m . For most natural concept classes (sometimes called naming invariant classes (Kearns, 1989)) where the actual attribute names are not important to the definition of the class, the definition of C(m) is the same as if the set S used were fixed to fa 1 ; am g. Theorem 4 If for all m, C(m) is learnable in the standard mistake bound model with membership queries using at most Mm ....

Kearns, M. (1989). The Computational Complexity of Machine Learning. PhD thesis, Harvard University Center for Research in Computing Technology. Technical Report TR-13-89. Also published by MIT Press as an ACM Distinguished Dissertation.

....factor, this bound is optimal for a number of spaces H . 15 Conclusions There are many aspects of learning theory not discussed in this work. We have barely touched on the computational complexity of PAC learning and its variants. Further discussion of this may be found, for example, in [73, 20, 9, 83, 63, 64, 91, 58, 70]. There are also many more variants of the PAC model which we have not mentioned here. Throughout the discussion here, it has been assumed that there is some fixed hypothesis space. This is natural in the context of neural networks where one has in mind a fixed architecture. However, there is a ....

M. J. Kearns. The Computational Complexity of Machine Learning. ACM Distinguished Dissertation Series. The MIT Press, Cambridge, MA., 1989.

....Problem is the canonical uncomputable task (Turing 1936) Valiant (Valiant 1984) proposed a formal analysis of learning as the phenomenon of knowledge acquisition in the absence of explicit programming. The methodology was systematically organized into a consistent and rigorous framework by Kearns (Kearns 1990), which we follow. We consider two uncomputable problems and show that they are learnable within this formal model of learnability. While the problems are learnable, they are not polynomially learnable, even though we do derive polynomial time bounds on the learning algorithm. 1.1 ORGANIZATION ....

....Finally, section 5 states some important limitations on our results. Major limitations are an impoverished knowledge representation capability, and the fact that positive instances are a priori known to be classified relative to the Halting Problem (these correspond to severe restrictions on what Kearns (Kearns 1990) terms the hypothesis class and the target class, respectively) 1.2 BACKGROUND Let C (the target class) and H (the hypothesis class) be representation classes over X (the domain, or instance space) Then C is learnable from examples by H (Kearns 1990, p. 11) if there is an algorithm A with ....

[Article contains additional citation context not shown here]

Kearns, M. J. (1990). The Computational Complexity of Machine Learning, MIT Press, Cambridge, Massachusetts, USA.

....Problem is the canonical uncomputable task (Turing 1936) Valiant (Valiant 1984) proposed a formal analysis of learning as the phenomenon of knowledge acquisition in the absence of explicit programming. The methodology was systematically organized into a consistent and rigorous framework by Kearns (Kearns 1990), which we follow. We consider two uncomputable problems and show that they are learnable within this formal model of learnability. While the problems are learnable, they are not polynomially learnable, even though we do derive polynomial time bounds on the learning algorithm. 1.1 ORGANIZATION ....

....Finally, section 5 states some important limitations on our results. Major limitations are an impoverished knowledge representation capability, and the fact that positive instances are a priori known to be classified relative to the Halting Problem (these correspond to severe restrictions on what Kearns (Kearns 1990) terms the hypothesis class and the target class, respectively) 1.2 BACKGROUND Let C (the target class) and H (the hypothesis class) be representation classes over X (the domain, or instance space) Then C is learnable from examples by H (Kearns 1990, p. 11) if there is an algorithm A with ....

[Article contains additional citation context not shown here]

Kearns, M. J. (1990). The Computational Complexity of Machine Learning, MIT Press, Cambridge, Massachusetts, USA.

....such a variant of SC, in which instead of the entire ground set M , only p fraction of it is asked to be covered by subsets for some 0# p# 1. The greedy heuristic for SC can be easily adapted to this version, modifying only its stopping criteria. The partial SC was first studied by Kearns [18] in relation to learning, and the performance of the greedy heuristic was estimated to be at most 2H( M ) 3. Later Slavk showed that it is bounded by H(C9 max j#N j , #p M # ) 32] We shall see that the same bound follows from the Wolsey s theorem(oremTC 1) for a more general SSC and ....

M.J. Kearns, The Computational Complexity of Machine Learning, MIT Press, Cambridge, MA, 1990.

....or correct on all but some polynomiallybounded subset of their instances. Such a framework is described in [SchU86, Section 3] and [BDG90, Section 6] This framework is also applicable to optimal cost solution functions. Results from the growing literature on computational learning theory [Kea90, LV90a, MHJ89] and the computational complexity of local search heuristics [JPY88, Yan90] may also be applicable to the further analysis of phylogenetic inference problems. 75 ....

Kearns, M. J. The Computational Complexity of Machine Learning. MIT Press, Cambridge, MA, 1990.

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Michael Kearns. The Computational Complexity of Machine Learning. MIT Press, 1990.

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Michael Kearns. The Computational Complexity of Machine Learning. The MIT Press, 1990.

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Kearns, M.J. (1990). The Computational Complexity of Machine Learning. Cambridge, MA, London, MIT Press.

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M. Kearns, The Computational Complexity of Machine Learning. PhD thesis, Harvard University Center for Research in Computing Technology, Technical Report TR-13-89, 1989.

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Kearns, M. J. (1990). The computational complexity of machine learning. ACM Distinguished Dissertation. Massachusetts: MIT Press.

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Kearns, M. (1990). The Computational Complexity of Machine Learning. The MIT Press.

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Michael Kearns. The Computational Complexity of Machine Learning. PhD thesis, Harvard University Center for Research in Computing Technology, May 1989. Technical Report TR-13-89. Also published by MIT Press as an ACM Distinguished Dissertation.

No context found.

M. Kearns. The computational complexity of machine learning. The MIT Press, 1990.

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Kearns, M. (1990). The Computational Complexity of Machine Learning. The MIT Press.

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M. J. Kearns. The Computational Complexity of Machine Learning. ACM Distinguished Dissertation Series. The MIT Press, Cambridge, MA., 1989.

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M. J. Kearns. The Computational Complexity of Machine Learning. ACM Distinguished Dissertation Series. The MIT Press, Cambridge, MA., 1989.

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Kearns, Michael J. "The Computational Complexity of Machine Learning" An ACM Dist. Dissert. The MIT Press 1989.

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Michael J. Kearns. The Computational Complexity of Machine Learning. MIT Press, Cambridge, Massachusetts, 1990.

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Michael Kearns. The Computational Complexity of Machine Learning. MIT Press, 1990.

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