A. Ehrenfeucht, D. Haussler, M. Kearns, and L. Valiant. A general lower bound on the number of examples needed for learning. Inf. and Comput, 82:246--261, 1989.  Home/Search Document Not in Database Summary Related Articles Check |
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Analysis of Data with Threshold Decision Lists - Martin Anthony December (Correct)
....functions. We say that a decision list defined on f0; 1g is a 1 decision list if the Boolean function in each test is given by a single literal. So, for each i, there is some l i such that either f i (y) 1 if and only if y l i = 1, or f i (y) 1 if and only if y l i = 0. Then, it is known [13] (see also [6, 2] that any 1 decision list is a threshold function. In an easy analogue of this, any threshold decision list is a threshold function of threshold functions [3] But a threshold function of threshold functions is nothing more than a two layer threshold network, one of the simplest ....
A. Ehrenfeucht, D. Haussler, M. Kearns, and L. Valiant. A general lower bound on the number of examples needed for learning. Information and Computation, 82, 1989: 247-- 261.
Sharpening Occam's Razor - Li, Tromp, Vitanyi (Correct)
....two versions. The VC dimension based version of Occam s razor theorem (Theorem 3.1. 1 of [3] gives the following upper bound on sample complexity: For a hypothesis space H with V Cdim(H) d, 1 d #, d log log ) 1) The following lower bound was proved by Ehrenfeucht et al. [6]. m(H, #, #) max( 32# ) 2) The upper bound in (1) and the lower bound in (2) di#er by a factor #(log ) It was shown in [8] that this factor is, in a sense, unavoidable. When H is finite, one can directly obtain the following bound on sample complexity for a consistent ....
A. Ehrenfeucht, D. Haussler, M. Kearns, L. Valiant. A general lower bound on the number of examples needed for learning. Inform. Computation, 82(1989), 247-261.
Decision Lists and Threshold Decision Lists - Martin Anthony December (Correct)
....[w, #] The vector w is known as the weight vector, and # is known as the threshold. We denote the class of threshold functions on by T n . Note that any t T n will satisfy t [w, #] for ranges of w and #. We have the following connection between 1 decision lists and threshold functions [7] (see also [3] Theorem 5.1 Any 1 decision list is a threshold function. Proof: We prove this by induction on the number of terms in the decision list. Since the identically one function 1 is regarded as a monomial of length 0, we may assume that decision lists output Suppose, for the base case ....
Andrzej Ehrenfeucht, David Haussler, Michael Kearns, and Leslie Valiant. A general lower bound on the number of examples needed for learning. Information and Computation, 82, 1989: 247--261.
Quantum versus Classical Learnability - Servedio, Gortler (2000) (1 citation) (Correct)
....which are informationtheoretically necessary and sucient to PAC learn C: For the lower bound, the following theorem is (a slight simpli cation of) a result due to Blumer et al. 7] Theorem 2.1.ii.b) a proof sketch is given in Appendix A. A stronger bound was later given by Ehrenfeucht et al. [16]. Theorem 13 Let C be any concept class and d = VC DIM(C) Then any (classical) PAC learning algorithm for C must have sample complexity d) 9 The following theorem is a quantum analogue of Theorem 13; the proof, which extends the techniques used in the proof of Theorem 10 using ideas from ....
A. Ehrenfeucht, D. Haussler, M. Kearns and L. Valiant. A general lower bound on the number of examples needed for learning, Inf. and Comput. 82 (1989), 246-261.
On The Sample Complexity Of Pac-Learning Using Random And Chosen .. - Eisenberg (1991) (19 citations) (Correct)
....concept class ; 1 e)ln(1 ) random examples are still required to pac learn , where e and are the usual pac learning parameters. Interestingly, this bound holds for any unknown probability distribution, unlike the standard proof (due to Ehrenfeucht, Haussler, Kearns, and Valiant [12]) which holds only for a particular distribution constructed by an adversary. Even if the unknown probability distribution is known to be smooth , at least (1 4e) ln(1 ) examples are required to pac learn from random examples (only) For the special case of learning haft spaces of an ....
.... ( lu( In(1 3) ln( l e) ln( ln(1 ) Thus, unless rn ln(L( In( n(1 fi) in other words, unless rn = f( 1 ( ln(1 ) Pr(do, c . which proves our theorem. 2. 2 Comparison of the Lower Bound to Previous Results We already know from Ehrenfeucht et al. [12] that for 1 2, an algorithm that can only draw random examples must see at least fi examples to pac learn, where VCdim( is the Vapnik Chervonenkis dimension of the class . Since our bound is within a constant factor of their lower bound (treating VCdim( as a constant as we let and go to ....
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Andrzej Ehrenfeucht, David Haussler, Michael Kearns, and Leslie Valiant. A gen- eral lower bound on the number of examples needed for learning. Information and Computation, 82(3):247-251, September 1989.
Noise Tolerant Algorithms for Learning and Searching - Aslam (1995) (3 citations) (Correct)
....constructing SQ algorithms which are nearly optimal with respect to these bounds. However, the robust PAC learning algorithms obtained by sim ulating even optimal SQ algorithms in the presence of noise are inefficient when compared to known lower bounds for PAC learning in the presence of noise [11, 20, 30]. In fact, the PAC learning algorithms obtained by simulating optimal SQ algorithms in the absence of noise are inefficient when compared to the tight bounds known for noise free PAC learning [7, 11] These shortcomings could be consequences of either inefficient simulations or a deficiency in the ....
.... are inefficient when compared to known lower bounds for PAC learning in the presence of noise [11, 20, 30] In fact, the PAC learning algorithms obtained by simulating optimal SQ algorithms in the absence of noise are inefficient when compared to the tight bounds known for noise free PAC learning [7, 11]. These shortcomings could be consequences of either inefficient simulations or a deficiency in the model itself. In this thesis, we show that both of these explanations are true, and we provide both new simulations and a variant of the SQ model which combat the current inefficiencies of PAC ....
[Article contains additional citation context not shown here]
Andrzej Ehrenfeucht, David Haussler, Michael Kearns, and Leslie Valiant. A general lower bound on the number of examples needed for learning. Information and Computation, 82(3):247-251, September 1989.
On the Fourier Spectrum of Monotone Functions - Bshouty, Tamon (1996) (16 citations) (Correct)
....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 = g. The Vapnik Chernovenkis dimension of C, V Cdim(C) is the cardinality of the largest subset A which is shattered by C. Ehrenfeucht et al. [EHKV88] proved a sample complexity lower bound of V Cdim(C) for PAC learning any class C with error ffl and confidence ffi . It is easy to see that the VC dimension of monotone functions is at least n. Hence we get the following easy corollary. Corollary 2 Any PAC learning algorithm for ....
Andrzej Ehrenfeucht, David Haussler, Michael Kearns, and Leslie Valiant. A General Lower Bound on the Number of Examples Needed for Learning. In Proceedings of the 1988 Workshop on Computational Learning Theory, pages 139--154, 1988.
Noise Tolerant Algortihms for Learning and Searching - Aslam (1995) (Correct)
....for constructing SQ algorithms which are nearly optimal with respect to these bounds. However, the robust PAC learning algorithms obtained by simulating even optimal SQ algorithms in the presence of noise are inefficient when compared to known lower bounds for PAC learning in the presence of noise [11, 20, 30]. In fact, the PAC learning algorithms obtained by simulating optimal SQ algorithms in the absence of noise are inefficient when compared to the tight bounds known for noise free PAC learning [7, 11] These shortcomings could be consequences of either inefficient simulations or a deficiency in the ....
.... are inefficient when compared to known lower bounds for PAC learning in the presence of noise [11, 20, 30] In fact, the PAC learning algorithms obtained by simulating optimal SQ algorithms in the absence of noise are inefficient when compared to the tight bounds known for noise free PAC learning [7, 11]. These shortcomings could be consequences of either inefficient simulations or a deficiency in the model itself. In this thesis, we show that both of these explanations are true, and we provide both new simulations and a variant of the SQ model which combat the current inefficiencies of PAC ....
[Article contains additional citation context not shown here]
Andrzej Ehrenfeucht, David Haussler, Michael Kearns, and Leslie Valiant. A general lower bound on the number of examples needed for learning. Information and Computation, 82(3):247--251, September 1989.
Learning in the Presence of Malicious Errors - Michael Kearns Att (1993) (81 citations) Self-citation (Kearns) (Correct)
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A. Ehrenfeucht, D. Haussler, M. Kearns. L.G. Valiant. A general lower bound on the number of examples needed for learning. Information and Computation, 82(3), 1989, pp. 247-261.
Efficient Noise-Tolerant Learning From Statistical Queries - Kearns (1998) (100 citations) Self-citation (Kearns) (Correct)
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A. Ehrenfeucht, D. Haussler, M. Kearns, and L. Valiant. A general lower bound on the number of examples needed for learning. In First Workshop on Computatinal Learning Theory, pages 139--154, Cambridge, Mass. August 1988. Morgan Kaufmann.
An Augmented PAC Model for SemiSupervised Learning - Balcan, Blum (2005) (Correct)
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A. Ehrenfeucht, D. Haussler, M. Kearns, and L. Valiant. A general lower bound on the number of examples needed for learning. Inf. and Comput, 82:246--261, 1989.
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A. Ehrenfeucht, D. Haussler, M. Kearns, and L. Valiant. A general lower bound on the number of examples needed for learning. Inf. and Comput, 82:246--261, 1989.
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Ehrenfeucht, A., Haussler, D., Kearns, M., & Valiant, L. (1988). A general lower bound on the number of examples needed for learning. Proceedings of the 1988 Workshop on Computational Learning Theory (pp. 110-120). San Mateo, CA: Morgan Kaufmann.
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A Ehrenfeucht, D Haussler, M Kearns, and L Valiant. A general lower bound on the number of examples needed for learning. Information and Computation, 82:247--261, 1989.
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A. Ehrenfeucht, D. Haussler, M. Kearns and L. Valiant, A General Lower Bound on the Number of Examples Needed for Learning, Information and Computation 82(3) (1989) 247-261
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A. Ehrenfeucht, D. Haussler, M. Kearns, and L. Valiant. A general lower bound on the number of examples needed for learning. Information and Computation, 82(3):247--251, September 1989.
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Andrzej Ehrenfeucht, David Haussler, Michael J. Kearns, and Leslie G. Valiant. A General Lower Bound on the Number of Examples Needed for Learning. Information and Computation 82(3), 247--261, 1989.
Cost-Sensitive Learning by Cost-Proportionate Example.. - Zadrozny, Langford, Abe (2003) (2 citations) (Correct)
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Ehrenfeucht, A., Haussler, D., Kearns, M. & Valiant. A general lower bound on the number of examples needed for learning. Information and Computation, 82:3, 247-261, 1989.
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A. Ehrenfeucht, D. Haussler, M. Kearns, and L. G. Valiant. A general lower bound on the number of examples needed for learning. Information and Computation, 82(3):247{ 251, 1989.
A PAC-style Model for Learning from Labeled and Unlabeled Data - Balcan, Blum (2004) (1 citation) (Correct)
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A. Ehrenfeucht, D. Haussler, M. Kearns, and L. Valiant. A general lower bound on the number of examples needed for learning. Inf. and Comput, 82:246--261, 1989.
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A. Ehrenfeucht, D. Haussler, M. Kearns, and L. Valiant. A general lower bound on the number of examples needed for learning. Information and Computation, 82, 1989: 247-- 261.
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Andrzej Ehrenfeucht, David Haussler, Michael Kearns, and Leslie Valiant. A general lower bound on the number of examples needed for learning. Information and Computation, 82: 247--261, 1989.
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A. Ehrenfeucht, D. Haussler, M. Kearns, and L. Valiant. A general lower bound on the number of examples needed for learning. Information and Computation, 82, 1989: 247-- 261.
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Andrzej Ehrenfeucht, David Haussler, Michael Kearns, and Leslie Valiant. A general lower bound on the number of examples needed for learning. Information and Computation, 82: 247--261, 1989.
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Ehrenfeucht, A., Haussler, D., Kearns, M. & Valiant, L. (1989). A general lower bound on the number of examples needed for learning. Information and Computation, 82:3, 247-261.
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