Yishay Mansour. An O(n log log n ) learning algorithm for DNF under the uniform distribution. In Fifth Annual Workshop on Computational Learning Theory, pages 53--61, 1992.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....another algorithm for solving the same parity nding problem solved by Levin, but they assumed that a quantity called the L 1 norm of the target function is polynomially bounded and is known. However, the L 1 norm is not polynomially bounded for the class of polynomial size DNF expressions [20]. In this section we describe an algorithm for learning DNF with respect to uniform that is (attribute) ecient in terms of its use of random bits (its randomness complexity) as well as its sample complexity. Randomization is used several times in the improved Levin s algorithm (given in Figure 3) ....

Yishay Mansour. An O(n log log n ) Learning Algorithm for DNF under the Uniform Distribution. In Proceedings of Fifth Annual Conference on Computational Learning Theory, pages 53-61, 1992.

.... This result was strengthened by Blum and Rudich [7] who gave a polynomial time algorithm for exact learning O(log n) term DNF using membership and equivalence queries; several other polynomial time algorithms for O(log n) term DNF have since been given in this model [3, 9, 10, 25] Mansour [27] gave a n O(log log n) time membership query algorithm which learns polynomial size DNF under the uniform distribution. In a celebrated result, Jackson [18] gave a polynomial time membership query algorithm for learning polynomial size DNF under constant bounded product distributions. His ....

....low Fourier coecients, then since there are n c Fourier coecients corresponding to subsets of c variables the algorithm requires roughly n c time steps. Linial et al. showed that for AC 0 circuits c is essentially poly(log n) this result was later sharpened for DNF formulae by Mansour [27]. Our algorithm extends this approach in the following way: Let C AC 0 be a class of Boolean functions which we would like to learn. Suppose that C has the following properties: 1. For every f 2 C there is a set S f of important variables such that almost all of the power spectrum of f is ....

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Y. Mansour. An O(n log log n ) learning algorithm for DNF under the uniform distribution, J. Comput. Syst. Sci. 50 (1995), 543-550.

....standard class of decision trees (and no results at all for the extended class they study) However, Bshouty [Bsh93] subsequently gave an efficient (non Fourier) algorithm for learning standard decision trees with membership queries over any distribution. On a different front, Mansour [Man92] combined the above lemma with Theorem 4.4 to get a tight bound on the number of significant Fourier coefficients in DNF expressions, resulting in an n O(log log n log 1 ) runtime when using the KM algorithm to learn DNF over the uniform distribution. Kushilevitz and Mansour also gave ....

....it must also be learnable without a task that seems significantly more formidable. Blum et al. BFJ 94] have also shown that DNF is not even weakly learnable, even with respect to uniform, in a certain noisy statistical query model that is closely related to the PAC model. Finally, in [Man92] Mansour constructed a family of DNF functions that cannot be approximated by any polynomial size set of its Fourier coefficients, suggesting that direct application of currently known Fourier methods is probably not enough to PAC learn DNF. On the other hand, many recent results have come ....

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Yishay Mansour. An O(n log log n) learning algorithm for DNF under the uniform distribution. In Fifth Annual Workshop on Computational Learning Theory, pages 53--61, 1992.

....respect to the uniform distribution using membership queries. In other words, Alice does have a winning (probabilistic) strategy for the original game above. This improves on two previous DNF learning algorithms in the same uniform withmembership model: Mansour s quasi polynomial time algorithm [43] and a polynomial time weak learner due to Blum et al. 10] Our algorithm for DNF learning is largely the combination of two powerful tools. One of these is a beautiful technique due to Goldreich and Levin [29] Given a black box that will answer membership queries for a Boolean function f over ....

.... the weak parity, or WP, algorithm (it has also been called the KM algorithm [10] Kushilevitz and Mansour showed that the WP algorithm could be used to learn parity decision trees with respect to the uniform distribution [37] and it has since been the basis of other learning algorithms as well [43, 10]. Actually, the WP algorithm is somewhat more general than we have described thus far. The basic WP algorithm finds, with probability at least 1 Gamma ffi, close approximations to all of the large magnitude Fourier coefficients of a Boolean function f on f0; 1g n . Since on this domain a ....

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Y. Mansour, An O(n log log n ) learning algorithm for DNF under the uniform distribution, in Fifth Annual Workshop on Computational Learning Theory, 1992, pp. 53--61.

.... this result was later strengthened by Blum et al. 3] to SAT k DNF for any constant k: Bellare [5] gave a polynomial time membership query algorithm for learning O(log n) term DNF under the uniform distribution (a somewhat more general result was given by Blum and Rudich [6] Mansour [23] gave a n O(log log n) time membership query algorithm which learns arbitrary polynomial size DNF under the uniform distribution. In a celebrated result, Jackson [15] gave a polynomial time membership query algorithm for learning polynomial size DNF under constant bounded product distributions. ....

....then since there are Gamma n c Delta Fourier coefficients corresponding to subsets of c variables the algorithm requires roughly n c time steps. Linial et al. showed that for AC 0 circuits c is essentially poly(log n) this result was later sharpened for DNF formulae by Mansour [23]. Our algorithm extends this approach in the following way: Let C ae AC 0 be a class of Boolean functions which we would like to learn. Suppose that C has the following properties: 1. For every f 2 C there is a set S f of important variables such that almost all of the power spectrum of f is ....

[Article contains additional citation context not shown here]

Y. Mansour. An O(n log log n ) learning algorithm for DNF under the uniform distribution, J. Comput. Syst. Sci. 50 (1995), 543-550.

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Yishay Mansour. An O(n log log n ) learning algorithm for DNF under the uniform distribution. In Fifth Annual Workshop on Computational Learning Theory, pages 53--61, 1992.

....does not rely on any unproven assumptions, and demonstrates that no straightforward modi cation of the existing algorithms for learning various restricted forms of DNF and decision trees will solve the general problem. All of our results rely heavily on the Fourier representation of functions [15, 13, 17], demonstrating once again the utility of these tools in computational learning theory. 1 2 De nitions and Notation 2.1 Learning Models A concept is a boolean function on an instance space X, and for convenience we de ne boolean functions to have outputs in f 1; 1g. A concept class F is a set ....

Yishay Mansour. An O(n log log n ) learning algorithm for DNF under the uniform distribution. In Fifth Annual Workshop on Computational Learning Theory, pages 53-61, 1992.

....The same statement also applies to several well studied algorithms proposed in the experimental machine learning community, including the ID3 algorithm for learning decision trees [22] and its variants. All of our results rely heavily on the Fourier representation of functions on the hypercube [18, 16, 20], demonstrating once again the utility of spectral analysis tools in computational learning theory. 2 Definitions and Notation 2.1 Learning on the Uniform Distribution Using Membership Queries A concept is a boolean function on an input space X (which in this paper will always be f0; 1g n ) ....

Yishay Mansour. An O(n log log n ) learning algorithm for DNF under the uniform distribution. In Fifth Annual Workshop on Computational Learning Theory, pages 53--61, 1992.

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Y. Mansour. An O(n log log n ) learning algorithm for DNF under the uniform distribution. Journal of Computer and System Sciences, 50(3), 1995.

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Y. Mansour. An O(n log log n ) learning algorithm for DNF under the uniform distribution. Journal of Computer and System Sciences, 50:543-550, 1995.

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Y. Mansour. An O(n log log n ) learning algorithm for DNF under the uniform distribution. Journal of Computer and System Sciences, 50:543--550, 1995.

No context found.

Y. Mansour. An O(n log log n ) learning algorithm for DNF under the uniform distribution. Journal of Computer and System Sciences, 50:543--550, 1995.

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Y. Mansour. An O(n log log n ) learning algorithm for DNF under the uniform distribution. Journal of Computing and Sys. Sci., 50:543--550, 1995.

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Y. Mansour. An O(n log log n ) Learning Algorithm for DNF under the Uniform Distribution. In Proceedings of Fifth Annual Conference on Computational Learning Theory, pages 53--61, 1992.

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