N. Bshouty, R. Cleve, S. Kannan, and C. Tamon. Oracles and Queries that are Sufficient for Exact Learning. Proceedings of the Seventh Annual ACM Conference on Computational Learning Theory, pages 130--139, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....DNF with restricted reads . The polynomial time learnability of general DNF formulas has been a central question in computational learning theory since it was posed by Valiant in 1984 [59] DNF formulas have recently been shown to be learnable in models such as the superset and subset query model [20], and the PAC model with membership queries under the uniform distribution [39] However, it remains an open question to determine whether DNF formulas are learnable in polynomial time in two of the most widely studied and natural models: the PAC model, and the model of membership and equivalence ....

N. Bshouty, R. Cleve, S. Kannan, and C. Tamon, Oracles and queries that are sufficient for exact learning. In Proceedings of the Seventh Annual ACM Conference on Computational Learning Theory, pages 130--137, ACM Press, New York, July 1994.

....exactly learnable in the UAV model using only the UAV MQ oracle. Furthermore, it is known [5] that a polynomial number of calls to the MQ oracle is not sufficient. This demonstrates (as one would expect) that the UAV MQ oracle is more powerful than the MQ oracle. Bshouty, Cleve, Kannan and Tamon [17] show that DNF formulas can be learned by a randomized algorithm in expected polynomial time with equivalence queries and the aid of an NP oracle. Using this result, they also show that DNF formulas can be learned using subset and superset queries. The hypothesis class of their algorithms is the ....

N. H. Bshouty, R. Cleve, S. Kannan, and C. Tamon. Oracles and queries that are sufficient for exact learning. J. of Comput. Syst. Sci., 52(3):421-- 433, 1996. 23

....satisfies some particular property such as ever taking a nonzero value, but rather to precisely identify an unknown black box function from some restricted class of possible functions. The classical version of this problem has been well studied in the computational learning theory literature [2, 12, 22, 24, 25] and is known as the problem of exact learning from membership queries. The question stated above can thus be rephrased as follows: what is the relationship between the number of quantum versus classical membership queries which are required for exact learning We answer this question in this ....

....learning models considered in this paper there is a concept class which is polynomial time learnable in the quantum version but not in the classical version of the model. 1.3. Previous Work Our results draw on lower bound techniques from both quantum computation and computational learning theory [2, 5, 6, 8, 12, 24]. A detailed description of the relationship between our results and previous work on quantum versus classical black box query complexity is given in Section 3.4. In [19] Farhi et al. prove a lower bound on the number of functions which can be distinguished with k quantum queries. Ronald de Wolf ....

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N. Bshouty, R. Cleve, R. Gavalda, S. Kannan and C. Tamon. Oracles and queries that are sufficient for exact learning, J. Comput. Syst. Sci. 52(3) (1996), 421-433.

....the function g: If M is a probabilistic polynomial time (henceforth abbreviated p.p.t. algorithm which has access to an oracle g : f0; 1g 1 f0; 1g 2 ; then the running time of M g is bounded by p( 1 2 ) for some polynomial p: In the model of exact learning from membership queries [1, 9, 14, 18, 19], the learning algorithm is given access to an oracle for an unknown target concept c 2 Cn : When invoked on input x 2 f0; 1g n ; the oracle returns c(x) such an oracle call is known as a membership query) The goal of the learning algorithm is to construct a hypothesis h : f0; 1g n f0; 1g ....

N. Bshouty, R. Cleve, R. Gavalda, S. Kannan and C. Tamon. Oracles and queries that are sufficient for exact learning, J. Comput. Syst. Sci. 52(3) (1996), 421-433.

....class. Notice that this class contains the class of log n depth decision trees, shown to be exactly learnable in polynomial time [KM93] with membership queries. The output of the learning algorithm is not a log n depth decision tree but a representation based on Fourier coefficients. In [BCKT94], it was shown that log n DNF log n CNF is learnable with membership queries and an NP oracle, in a representation of depth 3 boolean formulas. Finally, in [HPRW95] it was shown that this class is properly learnable with membership queries and an oracle for NP coNP. It is open whether this ....

N. Bshouty, R. Cleve, S. Kannan, and C. Tamon. Oracles and Queries that are Sufficient for Exact Learning. Proceedings of the Seventh Annual ACM Conference on Computational Learning Theory, pages 130-- 139, 1994.

.... Sigma classes, we obtain results that improve trivial containments by n levels. Recently classes ZPP NP and AM co AM received much attention. Arvind and Kobler [AK97] and Goldreich and Zuckerman [GZ97] proved that MA is contained in ZPP NP . Kobler and Watanabe [KW95] and Bshouty et al. [BCGKT95] proved that the polynomialtime hierarchy is in ZPP NP , if NP has polynomial size circuits. More recently Arvind and Kobler [AK00] proved that AM co AM is low for ZPP NP , i.e. ZPP NP AM co AM ZPP NP . We note that this containment is a significant improvement over the naive bound. ....

N. Bshouty, R. Cleve, S. Kannan and C. Tamon, Oracles and Queries that are sufficient for Exact Learning, Proceedings of the 17th Annual ACM conference on Computational Learning Theory, 130--19 (1994).

....time polynomial in the size of the read k DNF) The result also holds for CNF. Furthermore, it is known that any algorithm that learns the class of monotone functions with membership queries must pose Omega Gammae 3 fjcnf(f)j; jdnf(f)jg) queries (where f is the monotone function to be compiled) [27, 8]. The result also applies to the class of monotone functions representable as read k CNF formulas when k 2. Finally, we note that while there is currently no known time efficient algorithm for learning the class of monotone functions with membership queries, the informationtheoretic complexity ....

N. Bshouty, R. Cleve, R. Gavald`a, S. Kannan, and C. Tamon. Oracles and queries that are sufficient for exact learning. Journal of Computer and System Sciences, 52(3):421--433, 1996.

....complexity theory research. e.g. consider the result MA ZPP NP [1, 12] which sharpens and improves Sipser s theorem BPP Sigma p 2 . The proof in [1] uses derandomization techniques based on hardness assumptions [21] Another example is the result that if SAT 2 P poly then PH = ZPP NP . [19, 4], which improves the classic Karp Lipton theorem 1 Actually [19] prove that every self reducible set 2 A in (NP co NP) poly is low for ZPP NP , i.e. ZPP NP A = ZPP NP . This stronger result is in a sense natural, since there is usually an underlying lowness result that implies a ....

....containment IP[P poly] Low( Sigma p 2 ) shown in [2] Our proof has a derandomization component in which the Nisan Wigderson pseudorandom generator [21] is used to derandomize the verifier in the IP[P poly] protocol. The rest of the proof is based on the random sampling technique as applied in [4, 16]. 1.2 NP=poly co NP=poly and subclasses As shown in [19] lowness proofs that work for P poly carry over easily to (NP co NP) poly. However there are technical hurdles in handling NP=poly co NP=poly: e.g. the best known collapse consequence of NP NP=poly co NP=poly is PH ZPP( Sigma ....

[Article contains additional citation context not shown here]

N. Bshouty, R. Cleve, R. Gavald` a, S. Kannan, and C. Tamon, Oracles and queries that are sufficient for exact learning, Journal of Computer and System Sciences, 52, pp. 421-- 433 1996.

....satisfies some particular property (such as ever taking a nonzero value) but rather to precisely identify a black box function which belongs to some restricted class of possible functions. The classical version of this problem has been well studied in the computational learning theory literature [1, 11, 19, 21, 22], and is known as the problem of exact learning from membership queries. The question stated above can thus be phrased as follows: what is the relationship between the number of quantum versus classical membership queries which are required for exact learning We answer this question in this ....

....paper, the model of exact learning from membership queries and the PAC model, make this rough notion precise in different ways. 2. 1 Classical Exact Learning from Membership Queries The model of exact learning from membership queries was introduced by Angluin [1] and has since been widely studied [1, 11, 19, 21, 22]. In this model the learning algorithm has access to a membership oracle MQ c where c 2 C n is the unknown target concept. When given an input string x 2 f0; 1g n ; in one time step the oracle MQ c returns the bit c(x) such an invocation is known as a membership query since the oracle s answer ....

[Article contains additional citation context not shown here]

N. Bshouty, R. Cleve, R. Gavald`a, S. Kannan and C. Tamon. Oracles and queries that are sufficient for exact learning, J. Comput. Syst. Sci. 52(3) (1996), 421-433.

....class because it is rich in its representational power and because it is simple and natural. While many subclasses of DNF have been shown to be learnable not much progress has been made for the general case. Two recent results illustrate the state of the art in DNF learning. Bshouty et.al. [7] gave a randomized algorithm, using restricted subset and superset queries, to learn DNF. In the PAC model, Jackson [17] has given an algorithm using membership queries to learn DNF against the uniform distribution. We demonstrate the power of our approach by giving a deterministic teacher learner ....

.... yes . Superset queries are symmetric. Thus, even if the learner is randomized, a T I L pair can simulate either subset of superset queries using equivalence queries. Some interesting results follow from the above theorems. The first of these uses a result of Bshouty, Cleve, Kannan and Tamon [7] in which they show that DNF formulas and polynomial size circuits are learnable by a randomized learner using only subset and superset queries. They do this by showing that equivalence queries and and NP oracle can be simulated 14 H. D. MATHIAS using subset and superset queries. They show that ....

Nader H. Bshouty, Richard Cleve, Sampath Kannan, and Christino Tamon. Oracles and queries that are sufficient for exact learning. In Proceedings of the Seventh Annual ACM Conference on Computational Learning Theory, pages 130--139, July 1994. A MODEL OF INTERACTIVE TEACHING 27

....class. Notice that this class contains the class of log n depth decision trees, shown to be exactly learnable in polynomial time [KM93] with membership queries. The output of the learning algorithm is not a log n depth decision tree but a representation based on Fourier coefficients. In [BCKT94], it was shown that log n DNF log n CNF is learnable with membership queries and an NP oracle, in a representation of depth 3 boolean formulas. Finally, in [HPRW95] it was shown that this class is properly learnable with membership queries and an oracle for NP co NP. It is open whether this ....

N. Bshouty, R. Cleve, S. Kannan, and C. Tamon. Oracles and Queries that are Sufficient for Exact Learning. Proceedings of the Seventh Annual ACM Conference on Computational Learning Theory, pages 130--139, 1994.

....natural Sigma p 2 op1 timization problems, although in [25] deciding the V C dimension is shown to be Sigma p 3 complete, and some limited (additive) inapproximability results are given. Some positive approximability results for the circuit minimization problem are implied by results in [13, 4]. Dispersers, first defined by Sipser [26] and their twosided analogues, extractors, have been the focus of much research in recent years (see the survey in [16] and have found applications in a wide range of areas, including simulating randomized algorithms with weak random sources [37, 27] ....

N. H. Bshouty, R. Cleve, R. Gavalda, S. Kannan, and C. Tamon. Oracles and queries that are sufficient for exact learning. Journal of Computer and System Sciences, 52(3):421-- 433, June 1996.

....A that is bounded truth table reducible to a sparse set is located in Low Sigma 0 = P. 6 Furthermore, it has been shown in [KS85] that all self reducible sets A in P=poly are Sigma P 2 low, i.e. Sigma P 2 (A) Sigma P 2 . Inspired by the work of Bshouty, Cleve, Kannan, and Tamon [BCKT94] the lowness of all selfreducible sets in P=poly has recently been improved from Sigma P 2 low to ZPP(NP) low [KW95] As shown in [BCKT94] by using a result of Jerrum, Valiant, and Vazirani [JVV86] the class of all circuits is exactly learnable in (randomized) expected polynomial time with ....

....self reducible sets A in P=poly are Sigma P 2 low, i.e. Sigma P 2 (A) Sigma P 2 . Inspired by the work of Bshouty, Cleve, Kannan, and Tamon [BCKT94] the lowness of all selfreducible sets in P=poly has recently been improved from Sigma P 2 low to ZPP(NP) low [KW95] As shown in [BCKT94] by using a result of Jerrum, Valiant, and Vazirani [JVV86] the class of all circuits is exactly learnable in (randomized) expected polynomial time with equivalence queries and the aid of an NP oracle. From this result it immediately follows that every set A in P=poly has an advice function that ....

[Article contains additional citation context not shown here]

N. Bshouty, R. Cleve, S. Kannan, and C. Tamon, Oracles and queries that are sufficient for exact learning, Proc. 7th COLT (1994) 130--139.

....for a normal form is the smallest equivalent Boolean formula (under some suitable total ordering) However, computing this seems to require a Sigma p 2 oracle, and our Verifier only has an NP oracle available. To overcome this difficulty, we use a result from learning theory by Bshouty et.al. [BCGKT95]. Lemma 3.1 [BCGKT95] There is a probabilistic polynomial time algorithm having access to an NP oracle that learns a Boolean formula using equivalence queries. 1 The scenario is roughly as follows. There is a Boolean formula F given in a black box . A probabilistic polynomial time machine, the ....

....the smallest equivalent Boolean formula (under some suitable total ordering) However, computing this seems to require a Sigma p 2 oracle, and our Verifier only has an NP oracle available. To overcome this difficulty, we use a result from learning theory by Bshouty et.al. BCGKT95] Lemma 3. 1 [BCGKT95] There is a probabilistic polynomial time algorithm having access to an NP oracle that learns a Boolean formula using equivalence queries. 1 The scenario is roughly as follows. There is a Boolean formula F given in a black box . A probabilistic polynomial time machine, the learner , which cannot ....

[Article contains additional citation context not shown here]

N. Bshouty, R. Cleve, R. Gavald`a, S. Kannan, C. Tamon. Oracles and queries that are sufficient for exact learning. ECCC TR95-015, 1995. Available via: http://www.eccc.uni-trier.de/eccc/

....polynomial time. We show that this does not hold in the randomized membership query model. In the mistakebound model, we consider the problem of learning attribute efficiently using hypotheses that are formulas of small depth. Our results extend the work of Blum et al. 4] and Bshouty et al. [7]. 1 Introduction Consider the problem of learning an unknown Boolean function on n variables where n is large. Suppose that the output of this function is completely determined by the values of a fixed set of r of the n variables, where r is small. Thus our real task is to learn a function of r ....

....size Boolean formulas of depth 2 are not sufficient for attributeefficient learning of this class. Littlestone s WINNOW algorithm learns this class log n attributeefficiently with hypotheses that are threshold functions [15] Our techniques extend the results of Bshouty, Cleve, Kannan, and Tamon [7] on equivalence query learning with simple hypotheses. 2 Definitions We use log to denote the logarithm base 2, and ln to denote the natural logarithm. Let V n = fx 1 ; x 2 ; x n g. Let a 2 f0; 1g be an assignment to the variables in V n . We consider a to be a function from V n to ....

[Article contains additional citation context not shown here]

N. H. Bshouty, R. Cleve, S. Kannan, and C. Tamon. Oracles and queries that are sufficient for exact learning. In Proc. 7th Annu. ACM Workshop on Comput. Learning Theory, pages 130--139. ACM Press, New York, NY, 1994. 30

....time PAC learning algorithm for DNF under any distribution. This research was supported in part by the NSERC of Canada. 1 Introduction One of the outstanding open problems in computational learning theory is whether polynomial size DNF formulas are learnable in polynomial time. In [BCKT94] Bshouty et al. showed that by using an NP oracle, DNF is exactly learnable from equivalence queries. So, if P=NP, exact learning of DNF from equivalence queries is possible. This raises the question of whether learning DNF in polynomial time implies P=NP, or whether learning DNF in time t implies ....

N. H. Bshouty and R. Cleve and S. Kannan and C. Tamon. Oracles and Queries that are Sufficient for Exact Learning. Proc. 7th Annu. ACM Workshop on Comput. Learning Theory. 1994, 130--139. 5

....polynomial time. We show that this does not hold in the randomized membership query model. In the mistake bound model, we consider the problem of learning attribute efficiently using hypotheses that are formulas of small depth. Our results extend the work of Blum et al. 3] and Bshouty et al. [5]. 1 Introduction Consider the problem of learning an unknown Boolean function on n variables where n is large. Suppose that the output of this function is completely determined by the values of a fixed set of r of the n variables, where r is small. Thus our real task is to learn a function of r ....

....size Boolean formulas of depth 2 are not sufficient for attributeefficient learning of this class. Littlestone s WINNOW algorithm learns this class log n attributeefficiently with hypotheses that are threshold functions [10] Our techniques extend the results of Bshouty, Cleve, Kannan, and Tamon [5] on equivalence query learning with simple hypotheses. 2 Definitions All logarithms given in this paper are base 2. Let V n = fx 1 ; x 2 ; x n g. Let a 2 f0; 1g be an assignment to the variables in V n . We consider a to be a function from V n to f0; 1g. If x i 2 V n , and z 2 f0; ....

[Article contains additional citation context not shown here]

N. H. Bshouty, R. Cleve, S. Kannan, and C. Tamon. Oracles and queries that are sufficient for exact learning. In Proc. 7th Annu. ACM Workshop on Comput. Learning Theory, pages 130--139. ACM Press, New York, NY, 1994.

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N. Bshouty, R. Cleve, S. Kannan, and C. Tamon. Oracles and Queries that are Sufficient for Exact Learning. Proceedings of the Seventh Annual ACM Conference on Computational Learning Theory, pages 130--139, 1994.

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N. H. Bshouty, R. Cleve, S. Kannan, and C. Tamon. Oracles and queries that are sufficient for exact learning. In Proc. 7th Annu. ACM Conf. on Comput. Learning Theory, pages 130--139. ACM Press, New York, NY, 1994.

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N.H. Bshouty, R. Cleve, R. Gavald`a, S. Kannan, and C. Tamon. Oracles and queries that are sufficient for exact learning. Journal of Computer and System Sciences, 52:421-- 433, 1996.

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Bshouty, Cleve, Gavalda, Kannan, and Tamon. Oracles and queries that are sufficient for exact learning. JCSS: Journal of Computer and System Sciences, 52:421--433, 1996.

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N. Bshouty, R. Cleve, R. Gavald`a, S. Kannan, and C. Tamon. Oracles and queries that are sufficient for exact learning. Journal of Computer and System Sciences, 52:421--433, 1996.

No context found.

N. Bshouty, R. Cleve, R. Gavald`a, S. Kannan, and C. Tamon. Oracles and queries that are sufficient for exact learning. Journal of Computer and System Sciences, 52(3):421-- 433, 1996.

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N. Bshouty, R. Cleve, R. Gavald a, S. Kannan, and C. Tamon. Oracles and queries that are sufficient for exact learning. Journal of Computer and System Sciences, 52(3):421--433, June 1996.

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N.H. Bshouty, R. Cleve, R. Gavald`a, S. Kannan, and C. Tamon. Oracles and Queries that are Sufficient for Exact Learning. Electronic Colloquium on Complexity. Technical Report TR95-015, 1995.

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