Above are papers related to the following paper: [Paper_ID] Paper #25805. 	[Title] Weakly Learning DNF and Characterizing Statistical Query Learning Using Fourier Analysis [Abstract] We present new results, both positive and negative, on the well-studied problem of learning disjunctive normal form (DNF) expressions. We first prove that an algorithm due to Kushilevitz and Mansour [16] can be used to weakly learn DNF using membership queries in polynomial time, with respect to the uniform distribution on the inputs. This is the first positive result for learning unrestricted DNF expressions in polynomial time in any nontrivial formal model of learning. It provides a sharp contrast with the results of Kharitonov [15], who proved that AC 0 is not efficiently learnable in the same model (given certain plausible cryptographic assumptions). We also present efficient learning algorithms in various models for the read-k and SAT-k subclasses of DNF. For our negative results, we turn our attention to the recently introduced statistical query model of learning [11]. This model is a restricted version of the popular Probably Approximately Correct (PAC) model [23], and practically every class known to be efficiently learnable in the PAC model is in fact learnable in the statistical query model [11]. Here we give a general characterization of the complexity of statistical query learning in terms of the number of uncorrelated functions in the concept class. This is a distribution-dependent quantity yielding upper and lower bounds on the number of statistical queries required for learning on any input distribution. As a corollary, we obtain that DNF expressions and decision trees are not even weakly learnable with fl This research is sponsored in part by the Wright Laboratory, Aeronautical Systems Center, Air Force Materiel Command, USAF, and the Advanced Research Projects Agency (ARPA) under grant number F33615-93-1-1330. Support also is sponsored by the National Science Foundation under Grant No. CC-9119319. Blum also supported in part by NSF National Young Investigator grant CCR-9357793. Views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing official policies or endorsements, either expressed or implied, of Wright Laboratory or the United States Government, or NSF. respect to the uniform input distribution in polynomial time in the statistical query model. This result is information-theoretic and therefore does not rely on any unproven assumptions. It demonstrates that no simple modification of the existing algorithms in the computational learning theory literature for learning various restricted forms of DNF and decision trees from passive random examples (and also several algorithms proposed in the experimental machine learning communities, such as the ID3 algorithm for decision trees [22] and its variants) will solve the general problem. The unifying tool for all of our results is the Fourier analysis of a finite class of boolean functions on the hypercube. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1118209. 	[Title] Teaching a Smarter Learner [Abstract] We introduce a formal model of teaching in which the teacher is tailored to a particular learner, yet the teaching protocol is designed so that no collusion is possible. Not surprisingly, such a model remedies the non-intuitive aspects of other models in which the teacher must successfully teach any consistent learner. We prove that any class that can be exactly identified by a deterministic polynomial-time algorithm with access to a very rich set of example-based queries is teachable by a computationally unbounded teacher and a polynomial-time learner. In addition, we present other general results relating this model of teaching to various previous results. We also consider the problem of designing teacher/learner pairs in which both the teacher and learner are polynomial-time algorithms and describe teacher/learner pairs for the classes of 1-decision lists and Horn sentences. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1121537. 	[Title] How Many Queries are Needed to Learn? [Abstract] We investigate the query complexity of exact learning in the membership and (proper) equivalence query model. We give a complete characterization of concept classes that are learnable with a polynomial number of polynomial sized queries in this model. We give applications of this characterization, including results on learning a natural subclass of DNF formulas, and on learning with membership queries alone. Query complexity has previously been used to prove lower bounds on the time complexity of exact learning. We show a new relationship between query complexity and time complexity in exact learning: If any "honest" class is exactly and properly learnable with polynomial query complexity, but not learnable in polynomial time, then P 6= NP. In particular, we show that an honest class is exactly polynomial-query learnable if and only if it is learnable using an oracle for p Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #45189. 	[Title] An Experimental and Theoretical Comparison of Model Selection Methods on simple model selection problems, the [Abstract] We investigate the problem of model selection in the setting of supervised learning of boolean functions from independent random examples. More precisely, we compare methods for finding a balance between the complexity of the hypothesis chosen and its observed error on a random training sample of limited size, when the goal is that of minimizing the resulting generalization error. We undertake a detailed comparison of three well-known model selection methods | a variation of Vapnik's Guaranteed Risk Minimization (GRM), an instance of Rissanen's Minimum Description Length Principle (MDL), and cross validation (CV). We introduce a general class of model selection methods (called penalty-based methods) that includes both GRM and MDL, and provide general methods for analyzing such rules. We provide both controlled experimental evidence and formal theorems to support the following conclusions: * The class of penalty-based methods is fundamentally handicapped in the sense that there exist two types of model selection problems for which every penalty-based method must incur large generalization error on at least one, while CV enjoys small generalization error Despite the inescapable incomparability of model selection methods under certain circumstances, we conclude with a discussion of our belief that the balance of the evidence provides specific reasons to prefer CV to other methods, unless one is in possession of detailed problem-specific information. on both. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1110028. 	[Title] Learning Using Group Representations (Extended Abstract) [Abstract] We consider the problem of learning functions over a fixed distribution. An algorithm by Kushilevitz and Mansour [7] learns any boolean function over f0; 1g n in time polynomial in the L 1 -norm of the Fourier transform of the function. We show that the KM-algorithm is a special case of a more general class of learning algorithms. This is achieved by extending their ideas using representations of finite groups. We introduce some new classes of functions which can be learned using this generalized KM algorithm. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12182. 	[Title] How to Use Expert Advice (Extended Abstract) [Abstract] We analyze algorithms that predict a binary value by combining the predictions of several prediction strategies, called experts. Our analysis is for worst-case situations, i.e., we make no assumptions about the way the sequence of bits to be predicted is generated. We measure the performance of the algorithm by the difference between the expected number of mistakes it makes on the bit sequence and the expected number of mistakes made by the best expert on this sequence, where the expectation is taken with respect to the randomization in the predictions. We show that the minimum achievable difference is on the order of the square root of the number of mistakes of the best expert, and we give efficient algorithms that achieve this. Our upper and lower bounds have matching leading constants in most cases. We give implications of this result on the performance of batch learning algorithms in a PAC setting which improve on the best results currently known in this context. We also extend our analysis to the case in which log loss is used instead of the expected number of mistakes. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #68505. 	[Title] On Learning Conjunctions with Malicious Noise [Abstract] We show how to learn monomials in the presence of malicious noise, when the underlined distribution is a product distribution. We show that our results apply not only to product distributions but to a wide class of distributions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #976284. 	[Title] Algorithmic Stability and Sanity-Check Bounds for Leave-One-Out Cross-Validation [Abstract] In this paper we prove sanity-check bounds for the error of the leave-one-out cross-validation estimate of the generalization error: that is, bounds showing that the worst-case error of this estimate is not much worse than that of the training error estimate. The name sanity-check refers to the fact that although we often expect the leave-one-out estimate to perform considerably better than the training error estimate, we are here only seeking assurance that its performance will not be considerably worse. Perhaps surprisingly, such assurance has been given only for rather limited cases in the prior literature on cross-validation. Any nontrivial bound on the error of leave-one-out must rely on some notion of algorithmic stability. Previous bounds relied on the rather strong notion of hypothesis stability, whose application was primarily limited to nearest-neighbor and other local algorithms. Here we introduce the new and weaker notion of error stability, and apply it to obtain sanity-check bounds for leave-one-out for other classes of learning algorithms, including training error minimization procedures and Bayesian algorithms. We also provide lower bounds demonstrating the necessity of error stability for proving bounds on the error of the leave-one-out estimate, and the fact that for training error minimization algorithms, in the worst case such bounds must still depend on the Vapnik-Chervonenkis dimension of the hypothesis class. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #164. 	[Title] Learning polynomials with queries: The highly noisy case  task for the case when F [Abstract] Given a function f mapping n-variate inputs from a finite field F into F , we consider the task of reconstructing a list of all n-variate degree d polynomials which agree with f on a tiny but non-negligible fraction, ffi, of the input space. We give a randomized algorithm for solving this task which accesses f as a black box and runs in time polynomial in 1 d=jF j). For the special case when d = 1, we solve this problem for all * def jF j &gt; 0. In this case the running time of our algorithm is bounded by a polynomial in 1 * ; n and exponential in d. Our algorithm generalizes a previously known algorithm, due to Goldreich and Levin, that solves this Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1121063. 	[Title] Implementation Issues in the Fourier Transform Algorithm [Abstract] The Fourier transform of boolean functions has come to play an important role in proving many important learnability results. We aim to demonstrate that the Fourier transform techniques are also a useful and practical algorithm in addition to being a powerful theoretical tool. We describe the more prominent changes we have introduced to the algorithm, ones that were crucial and without which the performance of the algorithm would severely deteriorate. One of the benefits we present is the confidence level for each prediction which measures the likelihood the prediction is correct. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12199. 	[Title] Learning k-term DNF Formulas with an Incomplete Membership Oracle [Abstract] We consider the problem of learning k-term DNF formulas using equivalence queries and incomplete membership queries as defined by Angluin and Slonim. We demonstrate that this model can be applied to non-monotone classes. Namely, we describe a polynomial-time algorithm that exactly identifies a k-term DNF formula with a k-term DNF hypothesis using incomplete membership queries and equivalence queries from the class of DNF formulas. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #9515. 	[Title] Tracking Drifting Concepts By Minimizing Disagreements [Abstract] In this paper we consider the problem of tracking a subset of a domain (called the target) which changes gradually over time. A single (unknown) probability distribution over the domain is used to generate random examples for the learning algorithm and measure the speed at which the target changes. Clearly, the more rapidly the target moves, the harder it is for the algorithm to maintain a good approximation of the target. Therefore we evaluate algorithms based on how much movement of the target can be tolerated between examples while predicting with accuracy *. Furthermore, the complexity of the class H of possible targets, as measured by d, its VC-dimension, also effects the difficulty of tracking the target concept. We show that if the problem of minimizing the number of disagreements with a sample from among concepts in a class H can be approximated to within a factor k, then there is a simple tracking algorithm for H which can achieve a probability * of making a mistake if the target movement rate is at most a constant times * 2 =(k(d + k) ln 1 * ), where d is the Vapnik-Chervonenkis dimension of H. Also, we show that if H is properly PAC-learnable, then there is an efficient (randomized) algorithm that with high probability approximately minimizes disagreements to within a factor of 7d + 1, yielding an efficient tracking algorithm for H which tolerates drift rates up to a constant times * 2 =(d 2 ln 1 In addition, we prove complementary results for the classes of halfspaces and axis-aligned hy- perrectangles showing that the maximum rate of drift that any algorithm (even with unlimited computational power) can tolerate is a constant times * 2 =d. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12210. 	[Title] Efficient Distribution-free Learning of Probabilistic Concepts [Abstract] In this paper we investigate a new formal model of machine learning in which the concept (boolean function) to be learned may exhibit uncertain or probabilistic behavior|thus, the same input may sometimes be classified as a positive example and sometimes as a negative example. Such probabilistic concepts (or p-concepts) may arise in situations such as weather prediction, where the measured variables and their accuracy are insufficient to determine the outcome with certainty. We adopt from the Valiant model of learning [27] the demands that learning algorithms be efficient and general in the sense that they perform well for a wide class of p-concepts and for any distribution over the domain. In addition to giving many efficient algorithms for learning natural classes of p-concepts, we study and develop in detail an underlying theory of learning p-concepts. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #124734. 	[Title] On Learning Visual Concepts and DNF Formulae [Abstract] We consider the problem of learning DNF formulae in the mistake-bound and the PAC models. We develop a new approach, which is called polynomial explainability, that is shown to be useful for learning some new subclasses of DNF (and CNF) formulae that were not known to be learnable before. Unlike previous learnability results for DNF (and CNF) formulae, these subclasses are not limited in the number of terms or in the number of variables per term; yet, they contain the subclasses of k-DNF and k-term-DNF (and the corresponding classes of CNF) as special cases. We apply our DNF results to the problem of learning visual concepts and obtain learning algorithms for several natural subclasses of visual concepts that appear to have no natural boolean counterpart. On the other hand, we show that learning some other natural subclasses of visual concepts is as hard as learning the class of all DNF formulae. We also consider the robustness of these results under various types of noise. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12350. 	[Title] Cryptographic Limitations on Learning Boolean Formulae and Finite Automata [Abstract] In this paper we prove the intractability of learning several classes of Boolean functions in the distribution-free model (also called the Probably Approximately Correct or PAC model) of learning from examples. These results are representation independent, in that they hold regardless of the syntactic form in which the learner chooses to represent its hypotheses. Our methods reduce the problems of cracking a number of well-known public-key cryptosys- tems to the learning problems. We prove that a polynomial-time learning algorithm for Boolean formulae, deterministic finite automata or constant-depth threshold circuits would have dramatic consequences for cryptography and number theory: in particular, such an algorithm could be used to break the RSA cryptosystem, factor Blum integers (composite numbers equivalent to 3 modulo 4), and detect quadratic residues. The results hold even if the learning algorithm is only required to obtain a slight advantage in prediction over random guessing. The techniques used demonstrate an interesting duality between learning and cryptography. We also apply our results to obtain strong intractability results for approximating a gener - alization of graph coloring. fl This research was conducted while the author was at Harvard University and supported by an A.T.& T. Bell Laboratories scholarship. y Supported by grants ONR-N00014-85-K-0445, NSF-DCR-8606366 and NSF-CCR-89-02500, DAAL03-86-K-0171, DARPA AFOSR 89-0506, and by SERC. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #157761. 	[Title] On the Complexity of Function Learning [Abstract] The majority of results in computational learning theory are concerned with concept learning, i.e. with the special case of function learning for classes of functions with range f0; 1g. Much less is known about the theory of learning functions with a larger range such as IN or IR. In particular relatively few results exist about the general structure of common models for function learning, and there are only very few nontrivial function classes for which positive learning results have been exhibited in any of these models. We introduce in this paper the notion of a binary branching adversary tree for function learning, which allows us to give a somewhat surprising equivalent characterization of the optimal learning cost for learning a class of real-valued functions (in terms of a max-min definition which does not involve any "learning" model). Another general structural result of this paper relates the cost for learning a union of function classes to the learning costs for the individual function classes. Furthermore, we exhibit an efficient learning algorithm for learning convex piecewise linear functions from IR d into IR. Previously, the class of linear functions from IR d into IR was the only class of functions with multi-dimensional domain that was known to be learnable within the rigorous framework of a formal model for on-line learning. Finally we give a sufficient condition for an arbitrary class F of functions from IR into IR that allows us to learn the class of all functions that can be written as the pointwise maximum of k functions from F . This allows us to exhibit a number of further nontrivial classes of functions from IR into IR for which there exist efficient learning algorithms. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #10177. 	[Title] Learning in the Presence of Malicious Errors [Abstract] In this paper we study an extension of the distribution-free model of learning introduced by Valiant [23] (also known as the probably approximately correct or PAC model) that allows the presence of malicious errors in the examples given to a learning algorithm. Such errors are generated by an adversary with unbounded computational power and access to the entire history of the learning algorithm's computation. Thus, we study a worst-case model of errors. Our results include general methods for bounding the rate of error tolerable by any learning algorithm, efficient algorithms tolerating nontrivial rates of malicious errors, and equivalences between problems of learning with errors and standard combinatorial optimization problems. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #4804. 	[Title] Toward Efficient Agnostic Learning [Abstract] In this paper we initiate an investigation of generalizations of the Probably Approximately Correct (PAC) learning model that attempt to significantly weaken the target function assumptions. The ultimate goal in this direction is informally termed agnostic learning, in which we make virtually no assumptions on the target function. The name derives from the fact that as designers of learning algorithms, we give up the belief that Nature (as represented by the target function) has a simple or succinct explanation. We give a number of positive and negative results that provide an initial outline of the possibilities for agnostic learning. Our results include hardness results for the most obvious generalization of the PAC model to an agnostic setting, an efficient and general agnostic learning method based on dynamic programming, relationships between loss functions for agnostic learning, and an algorithm for a learning problem that involves hidden variables. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1112574. 	[Title] Learning Switching Concepts [Abstract] We consider learning in situations where the function used to classify examples may switch back and forth between a small number of different concepts during the course of learning. We examine several models for such situations: oblivious models in which switches are made independent of the selection of examples, and more adversarial models in which a single adversary controls both the concept switches and example selection. We show relationships between the more benign models and the p-concepts of Kearns and Schapire, and present polynomial-time algorithms for learning switches between two k-DNF formulas. For the most adversarial model, we present a model of success patterned after the popular competitive analysis used in studying on-line algorithms. We describe a randomized query algorithm for such adversarial switches between two monotone disjunctions that is "1-competitive" in that the total number of mistakes plus queries is with high probability bounded by the number of switches plus some fixed polynomial in n (the number of variables). We also use notions described here to provide sufficient conditions under which learning a p-concept class "with a decision rule" implies being able to learn the class "with a model of probability." Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1108167. 	[Title] On Learning Read-k-Satisfy-j DNF [Abstract] We study the learnability of Read-k-Satisfy-j (RkSj) DNF formulas. These are boolean formulas in disjunctive normal form (DNF), in which the maximum number of occurrences of a variable is bounded by k, and the number of terms satisfied by any assignment is at most j. After motivating the investigation of this class of DNF formulas, we present an algorithm that with high probability finds a DNF formula that is logically equivalent to any unknown RkSj DNF formula to be learned. The algorithm uses the well-studied protocol of equivalence and membership queries, and runs in polynomial time for k j = O( log n log log n ), where n is the number of input variables. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #77515. 	[Title] Prediction, Learning, Uniform Convergence, and Scale-sensitive Dimensions [Abstract] We present a new general-purpose algorithm for learning classes of [0; 1]-valued functions in a generalization of the prediction model, and prove a general upper bound on the expected absolute error of this algorithm in terms of a scale-sensitive generalization of the Vapnik dimension proposed by Alon, Ben-David, Cesa-Bianchi and Haussler. We give lower bounds implying that our upper bounds cannot be improved by more than a constant factor in general. We apply this result, together with techniques due to Haussler and to Benedek and Itai, to obtain new upper bounds on packing numbers in terms of this scale-sensitive notion of dimension. Using a different technique, we obtain new bounds on packing numbers in terms of Kearns and Schapire's fat-shattering function. We show how to apply both packing bounds to obtain improved general bounds on the sample complexity of agnostic learning. For each * &gt; 0, we establish weaker sufficient and stronger necessary conditions for a class of [0; 1]-valued functions to be agnostically learnable to within *, and to be an *-uniform Glivenko-Cantelli class. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #166989. 	[Title] An O(n log log n Learning Algorithm for DNF under the Uniform Distribution [Abstract] We show that a DNF with terms of size at most d can be approximated by a function with at most d O(d log1=") non zero Fourier coefficients such that the expected error squared, with respect to the uniform distribution, is at most ". This property is used to derive a learning algorithm for DNF, under the uniform distribution. The learning algorithm uses queries and learns, with respect to the uniform distribution, a DNF with terms of size at most d in time polynomial in n and d O(d log 1=") . The interesting implications are for the case when " is constant. In this case our algorithm learns a DNF with a polynomial number of terms in time n O(log log n) , and a DNF with terms of size at most O(log n= log log n) in polynomial time. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1108175. 	[Title] Cognitive Computation (Extended Abstract) [Abstract] Cognitive computation is discussed as a discipline that links together neurobiology, cognitive psychology and artificial intelligence. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #989397. 	[Title] PAC Learning Intersections of Halfspaces with Membership Queries (Extended Abstract) [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #27606. 	[Title] Statistical Queries and Faulty PAC Oracles [Abstract] In this paper we study learning in the PAC model of Valiant [18] in which the example oracle used for learning may be faulty in one of two ways: either by misclassifying the example or by distorting the distribution of examples. We first consider models in which examples are misclassified. Kearns [12] recently showed that efficient learning in a new model using statistical queries is a sufficient condition for PAC learning with classification noise. We show that efficient learning with statistical queries is sufficient for learning in the PAC model with malicious error rate proportional to the required statistical query accuracy. One application of this result is a new lower bound for tolerable malicious error in learning monomials of k literals. This is the first such bound which is independent of the number of irrelevant attributes n. We also use the statistical query model to give sufficient conditions for using distribution specific algorithms on distributions outside their prescribed domains. A corollary of this result expands the class of distributions on which we can weakly learn monotone Boolean formulae. We also consider new models of learning in which examples are not chosen according to the distribution on which the learner will be tested. We examine three variations of distribution noise and give necessary and sufficient conditions for polynomial time learning with such noise. We show containments and separations between the various models of faulty oracles. Finally, we examine hypothesis boosting algorithms in the context of learning with distribution noise, and show that Schapire's result regarding the strength of weak learnabil-ity [17] is in some sense tight in requiring the weak learner to be nearly distribution free. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12247. 	[Title] Warning: missing six few referencesfixed in proceedings. Learning with Queries but Incomplete Information (Extended Abstract) [Abstract] We investigate learning with membership and equivalence queries assuming that the information provided to the learner is incomplete. By incomplete we mean that some of the membership queries may be answered by I don't know. This model is a worst-case version of the incomplete membership query model of Angluin and Slonim. It attempts to model practical learning situations, including an experiment of Lang and Baum that we describe, where the teacher may be unable to answer reliably some queries that are critical for the learning algorithm. We present algorithms to learn monotone k-term DNF with membership queries only, and to learn monotone DNF with membership and equivalence queries. Compared to the complete information case, the query complexity increases by an additive term linear in the number of I don't know answers received. We also observe that the blowup in the number of queries can in general be exponential for both our new model and the incomplete membership model. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #42207. 	[Title] Asking Questions to Minimize Errors [Abstract] A number of efficient learning algorithms achieve exact identification of an unknown function from some class using membership and equivalence queries. Using a standard transformation such algorithms can easily be converted to on-line learning algorithms that use membership queries. Under such a transformation the number of equivalence queries made by the query algorithm directly corresponds to the number of mistakes made by the on-line algorithm. In this paper we consider several of the natural classes known to be learnable in this setting, and investigate the minimum number of equivalence queries with accompanying counterexamples (or equivalently the minimum number of mistakes in the on-line model) that can be made by a learning algorithm that makes a polynomial number of membership queries and uses polynomial computation time. We are able both to reduce the number of equivalence queries used by the previous algorithms and often to prove matching lower bounds. As an example, consider the class of DNF formulas over n variables with at most k = O(log n) terms. Previously, the algorithm of Blum and Rudich [BR92] provided the best known upper bound of 2 O(k) log n for the minimum number of equivalence queries needed for exact identification. We greatly improve on this upper bound showing that exactly k counterexamples are needed if the learner knows k a priori and exactly k +1 counterexamples are needed if the learner does not know k a priori. This exactly matches known lower bounds [BC92]. For many of our results we obtain a complete characterization of the tradeoff between the number of membership and equivalence queries needed for exact identification. The classes we consider here are monotone DNF formulas, Horn sentences, O(log n)-term DNF formulas, read-k sat-j DNF formulas, read-once formulas over various bases, and deterministic finite automata. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #385251. 	[Title] A Quantum Computational Learning Algorithm [Abstract] An interesting classical result due to Jackson allows polynomial-time learning of the function class DNF using membership queries. Since in most practical learning situations access to a membership oracle is unrealistic, this paper explores the possibility that quantum computation might allow a learning algorithm for DNF that relies only on example queries. A natural extension of Fourier-based learning into the quantum domain is presented. The algorithm requires only an example oracle, and it runs in O( 2 n ) time, a result that appears to be classically impossible. The algorithm is unique among quantum algorithms in that it does not assume a priori knowledge of a function and does not operate on a superposition that includes all possible basis states. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #102884. 	[Title] Robust Trainability of Single Neurons [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #59626. 	[Title] General Bounds on Statistical Query Learning and PAC Learning with Noise via Hypothesis Boosting [Abstract] We derive general bounds on the complexity of learning in the Statistical Query model and in the PAC model with classification noise. We do so by considering the problem of boosting the accuracy of weak learning algorithms which fall within the Statistical Query model. This new model was introduced by Kearns [12] to provide a general framework for efficient PAC learning in the presence of classification noise. We first show a general scheme for boosting the accuracy of weak SQ learning algorithms, proving that weak SQ learning is equivalent to strong SQ learning. The boosting is efficient and is used to show our main result of the first general upper bounds on the complexity of strong SQ learning. Specifically, we derive simultaneous upper bounds with respect to * on the number of queries, O(log 2 1 * ), the Vapnik-Chervonenkis dimension of the query space, O(log 1 * ), and the inverse of the minimum tolerance, O( 1 * log 1 * ). In addition, we show that these general upper bounds are nearly optimal by describing a class of learning problems for which we simultaneously lower bound the number of queries by (log 1 * ) We further apply our boosting results in the SQ model to learning in the PAC model with classification noise. Since nearly all PAC learning algorithms can be cast in the SQ model, we can apply our boosting techniques to convert these PAC algorithms into highly efficient SQ algorithms. By simulating these efficient SQ algorithms in the PAC model with classification noise, we show that nearly all PAC algorithms can be converted into highly efficient PAC algorithms which tolerate classification noise. We give an upper bound on the sample complexity of these noise-tolerant PAC algorithms which is nearly optimal with respect to the noise rate. We also give upper bounds on space complexity and hypothesis size and show that these two measures are in fact independent of the noise rate. We note that the running times of these noise-tolerant PAC algorithms are efficient. This sequence of simulations also demonstrates that it is possible to boost the accuracy of nearly all PAC algorithms even in the presence of noise. This provides a partial answer to an open problem of Schapire [15] and the first theoretical evidence for an empirical result of Drucker, Schapire and Simard [4]. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6125. 	[Title] Boosting a weak learning algorithm by majority To be published in Information and Computation [Abstract] We present an algorithm for improving the accuracy of algorithms for learning binary concepts. The improvement is achieved by combining a large number of hypotheses, each of which is generated by training the given learning algorithm on a different set of examples. Our algorithm is based on ideas presented by Schapire in his paper "The strength of weak learnability", and represents an improvement over his results. The analysis of our algorithm provides general upper bounds on the resources required for learning in Valiant's polynomial PAC learning framework, which are the best general upper bounds known today. We show that the number of hypotheses that are combined by our algorithm is the smallest number possible. Other outcomes of our analysis are results regarding the representational power of threshold circuits, the relation between learnability and compression, and a method for parallelizing PAC learning algorithms. We provide extensions of our algorithms to cases in which the concepts are not binary and to the case where the accuracy of the learning algorithm depends on the distribution of the instances. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1153262. 	[Title] Rationality and Intelligence [Abstract] The long-term goal of our field is the creation and understanding of intelligence. Productive research in AI, both practical and theoretical, benefits from a notion of intelligence that is precise enough to allow the cumulative development of robust systems and general results. The concept of rational agency has long been considered a leading candidate to fulfill this role. This paper outlines a gradual evolution in the formal conception of rationality that brings it closer to our informal conception of intelligence and simultaneously reduces the gap between theory and practice. Some directions for future research are indicated. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1272. 	[Title] Learning a set of primitive actions with an Induction of decision trees. Machine Learning, 1(1):81-106, [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #20601. 	[Title] Learning Conjunctions of Horn Clauses [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #20602. 	[Title] Learning Read-Once Formulas with Queries [Abstract] A read-once formula is a boolean formula in which each variable occurs at most once. Such formulas are also called -formulas or boolean trees. This paper treats the problem of exactly identifying an unknown read-once formula using specific kinds of queries. The main results are a polynomial time algorithm for exact identification of monotone read-once formulas using only membership queries, and a polynomial time algorithm for exact identification of general read-once formulas using equivalence and membership queries (a protocol based on the notion of a minimally adequate teacher [1]). Our results improve on Valiant's previous results for read-once formulas [26]. We also show that no polynomial time algorithm using only membership queries or only equivalence queries can exactly identify all read-once formulas. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #95225. 	[Title] Learning Boolean Read-Once Formulas over Generalized Bases [Abstract] A read-once formula is one in which each variable appears on at most a single input. Angluin, Hellerstein, and Karpinski give a polynomial time algorithm that uses membership and equivalence queries to identify exactly read-once boolean formulas over the basis fAND; OR; NOTg [AHK93]. The goal of this work is to consider natural generalizations of these gates, in order to develop exact identification algorithms for more powerful classes of formulas. We show that read-once formulas over a basis of arbitrary boolean functions of constant fan-in k or less (i.e. any f : f0; 1g 1ck ! f0; 1g) are exactly identifiable in polynomial time using membership and equivalence queries. We show that read-once formulas over the basis of arbitrary symmetric boolean functions are also exactly identifiable in polynomial time in this model. Given standard cryptographic assumptions, there is no polynomial time identification algorithm for read-twice formulas over either of these bases using membership and equivalence queries. We further show that for any basis class B meeting certain technical conditions, any polynomial time identification algorithm for read-once formulas over B can be extended to a polynomial time identification algorithm for read-once formulas over the union of B and the arbitrary functions of fan-in k or less. As a result, read-once formulas over the union of arbitrary symmetric and arbitrary constant fan-in gates are also exactly identifiable in polynomial time using membership and equivalence queries. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12158. 	[Title] Randomly Fallible Teachers: Learning Monotone DNF with an Incomplete Membership Oracle [Abstract] We introduce a new fault-tolerant model of algorithmic learning using an equivalence oracle and an incomplete membership oracle, in which the answers to a random subset of the learner's membership queries may be missing. We demonstrate that, with high probability, it is still possible to learn monotone DNF formulas in polynomial time, provided that the fraction of missing answers is bounded by some constant less than one. Even when half the membership queries are expected to yield no information, our algorithm will exactly identify m-term, n-variable monotone DNF formulas with an expected O(mn 2 ) queries. The same task has been shown to require exponential time using equivalence queries alone. We extend the algorithm to handle some one-sided errors, and discuss several other possible error models. It is hoped that this work may lead to a better understanding of the power of membership queries and the effects of faulty teachers on query models of concept learning. Please summarise all the given information.

Paper #25805 has the title `Weakly Learning DNF and Characterizing Statistical Query Learning Using Fourier Analysis  
` and the abstract `We present new results, both positive and negative, on the well-studied problem of learning disjunctive normal form (DNF) expressions. We first prove that an algorithm due to Kushilevitz and Mansour [16] can be used to weakly learn DNF using membership queries in polynomial time, with respect to the uniform distribution on the inputs. This is the first positive result for learning unrestricted DNF expressions in polynomial time in any nontrivial formal model of learning. It provides a sharp contrast with the results of Kharitonov [15], who proved that AC 0 is not efficiently learnable in the same model (given certain plausible cryptographic assumptions). We also present efficient learning algorithms in various models for the read-k and SAT-k subclasses of DNF. For our negative results, we turn our attention to the recently introduced statistical query model of learning [11]. This model is a restricted version of the popular Probably Approximately Correct (PAC) model [23], and practically every class known to be efficiently learnable in the PAC model is in fact learnable in the statistical query model [11]. Here we give a general characterization of the complexity of statistical query learning in terms of the number of uncorrelated functions in the concept class. This is a distribution-dependent quantity yielding upper and lower bounds on the number of statistical queries required for learning on any input distribution. As a corollary, we obtain that DNF expressions and decision trees are not even weakly learnable with fl This research is sponsored in part by the Wright Laboratory, Aeronautical Systems Center, Air Force Materiel Command, USAF, and the Advanced Research Projects Agency (ARPA) under grant number F33615-93-1-1330. Support also is sponsored by the National Science Foundation under Grant No. CC-9119319. Blum also supported in part by NSF National Young Investigator grant CCR-9357793. Views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing official policies or endorsements, either expressed or implied, of Wright Laboratory or the United States Government, or NSF. respect to the uniform input distribution in polynomial time in the statistical query model. This result is information-theoretic and therefore does not rely on any unproven assumptions. It demonstrates that no simple modification of the existing algorithms in the computational learning theory literature for learning various restricted forms of DNF and decision trees from passive random examples (and also several algorithms proposed in the experimental machine learning communities, such as the ID3 algorithm for decision trees [22] and its variants) will solve the general problem. The unifying tool for all of our results is the Fourier analysis of a finite class of boolean functions on the hypercube. 
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Question: Which category should Paper #25805 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #25805 has the title `Weakly Learning DNF and Characterizing Statistical Query Learning Using Fourier Analysis  
` and the abstract `We present new results, both positive and negative, on the well-studied problem of learning disjunctive normal form (DNF) expressions. We first prove that an algorithm due to Kushilevitz and Mansour [16] can be used to weakly learn DNF using membership queries in polynomial time, with respect to the uniform distribution on the inputs. This is the first positive result for learning unrestricted DNF expressions in polynomial time in any nontrivial formal model of learning. It provides a sharp contrast with the results of Kharitonov [15], who proved that AC 0 is not efficiently learnable in the same model (given certain plausible cryptographic assumptions). We also present efficient learning algorithms in various models for the read-k and SAT-k subclasses of DNF. For our negative results, we turn our attention to the recently introduced statistical query model of learning [11]. This model is a restricted version of the popular Probably Approximately Correct (PAC) model [23], and practically every class known to be efficiently learnable in the PAC model is in fact learnable in the statistical query model [11]. Here we give a general characterization of the complexity of statistical query learning in terms of the number of uncorrelated functions in the concept class. This is a distribution-dependent quantity yielding upper and lower bounds on the number of statistical queries required for learning on any input distribution. As a corollary, we obtain that DNF expressions and decision trees are not even weakly learnable with fl This research is sponsored in part by the Wright Laboratory, Aeronautical Systems Center, Air Force Materiel Command, USAF, and the Advanced Research Projects Agency (ARPA) under grant number F33615-93-1-1330. Support also is sponsored by the National Science Foundation under Grant No. CC-9119319. Blum also supported in part by NSF National Young Investigator grant CCR-9357793. Views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing official policies or endorsements, either expressed or implied, of Wright Laboratory or the United States Government, or NSF. respect to the uniform input distribution in polynomial time in the statistical query model. This result is information-theoretic and therefore does not rely on any unproven assumptions. It demonstrates that no simple modification of the existing algorithms in the computational learning theory literature for learning various restricted forms of DNF and decision trees from passive random examples (and also several algorithms proposed in the experimental machine learning communities, such as the ID3 algorithm for decision trees [22] and its variants) will solve the general problem. The unifying tool for all of our results is the Fourier analysis of a finite class of boolean functions on the hypercube. 
`.
Question: Which category should Paper #25805 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Theory