Above are papers related to the following paper: [Paper_ID] Paper #111866. 	[Title] On Learning from Noisy and Incomplete Examples [Abstract] We investigate learnability in the PAC model when the data used for learning, attributes and labels, is either corrupted or incomplete. In order to prove our main results, we define a new complexity measure on statistical query (SQ) learning algorithms. The view of an SQ algorithm is the maximum over all queries in the algorithm, of the number of input bits on which the query depends. We show that a restricted view SQ algorithm for a class is a general sufficient condition for learnability in both the models of attribute noise and covered (or missing) attributes. We further show that since the algorithms in question are statistical, they can also simultaneously tolerate classification noise. Classes for which these results hold, and can therefore be learned with simultaneous attribute noise and classification noise, include k-DNF, k-term-DNF by DNF representations, conjunctions with few relevant variables, and over the uniform distribution, decision lists. These noise models are the first PAC models in which all training data, attributes and labels, may be corrupted by a random process. Previous researchers had shown that the class of k-DNF is learnable with attribute noise if the attribute noise rate is known exactly. We show that all of our attribute noise learnabil-ity results, either with or without classification noise, also hold when the exact noise rate is not Appeared in Proceedings of the Eighth Annual ACM Conference on Computational Learning Theory. ACM Press, July 1995. known, provided that the learner instead has a polynomially good approximation of the noise rate. In addition, we show that the results also hold when there is not one single noise rate, but a distinct noise rate for each attribute. Our results for learning with random covering do not require the learner to be told even an approximation of the covering rate and in addition hold in the setting with distinct covering rates for each attribute. Finally, we give lower bounds on the number of examples required for learning in the presence of attribute noise or covering. 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 #249858. 	[Title] 25 Learning in Hybrid Noise Environments Using Statistical Queries [Abstract] We consider formal models of learning from noisy data. Specifically, we focus on learning in the probability approximately correct model as defined by Valiant. Two of the most widely studied models of noise in this setting have been classification noise and malicious errors. However, a more realistic model combining the two types of noise has not been formalized. We define a learning environment based on a natural combination of these two noise models. We first show that hypothesis testing is possible in this model. We next describe a simple technique for learning in this model, and then describe a more powerful technique based on statistical query learning. We show that the noise tolerance of this improved technique is roughly optimal with respect to the desired learning accuracy and that it provides a smooth tradeoff between the tolerable amounts of the two types of noise. Finally, we show that statistical query simulation yields learning algorithms for other combinations of noise models, thus demonstrating that statistical query specification truly An important goal of research in machine learning is to determine which tasks can be automated, and for those which can, to determine their information and computation requirements. One way to answer these questions is through the development and investigation of formal models of machine learning which capture the task of learning under plausible assumptions. In this work, we consider the formal model of learning from examples called "probably approximately correct" (PAC) learning as defined by Valiant [Val84]. In this setting, a learner attempts to approximate an unknown target concept simply by viewing positive and negative examples of the concept. An adversary chooses, from some specified function class, a hidden f0; 1g-valued target function defined over some specified domain of examples and chooses a probability distribution over this domain. The goal of the learner is to output in both polynomial time and with high probability, an hypothesis which is "close" to the target function with respect to the distribution of examples. The learner gains information about the target function and distribution by interacting with an example oracle. At each request by the learner, this oracle draws an example randomly according to the hidden distribution, labels it according to the hidden target function, and returns the labelled example to the learner. A class of functions F is said to be PAC learnable if captures the generic fault tolerance of a learning algorithm. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #15429. 	[Title] A General Lower Bound on the Number of Examples Needed for Learning [Abstract] We prove a lower bound of ( 1 * ln 1 ffi + VCdim(C) * ) on the number of random examples required for distribution-free learning of a concept class C, where VCdim(C) is the Vapnik-Chervonenkis dimension and * and ffi are the accuracy and confidence parameters. This improves the previous best lower bound of ( 1 * ln 1 ffi + VCdim(C)), and comes close to the known general upper bound of O( 1 ffi + VCdim(C) * ln 1 * ) for consistent algorithms. We show that for many interesting concept classes, including kCNF and kDNF, our bound is actually tight to within a constant factor. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12197. 	[Title] Pac Learning, Noise, and Geometry [Abstract] This paper describes the probably approximately correct model of concept learning, paying special attention to the case where instances are points in Euclidean n-space. The problem of learning from noisy training data is also studied. 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 #68495. 	[Title] PAC-Learning PROLOG clauses with or without errors [Abstract] In a nutshell we can describe a generic ILP problem as following: given a set E of (positive and negative) examples of a target predicate, and some background knowledge B about the world (usually a logic program including facts and auxiliary predicates), the task is to find a logic program H (our hypothesis) such that all positive examples can be deduced from B and H, while no negative example can. In this paper we review some of the results achieved in this area and discuss the techniques used. Moreover we prove the following new results: * Predicates described by non-recursive, local clauses of at most k literals are PAC-learnable under any distribution. This generalizes a previous result that was valid only for constrained clauses. * Predicates that are described by k non-recursive local clauses are PAC-learnable under any distribution. This generalizes a previous result that was non construc tive and valid only under some class of distributions. Finally we introduce what we believe is the first theoretical framework for learning Prolog clauses in the presence of errors. To this purpose we introduce a new noise model, that we call the fixed attribute noise model, for learning propositional concepts over the Boolean domain. This new noise model can be of its own interest. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1119471. 	[Title] Learning from Incomplete Boundary Queries Using Split Graphs and Hypergraphs (Extended Abstract) [Abstract] We consider learnability with membership queries in the presence of incomplete information. In the incomplete boundary query model introduced by Blum et al. [7], it is assumed that membership queries on instances near the boundary of the target concept may receive a "don't know" answer. We show that zero-one threshold functions are efficiently learnable in this model. The learning algorithm uses split graphs when the boundary region has radius 1, and their generalization to split hypergraphs (for which we give a split-finding algorithm) when the boundary region has constant radius greater than 1. We use a notion of indistinguishability of concepts that is appropriate for this model. 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 #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 #64319. 	[Title] Improved Noise-Tolerant Learning and Generalized Statistical Queries [Abstract] The statistical query learning model can be viewed as a tool for creating (or demonstrating the existence of) noise-tolerant learning algorithms in the PAC model. The complexity of a statistical query algorithm, in conjunction with the complexity of simulating SQ algorithms in the PAC model with noise, determine the complexity of the noise-tolerant PAC algorithms produced. Although roughly optimal upper bounds have been shown for the complexity of statistical query learning, the corresponding noise-tolerant PAC algorithms are not optimal due to inefficient simulations. In this paper we provide both improved simulations and a new variant of the statistical query model in order to overcome these inefficiencies. We improve the time complexity of the classification noise simulation of statistical query algorithms. Our new simulation has a roughly optimal dependence on the noise rate. We also derive a simpler proof that statistical queries can be simulated in the presence of classification noise. This proof makes fewer assumptions on the queries themselves and therefore allows one to simulate more general types of queries. We also define a new variant of the statistical query model based on relative error, and we show that this variant is more natural and strictly more powerful than the standard additive error model. We demonstrate efficient PAC simulations for algorithms in this new model and give general upper bounds on both learning with relative error statistical queries and PAC simulation. We show that any statistical query algorithm can be simulated in the PAC model with malicious errors in such a way that the resultant PAC algorithm has a roughly optimal tolerable malicious error rate and sample complexity. Finally, we generalize the types of queries allowed in the statistical query model. We discuss the advantages of allowing these generalized queries and show that our results on improved simulations also hold for these queries. This paper is available from the Center for Research in Computing Technology, Division of Applied Sciences, Harvard University as technical report TR-17-94. Please summarise all the given information.

Paper #111866 has the title `On Learning from Noisy and Incomplete Examples  
` and the abstract `We investigate learnability in the PAC model when the data used for learning, attributes and labels, is either corrupted or incomplete. In order to prove our main results, we define a new complexity measure on statistical query (SQ) learning algorithms. The view of an SQ algorithm is the maximum over all queries in the algorithm, of the number of input bits on which the query depends. We show that a restricted view SQ algorithm for a class is a general sufficient condition for learnability in both the models of attribute noise and covered (or missing) attributes. We further show that since the algorithms in question are statistical, they can also simultaneously tolerate classification noise. Classes for which these results hold, and can therefore be learned with simultaneous attribute noise and classification noise, include k-DNF, k-term-DNF by DNF representations, conjunctions with few relevant variables, and over the uniform distribution, decision lists. These noise models are the first PAC models in which all training data, attributes and labels, may be corrupted by a random process. Previous researchers had shown that the class of k-DNF is learnable with attribute noise if the attribute noise rate is known exactly. We show that all of our attribute noise learnabil-ity results, either with or without classification noise, also hold when the exact noise rate is not Appeared in Proceedings of the Eighth Annual ACM Conference on Computational Learning Theory. ACM Press, July 1995. known, provided that the learner instead has a polynomially good approximation of the noise rate. In addition, we show that the results also hold when there is not one single noise rate, but a distinct noise rate for each attribute. Our results for learning with random covering do not require the learner to be told even an approximation of the covering rate and in addition hold in the setting with distinct covering rates for each attribute. Finally, we give lower bounds on the number of examples required for learning in the presence of attribute noise or covering.
`.
Question: Which category should Paper #111866 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #111866 has the title `On Learning from Noisy and Incomplete Examples  
` and the abstract `We investigate learnability in the PAC model when the data used for learning, attributes and labels, is either corrupted or incomplete. In order to prove our main results, we define a new complexity measure on statistical query (SQ) learning algorithms. The view of an SQ algorithm is the maximum over all queries in the algorithm, of the number of input bits on which the query depends. We show that a restricted view SQ algorithm for a class is a general sufficient condition for learnability in both the models of attribute noise and covered (or missing) attributes. We further show that since the algorithms in question are statistical, they can also simultaneously tolerate classification noise. Classes for which these results hold, and can therefore be learned with simultaneous attribute noise and classification noise, include k-DNF, k-term-DNF by DNF representations, conjunctions with few relevant variables, and over the uniform distribution, decision lists. These noise models are the first PAC models in which all training data, attributes and labels, may be corrupted by a random process. Previous researchers had shown that the class of k-DNF is learnable with attribute noise if the attribute noise rate is known exactly. We show that all of our attribute noise learnabil-ity results, either with or without classification noise, also hold when the exact noise rate is not Appeared in Proceedings of the Eighth Annual ACM Conference on Computational Learning Theory. ACM Press, July 1995. known, provided that the learner instead has a polynomially good approximation of the noise rate. In addition, we show that the results also hold when there is not one single noise rate, but a distinct noise rate for each attribute. Our results for learning with random covering do not require the learner to be told even an approximation of the covering rate and in addition hold in the setting with distinct covering rates for each attribute. Finally, we give lower bounds on the number of examples required for learning in the presence of attribute noise or covering.
`.
Question: Which category should Paper #111866 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