Above are papers related to the following paper: [Paper_ID] Paper #42221. 	[Title] Composite Geometric Concepts and Polynomial Predictability [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #42209. 	[Title] Learning Unions of Rectangles with Queries [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12194. 	[Title] Learning From a Consistently Ignorant Teacher [Abstract] One view of computational learning theory is that of a learner acquiring the knowledge of a teacher. We introduce a formal model of learning capturing the idea that teachers may have gaps in their knowledge. The goal of the learner is still to acquire the knowledge of the teacher, but now the learner must also identify the gaps. This is the notion of learning from a consistently ignorant teacher. We consider the impact of knowledge gaps on learning, for example, monotone DNF and d-dimensional boxes, and show that learning is still possible. Negatively, we show that knowledge gaps make learning conjunctions of Horn clauses as hard as learning DNF. We also present general results describing when known learning algorithms can be used to obtain learning algorithms using a consistently ignorant teacher. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #57922. 	[Title] A Note on Learning from Multiple-Instance Examples [Abstract] We describe a simple reduction from the problem of PAC-learning from multiple-instance examples to that of PAC-learning with one-sided random classification noise. Thus, all concept classes learnable with one-sided noise, which includes all concepts learnable in the usual 2-sided random noise model plus others such as the parity function, are learnable from multiple-instance examples. We also describe a more efficient (and somewhat technically more involved) reduction to the Statistical-Query model that results in a polynomial-time algorithm for learning axis-parallel rectangles with sample complexity ~ O(d 2 r=* 2 ), saving roughly a factor of r over the results of Auer et al. (1997). 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 #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 #1118658. 	[Title] A Framework for Multiple-Instance Learning [Abstract] Multiple-instance learning is a variation on supervised learning, where the task is to learn a concept given positive and negative bags of instances. Each bag may contain many instances, but a bag is labeled positive even if only one of the instances in it falls within the concept. A bag is labeled negative only if all the instances in it are negative. We describe a new general framework, called Diverse Density, for solving multiple-instance learning problems. We apply this framework to learn a simple description of a person from a series of images (bags) containing that person, to a stock selection problem, and to the drug activity prediction problem. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12169. 	[Title] Learning With Unreliable Boundary Queries [Abstract] We introduce a model for learning from examples and membership queries in situations where the boundary between positive and negative examples is somewhat ill-defined. In our model, queries near the boundary of a target concept may receive incorrect or "don't care" responses, and the distribution of examples has zero probability mass on the boundary region. The motivation behind our model is that in many cases the boundary between positive and negative examples is complicated or "fuzzy." However, one may still hope to learn successfully, because the typical examples that one sees do not come from that region. We present several positive results in this new model. We show how to learn the intersection of two arbitrary halfspaces when membership queries near the boundary may be answered incorrectly. Our algorithm is an extension of an algorithm of Baum [7, 6] that learns the intersection of two halfspaces whose bounding planes pass through the origin in the PAC-with-membership-queries model. We also describe algorithms for learning several subclasses of monotone DNF formulas. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6925. 	[Title] Solving the Multiple-Instance Problem with Axis-Parallel Rectangles [Abstract] The multiple instance problem arises in tasks where the training examples are ambiguous: a single example object may have many alternative feature vectors (instances) that describe it, and yet only one of those feature vectors may be responsible for the observed classification of the object. This paper describes and compares three kinds of algorithms that learn axis-parallel rectangles to solve the multiple-instance problem. Algorithms that ignore the multiple instance problem perform very poorly. An algorithm that directly confronts the multiple instance problem (by attempting to identify which feature vectors are responsible for the observed classifications) performs best, giving 89% correct predictions on a musk-odor prediction task. The paper also illustrates the use of artificial data to debug and compare these algorithms. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #148399. 	[Title] An Interactive Model of Teaching [Abstract] Previous teaching models in the learning theory community have been batch models. That is, in these models the teacher has generated a single set of helpful examples to present to the learner. In this paper we present an interactive model in which the learner has the ability to ask queries as in the query learning model of Angluin [1]. We show that this model is at least as powerful as previous teaching models. We also show that anything learnable with queries, even by a randomized learner, is teachable in our model. In all previous teaching models, all classes shown to be teachable are known to be efficiently learnable. An important concept class that is not known to be learnable is DNF formulas. We demonstrate the power of our approach by providing a deterministic teacher and learner for the class of DNF formulas. The learner makes only equivalence queries and all hypotheses are also DNF formulas. 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 #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 #248119. 	[Title] Learning Boxes in High Dimension [Abstract] We present exact learning algorithms that learn several classes of (discrete) boxes in f0; : : :; ` 1g n . In particular we learn: (1) The class of unions of O(log n) boxes in time poly(n; log `) (solving an open problem of [16, 12]; in [3] this class is shown to be learnable in time poly(n; `)). (2) The class of unions of disjoint boxes in time poly(n; t; log `), where t is the number of boxes. (Previously this was known only in the case where all boxes are disjoint in one of the dimensions; in [3] this class is shown to be learnable in time poly(n; t; `)). In particular our algorithm learns the class of decision trees over n variables, that take values in f0; : : :; ` 1g, with comparison nodes in time poly(n; t; log `), where t is the number of leaves (this was an open problem in [9] which was shown in [4] to be learnable in time poly(n; t; `)). (3) The class of unions of O(1)-degenerate boxes (that is, boxes that depend only on O(1) variables) in time poly(n; t; log `) (generalizing the learnability of O(1)-DNF and of boxes in O(1) dimensions). The algorithm for this class uses only equivalence queries and it can also be used to learn the class of unions of O(1) boxes (from equivalence queries only). fl A preliminary version of this paper appeared in the proceedings of the EuroCOLT '97 conference, published in volume 1208 of Lecture Notes in Artificial Intelligence, pages 3-15. Springer-Verlag, 1997. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #93273. 	[Title] Noise-Tolerant Parallel Learning of Geometric Concepts [Abstract] We present several efficient parallel algorithms for PAC-learning geometric concepts in a constant-dimensional space that are robust even against malicious misclassification noise of any rate less than 1=2. In particular we consider the class of geometric concepts defined by a polynomial number of (d 1)-dimensional hyperplanes against an arbitrary distribution where each hyperplane has a slope from a set of known slopes, and the class of geometric concepts defined by a polynomial number of (d 1)-dimensional hyperplanes (of unrestricted slopes) against a product distribution. Next we define a complexity measure of any set S of (d1)-dimensional surfaces that we call the variant of S and prove that the class of geometric concepts defined by surfaces of polynomial variant can be efficiently learned in parallel under a product distribution (even under malicious misclassifi-cation noise). Finally, we describe how boosting techniques can be used so that our algorithms' de pendence on * and ffi does not depend on d. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #57948. 	[Title] PAC Learning Axis-aligned Rectangles with Respect to Product Distributions from Multiple-instance Examples [Abstract] We describe a polynomial-time algorithm for learning axis-aligned rectangles in Q d with respect to product distributions from multiple-instance examples in the PAC model. Here, each example consists of n elements of Q d together with a label indicating whether any of the n points is in the rectangle to be learned. We assume that there is an unknown product distribution D over Q d such that all instances are independently drawn according to D. The accuracy of a hypothesis is measured by the probability that it would incorrectly predict whether one of n more points drawn from D was in the rectangle to be learned. Our algorithm achieves accuracy * with probability 1 ffi in Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1114526. 	[Title] Approximating Hyper-Rectangles: Learning and Pseudo-random Sets [Abstract] The PAC learning of rectangles has been studied because they have been found experimentally to yield excellent hypotheses for several applied learning problems. Also, pseudorandom sets for rectangles have been actively studied recently because (i) they are a subprob-lem common to the derandomization of depth-2 (DNF) circuits and derandomizing Randomized Logspace, and (ii) they approximate the distribution of n independent multivalued random variables. We present improved upper bounds for a class of such problems of approximating high-dimensional rectangles that arise in PAC learning and pseudorandomness. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #27199. 	[Title] Learning Unions of Boxes with Membership and Equivalence Queries [Abstract] We present two algorithms that use membership and equivalence queries to exactly identify the concepts given by the union of s discretized axis-parallel boxes in d-dimensional discretized Euclidean space where each coordinate can have n discrete values. The first algorithm receives at most sd counterexamples and uses time and membership queries polynomial in s and log n for d any constant. Further, all equivalence queries made can be formulated as the union of O(sd log s) axis-parallel boxes. Next, we introduce a new complexity measure that better captures the complexity of a union of boxes than simply the number of boxes and dimensions. Our new measure, , is the number of segments in the target polyhedron where a segment is a maximum portion of one of the sides of the polyhedron that lies entirely inside or entirely outside each of the other halfspaces defining the polyhedron. We then present an improvement of our first algorithm that uses time and queries polynomial in and log n. The hypothesis class used here is decision trees of height at most 2sd. Further we can show that the time and queries used by this algorithm are polynomial in d and log n for s any constant thus generalizing the exact learnability of DNF formulas with a constant number of terms. In fact, this single algorithm is efficient for either s or d constant. Please summarise all the given information.

Paper #42221 has the title `Composite Geometric Concepts and Polynomial Predictability  
` and the abstract `nan`.
Question: Which category should Paper #42221 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #42221 has the title `Composite Geometric Concepts and Polynomial Predictability  
` and the abstract `nan`.
Question: Which category should Paper #42221 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