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 #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 #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 #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 #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 #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 #93273 has the title `Noise-Tolerant Parallel Learning of Geometric Concepts  
` and the 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.
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Question: Which category should Paper #93273 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #93273 has the title `Noise-Tolerant Parallel Learning of Geometric Concepts  
` and the 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.
`.
Question: Which category should Paper #93273 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