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 #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 #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 #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 #4637. 	[Title] Learning to model sequences generated by switching distributions [Abstract] We study efficient algorithms for solving the following problem, which we call the switching distributions learning problem. A sequence S = 1 2 : : : n , over a finite alphabet S is generated in the following way. The sequence is a concatenation of K runs, each of which is a consecutive subsequence. Each run is generated by independent random draws from a distribution ~p i over S, where ~p i is an element in a set of distributions f~p 1 ; : : : ; ~p N g. The learning algorithm is given this sequence and its goal is to find approximations of the distributions ~p 1 ; : : : ; ~p N , and give an approximate segmentation of the sequence into its constituting runs. We give an efficient algorithm for solving this problem and show conditions under which the algorithm is guaranteed to work with high probability. 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 #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 #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 #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 #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.

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 #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 #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 #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 #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 #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 #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 #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 #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 #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 #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 #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 #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.

Paper #989397 has the title `PAC Learning Intersections of Halfspaces with Membership Queries (Extended Abstract)  
` and the abstract ` 
`.
Question: Which category should Paper #989397 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #989397 has the title `PAC Learning Intersections of Halfspaces with Membership Queries (Extended Abstract)  
` and the abstract ` 
`.
Question: Which category should Paper #989397 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