Above are papers related to the following paper: [Paper_ID] Paper #41666. 	[Title] Separating Formal Bounds from Practical Performance in Learning Systems [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #576257. 	[Title] Genetic Programming of Minimal Neural Nets Using Occam's Razor [Abstract] A genetic programming method is investigated for optimizing both the architecture and the connection weights of multilayer feedforward neural networks. The genotype of each network is represented as a tree whose depth and width are dynamically adapted to the particular application by specifically defined genetic operators. The weights are trained by a next-ascent hillclimb-ing search. A new fitness function is proposed that quantifies the principle of Occam's razor. It makes an optimal trade-off between the error fitting ability and the parsimony of the network. We discuss the results for two problems of differing complexity and study the convergence and scaling properties of the algorithm. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #210309. 	[Title] Metric Entropy and Minimax Risk in Classification [Abstract] We apply recent results on the minimax risk in density estimation to the related problem of pattern classification. The notion of loss we seek to minimize is an information theoretic measure of how well we can predict the classification of future examples, given the classification of previously seen examples. We give an asymptotic characterization of the minimax risk in terms of the metric entropy properties of the class of distributions that might be generating the examples. We then use these results to characterize the minimax risk in the special case of noisy two-valued classification problems in terms of the Assouad density and the Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #24966. 	[Title] A Practical Bayesian Framework for Backprop Networks [Abstract] A quantitative and practical Bayesian framework is described for learning of mappings in feedforward networks. The framework makes possible: (1) objective comparisons between solutions using alternative network architectures; (2) objective stopping rules for network pruning or growing procedures; (3) objective choice of magnitude and type of weight decay terms or additive regularisers (for penalising large weights, etc.); (4) a measure of the effective number of well-determined parameters in a model; (5) quantified estimates of the error bars on network parameters and on network output; (6) objective comparisons with alternative learning and interpolation models such as splines and radial basis functions. The Bayesian `evidence' automatically embodies `Occam's razor,' penalising over-flexible and over-complex models. The Bayesian approach helps detect poor underlying assumptions in learning models. For learning models well matched to a problem, a good correlation between generalisation ability and the Bayesian evidence is obtained. This paper makes use of the Bayesian framework for regularisation and model comparison described in the companion paper `Bayesian interpolation' (MacKay, 1991a). This framework is due to Gull and Skilling (Gull, 1989a). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1104007. 	[Title] Sequential PAC Learning [Abstract] We consider the use of "on-line" stopping rules to reduce the number of training examples needed to pac-learn. Rather than collect a large training sample that can be proved sufficient to eliminate all bad hypotheses a priori, the idea is instead to observe training examples one-at-a-time and decide "on-line" whether to stop and return a hypothesis, or continue training. The primary benefit of this approach is that we can detect when a hypothesizer has actually "converged," and halt training before the standard fixed-sample-size bounds. This paper presents a series of such sequential learning procedures for: distribution-free pac-learning, "mistake-bounded to pac" conversion, and distribution-specific pac-learning, respectively. We analyze the worst case expected training sample size of these procedures, and show that this is often smaller than existing fixed sample size bounds | while providing the exact same worst case pac-guarantees. We also provide lower bounds that show these reductions can at best involve constant (and possibly log) factors. However, empirical studies show that these sequential learning procedures actually use many times fewer training examples in prac tice. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1153160. 	[Title] Inductive Logic Programming [Abstract] A new research area, Inductive Logic Programming, is presently emerging. While inheriting various positive characteristics of the parent subjects of Logic Programming and Machine Learning, it is hoped that the new area will overcome many of the limitations of its forebears. The background to present developments within this area is discussed and various goals and aspirations for the increasing body of researchers are identified. Inductive Logic Programming needs to be based on sound principles from both Logic and Statistics. On the side of statistical justification of hypotheses we discuss the possible relationship between Algorithmic Complexity theory and Probably-Approximately-Correct (PAC) Learning. In terms of logic we provide a unifying framework for Muggleton and Buntine's Inverse Resolution (IR) and Plotkin's Relative Least General Generali-sation (RLGG) by rederiving RLGG in terms of IR. This leads to a discussion of the feasibility of extending the RLGG framework to allow for the invention of new predicates, previously discussed only within the context of IR. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #35854. 	[Title] Characterizations of Learnability for Classes of f0; ng-valued Functions [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1105433. 	[Title] Priors for Infinite Networks [Abstract] Technical Report CRG-TR-94-1 Department of Computer Science University of Toronto 10 King's College Road Toronto, Canada M5S 1A4 Abstract Bayesian inference begins with a prior distribution for model parameters that is meant to capture prior beliefs about the relationship being modeled. For multilayer perceptron networks, where the parameters are the connection weights, the prior lacks any direct meaning | what matters is the prior over functions computed by the network that is implied by this prior over weights. In this paper, I show that priors over weights can be defined in such a way that the corresponding priors over functions reach reasonable limits as the number of hidden units in the network goes to infinity. When using such priors, there is thus no need to limit the size of the network in order to avoid "overfitting". The infinite network limit also provides insight into the properties of different priors. A Gaussian prior for hidden-to-output weights results in a Gaussian process prior for functions, which can be smooth, Brownian, or fractional Brownian, depending on the hidden unit activation function and the prior for input-to-hidden weights. Quite different effects can be obtained using priors based on non-Gaussian stable distributions. In networks with more than one hidden layer, a combination of Gaussian and non-Gaussian priors appears most interesting. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #217115. 	[Title] On the Sample Complexity of Noise-Tolerant Learning [Abstract] In this paper, we further characterize the complexity of noise-tolerant learning in the PAC model. Specifically, we show a general lower bound of log(1=ffi) on the number of examples required for PAC learning in the presence of classification noise. Combined with a result of Simon, we effectively show that the sample complexity of PAC learning in the presence of classification noise is VC(F) "(12) 2 : Furthermore, we demonstrate the optimality of the general lower bound by providing a noise-tolerant learning algorithm for the class of symmetric Boolean functions which uses a sample size within a constant factor of this bound. Finally, we note that our general lower bound compares favorably with various general upper bounds for PAC learning in the presence of classification noise. 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 #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 #9513. 	[Title] On the Complexity of Learning from Drifting Distributions [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1111978. 	[Title] Consistency of Posterior Distributions for Neural Networks [Abstract] In this paper we show that the posterior distribution for feedforward neural networks is asymptotically consistent. This paper extends earlier results on universal approximation properties of neural networks to the Bayesian setting. The proof of consistency embeds the problem in a density estimation problem, then uses bounds on the bracketing entropy to show that the posterior is consistent over Hellinger neighborhoods. It then relates this result back to the regression setting. We show consistency in both the setting of the number of hidden nodes growing with the sample size, and in the case where the number of hidden nodes is treated as a parameter. Thus we provide a theoretical justification for using neural networks for nonparametric regression in a Bayesian framework. 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 #10169. 	[Title] Learning Boolean Concepts in the Presence of Many Irrelevant Features [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #40124. 	[Title] Probabilistic Networks: New Models and New Methods [Abstract] In this paper I describe the implementation of a probabilistic regression model in BUGS. BUGS is a program that carries out Bayesian inference on statistical problems using a simulation technique known as Gibbs sampling. It is possible to implement surprisingly complex regression models in this environment. I demonstrate the simultaneous inference of an interpolant and an input-dependent noise level. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #65212. 	[Title] Bayesian Training of Backpropagation Networks by the Hybrid Monte Carlo Method [Abstract] It is shown that Bayesian training of backpropagation neural networks can feasibly be performed by the "Hybrid Monte Carlo" method. This approach allows the true predictive distribution for a test case given a set of training cases to be approximated arbitrarily closely, in contrast to previous approaches which approximate the posterior weight distribution by a Gaussian. In this work, the Hybrid Monte Carlo method is implemented in conjunction with simulated annealing, in order to speed relaxation to a good region of parameter space. The method has been applied to a test problem, demonstrating that it can produce good predictions, as well as an indication of the uncertainty of these predictions. Appropriate weight scaling factors are found automatically. By applying known techniques for calculation of "free energy" differences, it should also be possible to compare the merits of different network architectures. The work described here should also be applicable to a wide variety of statistical models other than neural networks. 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 #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 #253762. 	[Title] Bayesian Mixture Modeling by Monte Carlo Simulation [Abstract] It is shown that Bayesian inference from data modeled by a mixture distribution can feasibly be performed via Monte Carlo simulation. This method exhibits the true Bayesian predictive distribution, implicitly integrating over the entire underlying parameter space. An infinite number of mixture components can be accommodated without difficulty, using a prior distribution for mixing proportions that selects a reasonable subset of components to explain any finite training set. The need to decide on a "correct" number of components is thereby avoided. The feasibility of the method is shown empirically for a simple classification task. 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 #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 #23116. 	[Title] Bayesian Methods for Adaptive Models [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #89547. 	[Title] Rigorous Learning Curve Bounds from Statistical Mechanics [Abstract] In this paper we introduce and investigate a mathematically rigorous theory of learning curves that is based on ideas from statistical mechanics. The advantage of our theory over the well-established Vapnik-Chervonenkis theory is that our bounds can be considerably tighter in many cases, and are also more reflective of the true behavior (functional form) of learning curves. This behavior can often exhibit dramatic properties such as phase transitions, as well as power law asymptotics not explained by the VC theory. The disadvantages of our theory are that its application requires knowledge of the input distribution, and it is limited so far to finite cardinality function classes. We illustrate our results with many concrete examples of learning curve bounds derived from our theory. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #175576. 	[Title] PAC Learning of One-Dimensional Patterns [Abstract] Developing the ability to recognize a landmark from a visual image of a robot's current location is a fundamental problem in robotics. We consider the problem of PAC-learning the concept class of geometric patterns where the target geometric pattern is a configuration of k points on the real line. Each instance is a configuration of n points on the real line, where it is labeled according to whether or not it visually resembles the target pattern. To capture the notion of visual resemblance we use the Hausdorff metric. Informally, two geometric patterns P and Q resemble each other under the Hausdorff metric, if every point on one pattern is "close" to some point on the other pattern. We relate the concept class of geometric patterns to the landmark recognition problem and then present a polynomial-time algorithm that PAC-learns the class of one-dimensional geometric patterns. We also present some experimental results on how our algorithm performs. 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 #219239. 	[Title] Simulating Access to Hidden Information while Learning [Abstract] We introduce a new technique which enables a learner without access to hidden information to learn nearly as well as a learner with access to hidden information. We apply our technique to solve an open problem of Maass and Turan [18], showing that for any concept class F , the least number of queries sufficient for learning F by an algorithm which has access only to arbitrary equivalence queries is at most a factor of 1= log 2 (4=3) more than the least number of queries sufficient for learning F by an algorithm which has access to both arbitrary equivalence queries and membership queries. Previously known results imply that the 1= log 2 (4=3) in our bound is best possible. We describe analogous results for two generalizations of this model to function learning, and apply those results to bound the difficulty of learning in the harder of these models in terms of the difficulty of learning in the easier model. We bound the difficulty of learning unions of k concepts from a class F in terms of the difficulty of learning F . We bound the difficulty of learning in a noisy environment for deterministic algorithms in terms of the difficulty of learning in a noise-free environment. We apply a variant of our technique to develop an algorithm transformation that allows probabilistic learning algorithms to nearly optimally cope with noise. A second variant enables us to improve a general lower bound of Turan [19] for the PAC-learning model (with queries). Finally, we show that logarithmically many membership queries never help to obtain computationally efficient learning algorithms. fl Supported by Air Force Office of Scientific Research grant F49620-92-J-0515. Most of this work was done while this author was at TU Graz supported by a Lise Meitner Fellowship from the Fonds zur Forderung der wissenschaftlichen Forschung (Austria). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #27627. 	[Title] Information-based objective functions for active data selection [Abstract] Learning can be made more efficient if we can actively select particularly salient data points. Within a Bayesian learning framework, objective functions are discussed which measure the expected informativeness of candidate measurements. Three alternative specifications of what we want to gain information about lead to three different criteria for data selection. All these criteria depend on the assumption that the hypothesis space is correct, which may prove to be their main weakness. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #943087. 	[Title] Theory and Practice of Vector Quantizers Trained on Small Training Sets [Abstract] We examine how the performance of a memoryless vector quantizer changes as a function of its training set size. Specifically, we study how well the training set distortion predicts test distortion when the training set is a randomly drawn subset of blocks from the test or training image(s). Using the Vapnik-Chervonenkis dimension, we derive formal bounds for the difference of test and training distortion of vector quantizer codebooks. We then describe extensive empirical simulations that test these bounds for a variety of bit rates and vector dimensions, and give practical suggestions for determining the training set size necessary to achieve good generalization from a codebook. We conclude that, by using training sets comprised of only a small fraction of the available data, one can produce results that are close to the results obtainable when all available data are used. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1107572. 	[Title] Sifting informative examples from a random source. [Abstract] We discuss two types of algorithms for selecting relevant examples that have been developed in the context of computation learning theory. The examples are selected out of a stream of examples that are generated independently at random. The first two algorithms are the so-called "boosting" algorithms of Schapire [ Schapire, 1990 ] and Fre-und [ Freund, 1990 ] , and the Query-by-Committee algorithm of Seung [ Seung et al., 1992 ] . We describe the algorithms and some of their proven properties, point to some of their commonalities, and suggest some possible future implications. Please summarise all the given information.

Paper #41666 has the title `Separating Formal Bounds from Practical Performance in Learning Systems  
` and the abstract `nan`.
Question: Which category should Paper #41666 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #41666 has the title `Separating Formal Bounds from Practical Performance in Learning Systems  
` and the abstract `nan`.
Question: Which category should Paper #41666 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