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 #128. 	[Title] Reinforcement Learning Algorithms for Average-Payoff Markovian Decision Processes [Abstract] Reinforcement learning (RL) has become a central paradigm for solving learning-control problems in robotics and artificial intelligence. RL researchers have focussed almost exclusively on problems where the controller has to maximize the discounted sum of payoffs. However, as emphasized by Schwartz (1993), in many problems, e.g., those for which the optimal behavior is a limit cycle, it is more natural and com-putationally advantageous to formulate tasks so that the controller's objective is to maximize the average payoff received per time step. In this paper I derive new average-payoff RL algorithms as stochastic approximation methods for solving the system of equations associated with the policy evaluation and optimal control questions in average-payoff RL tasks. These algorithms are analogous to the popular TD and Q-learning algorithms already developed for the discounted-payoff case. One of the algorithms derived here is a significant variation of Schwartz's R-learning algorithm. Preliminary empirical results are presented to validate these new algorithms. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #509315. 	[Title] A Computational View of Population Genetics (preliminary version) [Abstract] This paper contributes to the study of nonlinear dynamical systems from a computational perspective. These systems are inherently more powerful than their linear counterparts (such as Markov chains), which have had a wide impact in Computer Science, and they seem likely to play an increasing role in future. However, there are as yet no general techniques available for handling the computational aspects of discrete nonlinear systems, and even the simplest examples seem very hard to analyze. We focus in this paper on a class of quadratic systems that are widely used as a model in population genetics and also in genetic algorithms. These systems describe a process where random matings occur between parental chromosomes via a mechanism known as "crossover": i.e., children inherit pieces of genetic material from different parents according to some random rule. Our results concern two fundamental quantitative properties of crossover systems: 1. We develop a general technique for computing the Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #45188. 	[Title] A Bound on the Error of Cross Validation Using the Approximation and Estimation Rates, with [Abstract] We give an analysis of the generalization error of cross validation in terms of two natural measures of the difficulty of the problem under consideration: the approximation rate (the accuracy to which the target function can be ideally approximated as a function of the number of hypothesis parameters), and the estimation rate (the deviation between the training and generalization errors as a function of the number of hypothesis parameters). The approximation rate captures the complexity of the target function with respect to the hypothesis model, and the estimation rate captures the extent to which the hypothesis model suffers from overfitting. Using these two measures, we give a rigorous and general bound on the error of cross validation. The bound clearly shows the tradeoffs involved with making fl the fraction of data saved for testing too large or too small. By optimizing the bound with respect to fl, we then argue (through a combination of formal analysis, plotting, and controlled experimentation) that the following qualitative properties of cross validation behavior should be quite robust to significant changes in the underlying model selection problem: 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 #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 #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 #24974. 	[Title] EVALUATION OF GAUSSIAN PROCESSES AND OTHER METHODS FOR NON-LINEAR REGRESSION [Abstract]  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 #350362. 	[Title] Improving Regressors using Boosting Techniques [Abstract] In the regression context, boosting and bagging are techniques to build a committee of regressors that may be superior to a single regressor. We use regression trees as fundamental building blocks in bagging committee machines and boosting committee machines. Performance is analyzed on three non-linear functions and the Boston housing database. In all cases, boosting is at least equivalent, and in most cases better than bagging in terms of prediction error. 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 #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 #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 #3233. 	[Title] A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection [Abstract] We review accuracy estimation methods and compare the two most common methods: cross-validation and bootstrap. Recent experimental results on artificial data and theoretical results in restricted settings have shown that for selecting a good classifier from a set of classifiers (model selection), ten-fold cross-validation may be better than the more expensive leave-one-out cross-validation. We report on a large-scale experiment|over half a million runs of C4.5 and a Naive-Bayes algorithm|to estimate the effects of different parameters on these algorithms on real-world datasets. For cross-validation, we vary the number of folds and whether the folds are stratified or not; for bootstrap, we vary the number of bootstrap samples. Our results indicate that for real-word datasets similar to ours, the best method to use for model selection is ten-fold stratified cross validation, even if computation power allows using more folds. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #22563. 	[Title] A Comparative Study of ID3 and Backpropagation for English Text-to-Speech Mapping [Abstract] The performance of the error backpropagation (BP) and ID3 learning algorithms was compared on the task of mapping English text to phonemes and stresses. Under the distributed output code developed by Sejnowski and Rosenberg, it is shown that BP consistently out-performs ID3 on this task by several percentage points. Three hypotheses explaining this difference were explored: (a) ID3 is overfitting the training data, (b) BP is able to share hidden units across several output units and hence can learn the output units better, and (c) BP captures statistical information that ID3 does not. We conclude that only hypothesis (c) is correct. By augmenting ID3 with a simple statistical learning procedure, the performance of BP can be approached but not matched. More complex statistical procedures can improve the performance of both BP and ID3 substantially. A study of the residual errors suggests that there is still substantial room for improvement in learning methods for text-to-speech mapping. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #35. 	[Title] 4 Implementing Application Specific Routines  Genetic algorithms in search, optimization, and machine learning. Reading, MA: Addison-Wesley. [Abstract] To implement a specific application, you should only have to change the file app.c. Section 2 describes the routines in app.c in detail. If you use additional variables for your specific problem, the easiest method of making them available to other program units is to declare them in sga.h and external.h. However, take care that you do not redeclare existing variables. Two example applications files are included in the SGA-C distribution. The file app1.c performs the simple example problem included with the Pascal version; finding the maximum of x 10 , where x is an integer interpretation of a chromosome. A slightly more complex application is include in app2.c. This application illustrates two features that have been added to SGA-C. The first of these is the ithruj2int function, which converts bits i through j in a chromosome to an integer. The second new feature is the utility pointer that is associated with each population member. The example application interprets each chromosome as a set of concatenated integers in binary form. The lengths of these integer fields is determined by the user-specified value of field size, which is read in by the function app data(). The field size must be less than the smallest of the chromosome length and the length of an unsigned integer. An integer array for storing the interpreted form of each chromosome is dynamically allocated and assigned to the chromosome's utility pointer in app malloc(). The ithruj2int routine (see utility.c) is used to translate each chromosome into its associated vector. The fitness for each chromosome is simply the sum of the squares of these integers. This example application will function for any chromosome length. SGA-C is intended to be a simple program for first-time GA experimentation. It is not intended to be definitive in terms of its efficiency or the grace of its implementation. The authors are interested in the comments, criticisms, and bug reports from SGA-C users, so that the code can be refined for easier use in subsequent versions. Please email your comments to rob@galab2.mh.ua.edu, or write to TCGA: The authors gratefully acknowledge support provided by NASA under Grant NGT-50224 and support provided by the National Science Foundation under Grant CTS-8451610. We also thank Hillol Kargupta for donating his tournament selection implementation. Booker, L. B. (1982). Intelligent behavior as an adaptation to the task environment (Doctoral dissertation, Technical Report No. 243. Ann Arbor: University of Michigan, Logic of Computers Group). Dissertations Abstracts International, 43(2), 469B. (University Microfilms No. 8214966) 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 #1116328. 	[Title] Vapnik-Chervonenkis entropy of the spherical perceptron [Abstract] Perceptron learning of randomly labeled patterns is analyzed using a Gibbs distribution on the set of realizable labelings of the patterns. The entropy of this distribution is an extension of the Vapnik-Chervonenkis (VC) entropy, reducing to it exactly in the limit of infinite temperature. The close relationship between the VC and Gardner entropies can be seen within the replica formalism. There has been recent progress towards understanding the relationship between the statistical physics and Vapnik-Chervonenkis (VC) approaches to learning theory[1, 2, 3, 4]. The two approaches can be unified in a statistical mechanics based on the VC entropy. This paper treats the case of learning randomly labeled patterns, or the capacity problem, and extends some of the results of previous work[5, 6] to finite temperature. As will be explained in a companion paper, this extension is important for treating the generalization problem, which occurs in the context of learning patterns labeled by a target rule. Our general framework is illustrated for the simple perceptron sgn(w x), which maps an N -dimensional real-valued input x to a 1-valued output. Given a sample X = (x 1 ; : : : ; x m ) of inputs, the weight vector w determines a labeling L = (l 1 ; : : : ; l m ) of the sample via l i = sgn(w x i ). The weight vector w defines a normal hyperplane that separates the positive from the negative examples. The training error of a labeling L with respect to a reference labeling L 0 is defined by 1 m X 1 l i l 0 and is just the fraction of different labels in the two labelings. We consider the case in which the reference labeling is chosen at random, and address the issue of 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 #1105450. 	[Title] A Fast, Bottom-Up Decision Tree Pruning Algorithm with Near-Optimal Generalization [Abstract] In this work, we present a new bottom-up algorithm for decision tree pruning that is very efficient (requiring only a single pass through the given tree), and prove a strong performance guarantee for the generalization error of the resulting pruned tree. We work in the typical setting in which the given tree T may have been derived from the given training sample S, and thus may badly overfit S. In this setting, we give bounds on the amount of additional generalization error that our pruning suffers compared to the optimal pruning of T . More generally, our results show that if there is a pruning of T with small error, and whose size is small compared to jSj, then our algorithm will find a pruning whose error is not much larger. This style of result has been called an index of resolvability result by Barron and Cover in the context of density estimation. A novel feature of our algorithm is its locality | the decision to prune a subtree is based entirely on properties of that subtree and the sample reaching it. To analyze our algorithm, we develop tools of local uniform convergence, a generalization of the standard notion that may prove useful in other settings. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #82090. 	[Title] MIMIC: Finding Optima by Estimating Probability Densities [Abstract] In many optimization problems, the structure of solutions reflects complex relationships between the different input parameters. For example, experience may tell us that certain parameters are closely related and should not be explored independently. Similarly, experience may establish that a subset of parameters must take on particular values. Any search of the cost landscape should take advantage of these relationships. We present MIMIC, a framework in which we analyze the global structure of the optimization landscape. A novel and efficient algorithm for the estimation of this structure is derived. We use knowledge of this structure to guide a randomized search through the solution space and, in turn, to refine our estimate of the structure. Our technique obtains significant speed gains over other randomized optimization procedures. 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 #1130929. 	[Title] A model f w depending on a set of parameters w is used to estimate [Abstract] We have introduced earlier the use of regularisation in the learning procedure. It should now be understood that regularisation is most often a necessity to increase the quality of the results. Even when the unregularised solution is acceptable, it is likely that some regularisation will produce an improvement in performance. There does not exist any method giving directly the best value for the regularisation parameter ~, even in the linear case. The topic of this chapter is thus to propose some methods to estimate the best value. The best ~ being the one that leads to the smallest generalisation error, the methods presented and compared here propose estimators of the generalisation error. This estimation can then be used to approximate the best regularisation level. In sections 3.2 to 3.4 we present validation-based techniques. They estimate the generalisation error on the basis of some extra data. In sections 3.6 to 3.9, we deal with algebraic estimates of this error, that do not use any extra data, but rely on a number of assumptions. The contribution of this chapter is to present all these techniques and analyse them on the same ground. We also present some short derivations clarifying the links between different estimators of generalisation error, as well as a comparison between them. During the course of this chapter, the error will be the quadratic difference. For the validation-based methods, it is possible to consider any kind of error without modification of the method. On the other hand, the algebraic estimates are specific to the quadratic cost. Adapting them to another cost function would require to derive new expressions for the estimators. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #28471. 	[Title] Markov Decision Processes in Large State Spaces [Abstract] In this paper we propose a new framework for studying Markov decision processes (MDPs), based on ideas from statistical mechanics. The goal of learning in MDPs is to find a policy that yields the maximum expected return over time. In choosing policies, agents must therefore weigh the prospects of short-term versus long-term gains. We study a simple MDP in which the agent must constantly decide between exploratory jumps and local reward mining in state space. The number of policies to choose from grows exponentially with the size of the state space, N . We view the expected returns as defining an energy landscape over policy space. Methods from statistical mechanics are used to analyze this landscape in the thermodynamic limit N ! 1. We calculate the overall distribution of expected returns, as well as the distribution of returns for policies at a fixed Hamming distance from the optimal one. We briefly discuss the problem of learning optimal policies from empirical estimates of the expected return. As a first step, we relate our findings for the entropy to the limit of high-temperature learning. Numerical simulations support the theoretical results. 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 #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 #237376. 	[Title] Characterizing Rational versus Exponential Learning Curves [Abstract] We consider the standard problem of learning a concept from random examples. Here a learning curve can be defined to be the expected error of a learner's hypotheses as a function of training sample size. Haussler, Littlestone and Warmuth have shown that, in the distribution free setting, the smallest expected error a learner can achieve in the worst case over a concept class C converges rationally to zero error (i.e., fi(1=t) for training sample size t). However, recently Cohn and Tesauro have demonstrated how exponential convergence can often be observed in experimental settings (i.e., average error decreasing as e fi(t) ). By addressing a simple non-uniformity in the original analysis, this paper shows how the dichotomy between rational and exponential worst case learning curves can be recovered in the distribution free theory. These results support the experimental findings of Cohn and Tesauro: for finite concept classes, any consistent learner achieves exponential convergence, even in the worst case; but for continuous concept classes, no learner can exhibit sub-rational convergence for every target concept and domain distribution. A precise boundary between rational and exponential convergence is drawn for simple concept chains. Here we show that somewhere dense chains always force rational convergence in the worst case, but exponential convergence can always be achieved for nowhere dense chains. 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 #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 #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 #6213. 	[Title] Machine Learning Learning to Predict by the Methods of Temporal Differences Keywords: Incremental learning, prediction, [Abstract] This article introduces a class of incremental learning procedures specialized for prediction|that is, for using past experience with an incompletely known system to predict its future behavior. Whereas conventional prediction-learning methods assign credit by means of the difference between predicted and actual outcomes, the new methods assign credit by means of the difference between temporally successive predictions. Although such temporal-difference methods have been used in Samuel's checker player, Holland's bucket brigade, and the author's Adaptive Heuristic Critic, they have remained poorly understood. Here we prove their convergence and optimality for special cases and relate them to supervised-learning methods. For most real-world prediction problems, temporal-difference methods require less memory and less peak computation than conventional methods; and they produce more accurate predictions. We argue that most problems to which supervised learning is currently applied are really prediction problems of the sort to which temporal-difference methods can be applied to advantage. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #91975. 	[Title] Learning Curve Bounds for Markov Decision Processes with Undiscounted Rewards [Abstract] Markov decision processes (MDPs) with undis-counted rewards represent an important class of problems in decision and control. The goal of learning in these MDPs is to find a policy that yields the maximum expected return per unit time. In large state spaces, computing these averages directly is not feasible; instead, the agent must estimate them by stochastic exploration of the state space. In this case, longer exploration times enable more accurate estimates and more informed decision-making. The learning curve for an MDP measures how the agent's performance depends on the allowed exploration time, T . In this paper we analyze these learning curves for a simple control problem with undiscounted rewards. In particular, methods from statistical mechanics are used to calculate lower bounds on the agent's performance in the thermodynamic limit T ! 1, N ! 1, ff = T =N (finite), where T is the number of time steps allotted per policy evaluation and N is the size of the state space. In this limit, we provide a lower bound on the return of policies that appear optimal based on imperfect statistics. 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 #1999. 	[Title] WRAPPERS FOR PERFORMANCE ENHANCEMENT AND OBLIVIOUS DECISION GRAPHS [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #272720. 	[Title] A New Metric-Based Approach to Model Selection [Abstract] We introduce a new approach to model selection that performs better than the standard complexity-penalization and hold-out error estimation techniques in many cases. The basic idea is to exploit the intrinsic metric structure of a hypothesis space, as determined by the natural distribution of unlabeled training patterns, and use this metric as a reference to detect whether the empirical error estimates derived from a small (labeled) training sample can be trusted in the region around an empirically optimal hypothesis. Using simple metric intuitions we develop new geometric strategies for detecting overfitting and performing robust yet responsive model selection in spaces of candidate functions. These new metric-based strategies dramatically outperform previous approaches in experimental studies of classical polynomial curve fitting. Moreover, the technique is simple, efficient, and can be applied to most function learning tasks. The only requirement is access to an auxiliary collection of unlabeled training data. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #192850. 	[Title] Characterizing the generalization performance of model selection strategies [Abstract] We investigate the structure of model selection problems via the bias/variance decomposition. In particular, we characterize the essential aspects of a model selection task by the bias and variance profiles it generates over the sequence of hypothesis classes. With this view, we develop a new understanding of complexity-penalization methods: First, the penalty terms can be interpreted as postulating a particular profile for the variances as a function of model complexityif the postulated and true profiles do not match, then systematic under-fitting or over-fitting results, depending on whether the penalty terms are too large or too small. Second, we observe that it is generally best to penalize according to the true variances of the task, and therefore no fixed penalization strategy is optimal across all problems. We then use this characterization to introduce the notion of easy versus hard model selection problems. Here we show that if the variance profile grows too rapidly in relation to the biases, then standard model selection techniques become prone to significant errors. This can happen, for example, in regression problems where the independent variables are drawn from wide-tailed distributions. To counter this, we discuss a new model selection strategy that dramatically outperforms standard complexity-penalization and hold-out meth ods on these hard tasks. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #32083. 	[Title] Back Propagation is Sensitive to Initial Conditions [Abstract] This paper explores the effect of initial weight selection on feed-forward networks learning simple functions with the back-propagation technique. We first demonstrate, through the use of Monte Carlo techniques, that the magnitude of the initial condition vector (in weight space) is a very significant parameter in convergence time variability. In order to further understand this result, additional deterministic experiments were performed. The results of these experiments demonstrate the extreme sensitivity of back propagation to initial weight configuration. 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 #192734. 	[Title] Preventing "Overfitting" of Cross-Validation Data [Abstract] Suppose that, for a learning task, we have to select one hypothesis out of a set of hypotheses (that may, for example, have been generated by multiple applications of a randomized learning algorithm). A common approach is to evaluate each hypothesis in the set on some previously unseen cross-validation data, and then to select the hypothesis that had the lowest cross-validation error. But when the cross-validation data is partially corrupted such as by noise, and if the set of hypotheses we are selecting from is large, then "folklore" also warns about "overfitting" the cross-validation data [Klockars and Sax, 1986, Tukey, 1949, Tukey, 1953]. In this paper, we explain how this "overfitting" really occurs, and show the surprising result that it can be overcome by selecting a hypothesis with a higher cross-validation error, over others with lower cross-validation errors. We give reasons for not selecting the hypothesis with the lowest cross-validation error, and propose a new algorithm, LOOCVCV, that uses a computa-tionally efficient form of leave-one-out cross-validation to select such a hypothesis. Finally, we present experimental results for one domain, that show LOOCVCV consistently beating picking the hypothesis with the lowest cross-validation error, even when using reasonably large cross-validation sets. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1132385. 	[Title] Towards Robust Model Selection using Estimation and Approximation Error Bounds [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1106401. 	[Title] Model Selection based on Minimum Description Length [Abstract]  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 #114. 	[Title] Learning to Act using Real-Time Dynamic Programming [Abstract] fl The authors thank Rich Yee, Vijay Gullapalli, Brian Pinette, and Jonathan Bachrach for helping to clarify the relationships between heuristic search and control. We thank Rich Sutton, Chris Watkins, Paul Werbos, and Ron Williams for sharing their fundamental insights into this subject through numerous discussions, and we further thank Rich Sutton for first making us aware of Korf's research and for his very thoughtful comments on the manuscript. We are very grateful to Dimitri Bertsekas and Steven Sullivan for independently pointing out an error in an earlier version of this article. Finally, we thank Harry Klopf, whose insight and persistence encouraged our interest in this class of learning problems. This research was supported by grants to A.G. Barto from the National Science Foundation (ECS-8912623 and ECS-9214866) and the Air Force Office of Scientific Research, Bolling AFB (AFOSR-89-0526). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1113459. 	[Title] Near-Optimal Performance for Reinforcement Learning in Polynomial Time [Abstract] We present new algorithms for reinforcement learning and prove that they have polynomial bounds on the resources required to achieve near-optimal return in general Markov decision processes. After observing that the number of actions required to approach the optimal return is lower bounded by the mixing time T of the optimal policy (in the undiscounted case) or by the horizon time T (in the discounted case), we then give algorithms requiring a number of actions and total computation time that are only polynomial in T and the number of states, for both the undiscounted and discounted cases. An interesting aspect of our algorithms is their explicit handling of the Exploration-Exploitation trade-off. These are the first results in the reinforcement learning literature giving algorithms that provably converge to near-optimal performance in polynomial time for general Markov decision processes. 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.

Above are papers related to the following paper: [Paper_ID] Paper #65653. 	[Title] Pessimistic decision tree pruning based on tree size [Abstract] In this work we develop a new criteria to perform pessimistic decision tree pruning. Our method is theoretically sound and is based on theoretical concepts such as uniform convergence and the Vapnik-Chervonenkis dimension. We show that our criteria is very well motivated, from the theory side, and performs very well in practice. The accuracy of the new criteria is comparable to that of the current method used in C4.5. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #117. 	[Title] Generalized Markov Decision Processes: Dynamic-programming and Reinforcement-learning Algorithms [Abstract] The problem of maximizing the expected total discounted reward in a completely observable Markovian environment, i.e., a Markov decision process (mdp), models a particular class of sequential decision problems. Algorithms have been developed for making optimal decisions in mdps given either an mdp specification or the opportunity to interact with the mdp over time. Recently, other sequential decision-making problems have been studied prompting the development of new algorithms and analyses. We describe a new generalized model that subsumes mdps as well as many of the recent variations. We prove some basic results concerning this model and develop generalizations of value iteration, policy iteration, model-based reinforcement-learning, and Q-learning that can be used to make optimal decisions in the generalized model under various assumptions. Applications of the theory to particular models are described, including risk-averse mdps, exploration-sensitive mdps, sarsa, Q-learning with spreading, two-player games, and approximate max picking via sampling. Central to the results are the contraction property of the value operator and a stochastic-approximation theorem that reduces asynchronous convergence to synchronous convergence. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6771. 	[Title] Statistical Tests for Comparing Supervised Classification Learning Algorithms [Abstract] This paper reviews five statistical tests for determining whether one learning algorithm outperforms another on a particular learning task. These tests are compared experimentally to determine their probability of incorrectly detecting a difference when no difference exists (type 1 error). Two widely-used statistical tests are shown to have high probability of Type I error in certain situations and should never be used. These tests are (a) a test for the difference of two proportions and (b) a paired-differences t test based on taking several random train/test splits. A third test, a paired-differences t test based on 10-fold cross-validation, exhibits somewhat elevated probability of Type I error. A fourth test, McNemar's test, is shown to have low Type I error. The fifth test is a new test, 5x2cv, based on 5 iterations of 2-fold cross-validation. Experiments show that this test also has good Type I error. The paper also measures the power (ability to detect algorithm differences when they do exist) of these tests. The 5x2cv test is shown to be slightly more powerful than McNemar's test. The choice of the best test is determined by the computational cost of running the learning algorithm. For algorithms that can be executed only once, McNemar's test is the only test with acceptable Type I error. For algorithms that can be executed ten times, the 5x2cv test is recommended, because it is slightly more powerful and because it directly measures variation due to the choice of training set. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #66805. 	[Title] Where Genetic Algorithms Excel [Abstract] We analyze the performance of a Genetic Algorithm (GA) we call Culling and a variety of other algorithms on a problem we refer to as Additive Search Problem (ASP). ASP is closely related to several previously well studied problems, such as the game of Mastermind and additive fitness functions. We show that the problem of learning the Ising perceptron is reducible to a noisy version of ASP. Culling is efficient on ASP, highly noise tolerant, and the best known approach in some regimes. Noisy ASP is the first problem we are aware of where a Genetic Type Algorithm bests all known competitors. Standard GA's, by contrast, perform much more poorly on ASP than hillclimbing and other approaches even though the Schema theorem holds for ASP. We generalize ASP to k-ASP to study whether GA's will achieve `implicit parallelism' in a problem with many more schemata. GA's fail to achieve this implicit parallelism, but we describe an algorithm we call Explicitly Parallel Search that succeeds. We also compute the optimal culling point for selective breeding, which turns out to be independent of the fitness function or the population distribution. We also analyze a Mean Field Theoretic algorithm performing similarly to Culling on many problems. These results provide insight into when and how GA's can beat competing methods. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1152379. 	[Title] ANNEALED THEORIES OF LEARNING [Abstract] We study annealed theories of learning boolean functions using a concept class of finite cardinality. The naive annealed theory can be used to derive a universal learning curve bound for zero temperature learning, similar to the inverse square root bound from the Vapnik-Chervonenkis theory. Tighter, nonuniversal learning curve bounds are also derived. A more refined annealed theory leads to still tighter bounds, which in some cases are very similar to results previously obtained using one-step replica symmetry breaking. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1112319. 	[Title] Self bounding learning algorithms [Abstract] Most of the work which attempts to give bounds on the generalization error of the hypothesis generated by a learning algorithm is based on methods from the theory of uniform convergence. These bounds are a-priori bounds that hold for any distribution of examples and are calculated before any data is observed. In this paper we propose a different approach for bounding the generalization error after the data has been observed. A self-bounding learning algorithm is an algorithm which, in addition to the hypothesis that it outputs, outputs a reliable upper bound on the generalization error of this hypothesis. We first explore the idea in the statistical query learning framework of Kearns [10]. After that we give an explicit self bounding algorithm for learning algorithms that are based on local search. Please summarise all the given information.

Paper #89547 has the title `Rigorous Learning Curve Bounds from Statistical Mechanics  
` and the 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. 
`.
Question: Which category should Paper #89547 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #89547 has the title `Rigorous Learning Curve Bounds from Statistical Mechanics  
` and the 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. 
`.
Question: Which category should Paper #89547 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