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.

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 #3217. 	[Title] Theory and Applications of Agnostic PAC-Learning with Small Decision Trees [Abstract] We exhibit a theoretically founded algorithm T2 for agnostic PAC-learning of decision trees of at most 2 levels, whose computation time is almost linear in the size of the training set. We evaluate the performance of this learning algorithm T2 on 15 common real-world datasets, and show that for most of these datasets T2 provides simple decision trees with little or no loss in predictive power (compared with C4.5). In fact, for datasets with continuous attributes its error rate tends to be lower than that of C4.5. To the best of our knowledge this is the first time that a PAC-learning algorithm is shown to be applicable to real-world classification problems. Since one can prove that T2 is an agnostic PAC-learning algorithm, T2 is guaranteed to produce close to optimal 2-level decision trees from sufficiently large training sets for any (!) distribution of data. In this regard T2 differs strongly from all other learning algorithms that are considered in applied machine learning, for which no guarantee can be given about their performance on new datasets. We also demonstrate that this algorithm T2 can be used as a diagnostic tool for the investigation of the expressive limits of 2-level decision trees. Finally, T2, in combination with new bounds on the VC-dimension of decision trees of bounded depth that we derive, provides us now for the first time with the tools necessary for comparing learning curves of decision trees for real-world datasets with the theoretical estimates of PAC learning theory. 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 #8224. 	[Title] Mingers, 1989 J. Mingers. An empirical comparison of pruning methods for decision tree induction. Machine [Abstract] Ourston and Mooney, 1990b ] D. Ourston and R. J. Mooney. Improving shared rules in multiple category domain theories. Technical Report AI90-150, Artificial Intelligence Labora tory, University of Texas, Austin, TX, December 1990. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3235. 	[Title] Scaling Up the Accuracy of Naive-Bayes Classifiers: a Decision-Tree Hybrid [Abstract] Naive-Bayes induction algorithms were previously shown to be surprisingly accurate on many classification tasks even when the conditional independence assumption on which they are based is violated. However, most studies were done on small databases. We show that in some larger databases, the accuracy of Naive-Bayes does not scale up as well as decision trees. We then propose a new algorithm, NBTree, which induces a hybrid of decision-tree classifiers and Naive-Bayes classifiers: the decision-tree nodes contain uni-variate splits as regular decision-trees, but the leaves contain Naive-Bayesian classifiers. The approach retains the interpretability of Naive-Bayes and decision trees, while resulting in classifiers that frequently outperform both constituents, especially in the larger databases tested. 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 #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 #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 #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 #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 #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 #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 #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 #59626. 	[Title] General Bounds on Statistical Query Learning and PAC Learning with Noise via Hypothesis Boosting [Abstract] We derive general bounds on the complexity of learning in the Statistical Query model and in the PAC model with classification noise. We do so by considering the problem of boosting the accuracy of weak learning algorithms which fall within the Statistical Query model. This new model was introduced by Kearns [12] to provide a general framework for efficient PAC learning in the presence of classification noise. We first show a general scheme for boosting the accuracy of weak SQ learning algorithms, proving that weak SQ learning is equivalent to strong SQ learning. The boosting is efficient and is used to show our main result of the first general upper bounds on the complexity of strong SQ learning. Specifically, we derive simultaneous upper bounds with respect to * on the number of queries, O(log 2 1 * ), the Vapnik-Chervonenkis dimension of the query space, O(log 1 * ), and the inverse of the minimum tolerance, O( 1 * log 1 * ). In addition, we show that these general upper bounds are nearly optimal by describing a class of learning problems for which we simultaneously lower bound the number of queries by (log 1 * ) We further apply our boosting results in the SQ model to learning in the PAC model with classification noise. Since nearly all PAC learning algorithms can be cast in the SQ model, we can apply our boosting techniques to convert these PAC algorithms into highly efficient SQ algorithms. By simulating these efficient SQ algorithms in the PAC model with classification noise, we show that nearly all PAC algorithms can be converted into highly efficient PAC algorithms which tolerate classification noise. We give an upper bound on the sample complexity of these noise-tolerant PAC algorithms which is nearly optimal with respect to the noise rate. We also give upper bounds on space complexity and hypothesis size and show that these two measures are in fact independent of the noise rate. We note that the running times of these noise-tolerant PAC algorithms are efficient. This sequence of simulations also demonstrates that it is possible to boost the accuracy of nearly all PAC algorithms even in the presence of noise. This provides a partial answer to an open problem of Schapire [15] and the first theoretical evidence for an empirical result of Drucker, Schapire and Simard [4]. 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 #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 #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 #1272. 	[Title] Learning a set of primitive actions with an Induction of decision trees. Machine Learning, 1(1):81-106, [Abstract]  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.

Paper #1112319 has the title `Self bounding learning algorithms  
` and the 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.
`.
Question: Which category should Paper #1112319 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1112319 has the title `Self bounding learning algorithms  
` and the 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.
`.
Question: Which category should Paper #1112319 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