Above are papers related to the following paper: [Paper_ID] Paper #753047. 	[Title] The Central Classifier Bound ANew Error Bound for the Classifier Chosen by Early Stopping Key [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #4330. 	[Title] Hierarchical Mixtures of Experts and the EM Algorithm [Abstract] We present a tree-structured architecture for supervised learning. The statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM's). Learning is treated as a maximum likelihood problem; in particular, we present an Expectation-Maximization (EM) algorithm for adjusting the parameters of the architecture. We also develop an on-line learning algorithm in which the parameters are updated incrementally. Comparative simulation results are presented in the robot dynamics domain. This report describes research done at the Dept. of Brain and Cognitive Sciences, the Center for Biological and Computational Learning, and the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for CBCL is provided in part by a grant from the NSF (ASC-9217041). Support for the laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Dept. of Defense. The authors were supported by a grant from the McDonnell-Pew Foundation, by a grant from ATR Human Information Processing Research Laboratories, by a grant from Siemens Corporation, by by grant IRI-9013991 from the National Science Foundation, by grant N00014-90-J-1942 from the Office of Naval Research, and by NSF grant ECS-9216531 to support an Initiative in Intelligent Control at MIT. Michael I. Jordan is a NSF Presidential Young Investigator. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #753070. 	[Title] Similar Classifiers and VC Error Bounds [Abstract] We improve error bounds based on VC analysis for classes with sets of similar classifiers. We apply the new error bounds to separating planes and artificial neural networks. Key words machine learning, learning theory, generalization, Vapnik-Chervonenkis, separating planes, neural networks. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #753264. 	[Title] Improved Uniform Test Error Bounds [Abstract] We derive distribution-free uniform test error bounds that improve on VC-type bounds for validation. We show how to use knowledge of test inputs to improve the bounds. The bounds are sharp, but they require intense computation. We introduce a method to trade sharpness for speed of computation. Also, we compute the bounds for several test cases. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #753265. 	[Title] Validation of Average Error Rate Over Classifiers [Abstract] We examine methods to estimate the average and variance of test error rates over a set of classifiers. We begin with the process of drawing a classifier at random for each example. Given validation data, the average test error rate can be estimated as if validating a single classifier. Given the test example inputs, the variance can be computed exactly. Next, we consider the process of drawing a classifier at random and using it on all examples. Once again, the expected test error rate can be validated as if validating a single classifier. However, the variance must be estimated by validating all classifers, which yields loose or uncertain bounds. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #767763. 	[Title] Partition-Based Uniform Error Bounds [Abstract] This paper develops probabilistic bounds on out-of-sample error rates for several classifiers using a single set of in-sample data. The bounds are based on probabilities over partitions of the union of in-sample and out-of-sample data into in-sample and out-of-sample data sets. The bounds apply when in-sample and out-of-sample data are drawn from the same distribution. Partition-based bounds are stronger than VC-type bounds, but they require more computation. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1136631. 	[Title] Improved Hoeffding-Style Performance Guarantees for Accurate Classifiers [Abstract] We extend Hoeffding bounds to develop superior probabilistic performance guarantees for accurate classifiers. The original Hoeffding bounds on classifier accuracy depend on the accuracy itself as a parameter. Since the accuracy is not known a priori, the parameter value that gives the weakest bounds is used. We present a method that loosely bounds the accuracy using the old method and uses the loose bound as an improved parameter value for tighter bounds. We show how to use the bounds in practice, and we generalize the bounds for individual classifiers to form uniform bounds over multiple classifiers. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1136634. 	[Title] Validation of Voting Committees [Abstract] This paper contains a method to bound the test errors of voting committees with members chosen from a pool of trained classifiers. There are so many prospective committees that validating them directly does not achieve useful error bounds. Because there are fewer classifiers than prospective committees, it is better to validate the classifiers individually, then use linear programming to infer committee error bounds. We test the method using credit card data. Also, we extend the method to infer bounds for classifiers in general. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #175548. 	[Title] Neural Networks with Quadratic VC Dimension [Abstract] This paper shows that neural networks which use continuous activation functions have VC dimension at least as large as the square of the number of weights w. This result settles a long-standing open question, namely whether the well-known O(w log w) bound, known for hard-threshold nets, also held for more general sigmoidal nets. Implications for the number of samples needed for valid generalization are discussed. Please summarise all the given information.

Paper #753047 has the title `The Central Classifier Bound ANew Error Bound for the Classifier Chosen by Early Stopping Key
` and the abstract `nan`.
Question: Which category should Paper #753047 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #753047 has the title `The Central Classifier Bound ANew Error Bound for the Classifier Chosen by Early Stopping Key
` and the abstract `nan`.
Question: Which category should Paper #753047 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