Above are papers related to the following paper: [Paper_ID] Paper #193932. 	[Title] Lessons in Neural Network Training: Overfitting Lessons in Neural Network Training: Overfitting May be Harder [Abstract] For many reasons, neural networks have become very popular AI machine learning models. Two of the most important aspects of machine learning models are how well the model generalizes to unseen data, and how well the model scales with problem complexity. Using a controlled task with known optimal training error, we investigate the convergence of the backpropagation (BP) algorithm. We find that the optimal solution is typically not found. Furthermore, we observe that networks larger than might be expected can result in lower training and generalization error. This result is supported by another real world example. We further investigate the training behavior by analyzing the weights in trained networks (excess degrees of freedom are seen to do little harm and to aid convergence), and contrasting the interpolation characteristics of multi-layer perceptron neural networks (MLPs) and polynomial models (overfitting behavior is very different the MLP is often biased towards smoother solutions). Finally, we analyze relevant theory outlining the reasons for significant practical differences. These results bring into question common beliefs about neural network training regarding convergence and optimal network size, suggest alternate guidelines for practical use (lower fear of excess degrees of freedom), and help to direct future work (e.g. methods for creation of more parsimonious solutions, importance of the MLP/BP bias and possibly worse performance of improved training algorithms). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #105856. 	[Title] Vapnik-Chervonenkis Dimension of Recurrent Neural Networks [Abstract] Most of the work on the Vapnik-Chervonenkis dimension of neural networks has been focused on feedforward networks. However, recurrent networks are also widely used in learning applications, in particular when time is a relevant parameter. This paper provides lower and upper bounds for the VC dimension of such networks. Several types of activation functions are discussed, including threshold, polynomial, piecewise-polynomial and sigmoidal functions. The bounds depend on two independent parameters: the number w of weights in the network, and the length k of the input sequence. In contrast, for feedforward networks, VC dimension bounds can be expressed as a function of w only. An important difference between recurrent and feedforward nets is that a fixed recurrent net can receive inputs of arbitrary length. Therefore we are particularly interested in the case k w. Ignoring multiplicative constants, the main results say roughly the following: * For architectures with activation = any fixed nonlinear polynomial, the VC dimension is wk. * For architectures with activation = any fixed piecewise polynomial, the VC dimension is between wk and w 2 k. * For architectures with activation = H (threshold nets), the VC dimension is between w log(k=w) and minfwk log wk; w 2 + w log wkg. * For the standard sigmoid (x) = 1=(1 + e x ), the VC dimension is between wk and w 4 k 2 . An earlier version of this paper has appeared in Proc. 3rd European Workshop on Computational Learning Theory, LNCS 1208, pages 223-237, Springer, 1997. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6784. 	[Title] A Quantitative Study of Experimental Evaluations of Neural Network Learning Algorithms: Current Research Practice [Abstract] 190 articles about neural network learning algorithms published in 1993 and 1994 are examined for the amount of experimental evaluation they contain. 29% of them employ not even a single realistic or real learning problem. Only 8% of the articles present results for more than one problem using real world data. Furthermore, one third of all articles do not present any quantitative comparison with a previously known algorithm. These results suggest that we should strive for better assessment practices in neural network learning algorithm research. For the long-term benefit of the field, the publication standards should be raised in this respect and easily accessible collections of benchmark problems should be built. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #100197. 	[Title] Neural Networks and Statistical Models Proceedings of the Nineteenth Annual SAS Users Group International Conference, [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6775. 	[Title] Statistical Evaluation of Neural Network Experiments: Minimum Requirements and Current Practice [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1111240. 	[Title] On the Distribution of Performance from Multiple Neural Network Trials, On the Distribution of Performance [Abstract] Andrew D. Back was with the Department of Electrical and Computer Engineering, University of Queensland. St. Lucia, Australia. He is now with the Brain Information Processing Group, Frontier Research Program, RIKEN, The Institute of Physical and Chemical Research, 2-1 Hirosawa, Wako-shi, Saitama 351-01, Japan Abstract The performance of neural network simulations is often reported in terms of the mean and standard deviation of a number of simulations performed with different starting conditions. However, in many cases, the distribution of the individual results does not approximate a Gaussian distribution, may not be symmetric, and may be multimodal. We present the distribution of results for practical problems and show that assuming Gaussian distributions can significantly affect the interpretation of results, especially those of comparison studies. For a controlled task which we consider, we find that the distribution of performance is skewed towards better performance for smoother target functions and skewed towards worse performance Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #105865. 	[Title] Statistical Ideas for Selecting Network Architectures [Abstract] Choosing the architecture of a neural network is one of the most important problems in making neural networks practically useful, but accounts of applications usually sweep these details under the carpet. How many hidden units are needed? Should weight decay be used, and if so how much? What type of output units should be chosen? And so on. We address these issues within the framework of statistical theory for model This paper is principally concerned with architecture selection issues for feed-forward neural networks (also known as multi-layer perceptrons). Many of the same issues arise in selecting radial basis function networks, recurrent networks and more widely. These problems occur in a much wider context within statistics, and applied statisticians have been selecting and combining models for decades. Two recent discussions are [4, 5]. References [3, 20, 21, 22] discuss neural networks from a statistical perspective. choice, which provides a number of workable approximate answers. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #193931. 	[Title] What Size Neural Network Gives Optimal Generalization? Convergence Properties of Backpropagation [Abstract] Technical Report UMIACS-TR-96-22 and CS-TR-3617 Institute for Advanced Computer Studies University of Maryland College Park, MD 20742 Abstract One of the most important aspects of any machine learning paradigm is how it scales according to problem size and complexity. Using a task with known optimal training error, and a pre-specified maximum number of training updates, we investigate the convergence of the backpropagation algorithm with respect to a) the complexity of the required function approximation, b) the size of the network in relation to the size required for an optimal solution, and c) the degree of noise in the training data. In general, for a) the solution found is worse when the function to be approximated is more complex, for b) oversized networks can result in lower training and generalization error in certain cases, and for c) the use of committee or ensemble techniques can be more beneficial as the level of noise in the training data is increased. For the experiments we performed, we do not obtain the optimal solution in any case. We further support the observation that larger networks can produce better training and generalization error using a face recognition example where a network with many more parameters than training points generalizes better than smaller networks. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #350319. 	[Title] Averaging and Data Snooping [Abstract] Presenting and Analyzing the Results of AI Experiments: Data Averaging and Data Snooping, Proceedings of the Fourteenth National Conference on Artificial Intelligence, AAAI-97, AAAI Press, Menlo Park, California, pp. 362367, 1997. Copyright AAAI. Presenting and Analyzing the Results of AI Experiments: Abstract Experimental results reported in the machine learning AI literature can be misleading. This paper investigates the common processes of data averaging (reporting results in terms of the mean and standard deviation of the results from multiple trials) and data snooping in the context of neural networks, one of the most popular AI machine learning models. Both of these processes can result in misleading results and inaccurate conclusions. We demonstrate how easily this can happen and propose techniques for avoiding these very important problems. For data averaging, common presentation assumes that the distribution of individual results is Gaussian. However, we investigate the distribution for common problems and find that it often does not approximate the Gaussian distribution, may not be symmetric, and may be multimodal. We show that assuming Gaussian distributions can significantly affect the interpretation of results, especially those of comparison studies. For a controlled task, we find that the distribution of performance is skewed towards better performance for smoother target functions and skewed towards worse performance for more complex target functions. We propose new guidelines for reporting performance which provide more information about the actual distribution (e.g. box-whiskers plots). For data snooping, we demonstrate that optimization of performance via experimentation with multiple parameters can lead to significance being assigned to results which are due to chance. We suggest that precise descriptions of experimental techniques can be very important to the evaluation of results, and that we need to be aware of potential data snooping biases when formulating these experimental techniques (e.g. selecting the test procedure). Additionally, it is important to only rely on appropriate statistical tests and to ensure that any assumptions made in the tests are valid (e.g. normality of the distribution). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3191. 	[Title] Model Selection and Accounting for Model Uncertainty in Linear Regression Models [Abstract] 1 Adrian E. Raftery is Professor of Statistics and Sociology, David Madigan is Assistant Professor of Statistics, and Jennifer Hoeting is a Ph.D. Candidate, all at the Department of Statistics, GN-22, University of Washington, Seattle, WA 98195. The research of Raftery and Hoeting was supported by ONR Contract N-00014-91-J-1074. Madigan's research was partially supported by NSF grant no. DMS 92111627. The authors are grateful to Danika Lew for research assistance. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #14807. 	[Title] Exponentially many local minima for single neurons [Abstract] We show that for a single neuron with the logistic function as the transfer function the number of local minima of the error function based on the square loss can grow exponentially in the dimension. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3192. 	[Title] Bayesian Graphical Models for Discrete Data [Abstract] z York's research was supported by a NSF graduate fellowship. The authors are grateful to Julian Besag, David Bradshaw, Jeff Bradshaw, James Carlsen, David Draper, Ivar Heuch, Robert Kass, Augustine Kong, Steffen Lauritzen, Adrian Raftery, and James Zidek for helpful comments and discussions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #193918. 	[Title] A Unifying View of Some Training Algorithms for Multilayer Perceptrons with FIR Filter Synapses [Abstract] Recent interest has come about in deriving various neural network architectures for modelling time-dependent signals. A number of algorithms have been published for multilayer perceptrons with synapses described by finite impulse response (FIR) and infinite impulse response (IIR) filters (the latter case is also known as Locally Recurrent Globally Feedforward Networks). The derivations of these algorithms have used different approaches in calculating the gradients, and in this note, we present a short, but unifying account of how these different algorithms compare for the FIR case, both in derivation, and performance. New algorithms are subsequently presented. Simulation results have been performed to benchmark these algorithms. In this note, results are compared for the Mackey-Glass chaotic time series against a number of other methods including a standard multilayer perceptron, and a local approximation method. Please summarise all the given information.

Paper #193932 has the title `Lessons in Neural Network Training: Overfitting Lessons in Neural Network Training: Overfitting May be Harder
` and the abstract `For many reasons, neural networks have become very popular AI machine learning models. Two of the most important aspects of machine learning models are how well the model generalizes to unseen data, and how well the model scales with problem complexity. Using a controlled task with known optimal training error, we investigate the convergence of the backpropagation (BP) algorithm. We find that the optimal solution is typically not found. Furthermore, we observe that networks larger than might be expected can result in lower training and generalization error. This result is supported by another real world example. We further investigate the training behavior by analyzing the weights in trained networks (excess degrees of freedom are seen to do little harm and to aid convergence), and contrasting the interpolation characteristics of multi-layer perceptron neural networks (MLPs) and polynomial models (overfitting behavior is very different the MLP is often biased towards smoother solutions). Finally, we analyze relevant theory outlining the reasons for significant practical differences. These results bring into question common beliefs about neural network training regarding convergence and optimal network size, suggest alternate guidelines for practical use (lower fear of excess degrees of freedom), and help to direct future work (e.g. methods for creation of more parsimonious solutions, importance of the MLP/BP bias and possibly worse performance of improved training algorithms). 
`.
Question: Which category should Paper #193932 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #193932 has the title `Lessons in Neural Network Training: Overfitting Lessons in Neural Network Training: Overfitting May be Harder
` and the abstract `For many reasons, neural networks have become very popular AI machine learning models. Two of the most important aspects of machine learning models are how well the model generalizes to unseen data, and how well the model scales with problem complexity. Using a controlled task with known optimal training error, we investigate the convergence of the backpropagation (BP) algorithm. We find that the optimal solution is typically not found. Furthermore, we observe that networks larger than might be expected can result in lower training and generalization error. This result is supported by another real world example. We further investigate the training behavior by analyzing the weights in trained networks (excess degrees of freedom are seen to do little harm and to aid convergence), and contrasting the interpolation characteristics of multi-layer perceptron neural networks (MLPs) and polynomial models (overfitting behavior is very different the MLP is often biased towards smoother solutions). Finally, we analyze relevant theory outlining the reasons for significant practical differences. These results bring into question common beliefs about neural network training regarding convergence and optimal network size, suggest alternate guidelines for practical use (lower fear of excess degrees of freedom), and help to direct future work (e.g. methods for creation of more parsimonious solutions, importance of the MLP/BP bias and possibly worse performance of improved training algorithms). 
`.
Question: Which category should Paper #193932 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: Neural_Networks