Above are papers related to the following paper: [Paper_ID] Paper #671293. 	[Title] Selecting Input Variables Using Mutual Information and Nonparametric Density Estimation [Abstract] In learning problems where a connectionist network is trained with a finite sized training set, better generalization performance is often obtained when unneeded weights in the network are eliminated. One source of unneeded weights comes from the inclusion of input variables that provide little information about the output variables. We propose a method for identifying and eliminating these input variables. The method first determines the relationship between input and output variables using nonparametric density estimation and then measures the relevance of input variables using the information theoretic concept of mutual information. We present results from our method on a simple toy problem and a nonlinear time series. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1132418. 	[Title] NONPARAMETRIC SELECTION OF INPUT VARIABLES FOR CONNECTIONIST LEARNING [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1131267. 	[Title] Parallel Markov chain Monte Carlo sampling. [Abstract] Markov chain Monte Carlo (MCMC) samplers have proved remarkably popular as tools for Bayesian computation. However, problems can arise in their application when the density of interest is high dimensional and strongly correlated. In these circumstances the sampler may be slow to traverse the state space and mixing is poor. In this article we offer a partial solution to this problem. The state space of the Markov chain is augmented to accommodate multiple chains in parallel. Updates to individual chains are based around a genetic style crossover operator acting on `parent' states drawn from the population of chains. This process makes efficient use of gradient information implicitly encoded within the distribution of states across the population. Empirical studies support the claim that the crossover operator acting on a parallel population of chains improves mixing. This is illustrated with an example of sampling a high dimensional posterior probability density from a complex predictive model. By adopting a latent variable approach the methodology is extended to deal with variable selection and model averaging in high dimensions. This is illustrated with an example of knot selection for a spline interpolant. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1104261. 	[Title] Using Errors to Create Piecewise Learnable Partitions [Abstract] In this paper we describe an algorithm which exploits the error distribution generated by a learning algorithm in order to break up the domain which is being approximated into piecewise learnable partitions. Traditionally, the error distribution has been neglected in favor of a lump error measure such as RMS. By doing this, however, we lose a lot of important information. The error distribution tells us where the algorithm is doing badly, and if there exists a "ridge" of errors, also tells us how to partition the space so that one part of the space will not interfere with the learning of another. The algorithm builds a variable arity k-d tree whose leaves contain the partitions. Using this tree, new points can be predicted using the correct partition by traversing the tree. We instantiate this algorithm using memory based learners and cross-validation. Please summarise all the given information.

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

Above are papers related to the following paper: [Paper_ID] Paper #1131149. 	[Title] Least Absolute Shrinkage is Equivalent to Quadratic Penalization [Abstract] Adaptive ridge is a special form of ridge regression, balancing the quadratic penalization on each parameter of the model. This paper shows the equivalence between adaptive ridge and lasso (least absolute shrinkage and selection operator). This equivalence states that both procedures produce the same estimate. Least absolute shrinkage can thus be viewed as a particular quadratic penalization. From this observation, we derive an EM algorithm to compute the lasso solution. We finally present a series of applications of this type of algorithm in regres sion problems: kernel regression, additive modeling and neural net training. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #202639. 	[Title] PREDICTING SUNSPOTS AND EXCHANGE RATES WITH CONNECTIONIST NETWORKS [Abstract] We investigate the effectiveness of connectionist networks for predicting the future continuation of temporal sequences. The problem of overfitting, particularly serious for short records of noisy data, is addressed by the method of weight-elimination: a term penalizing network complexity is added to the usual cost function in back-propagation. The ultimate goal is prediction accuracy. We analyze two time series. On the benchmark sunspot series, the networks outperform traditional statistical approaches. We show that the network performance does not deteriorate when there are more input units than needed. Weight-elimination also manages to extract some part of the dynamics of the notoriously noisy currency exchange rates and makes the network solution interpretable. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #145176. 	[Title] Bayesian Non-linear Modelling for the Prediction Competition [Abstract] The 1993 energy prediction competition involved the prediction of a series of building energy loads from a series of environmental input variables. Non-linear regression using `neural networks' is a popular technique for such modeling tasks. Since it is not obvious how large a time-window of inputs is appropriate, or what preprocessing of inputs is best, this can be viewed as a regression problem in which there are many possible input variables, some of which may actually be irrelevant to the prediction of the output variable. Because a finite data set will show random correlations between the irrelevant inputs and the output, any conventional neural network (even with reg-ularisation or `weight decay') will not set the coefficients for these junk inputs to zero. Thus the irrelevant variables will hurt the model's performance. The Automatic Relevance Determination (ARD) model puts a prior over the regression parameters which embodies the concept of relevance. This is done in a simple and `soft' way by introducing multiple regularisation constants, one associated with each input. Using Bayesian methods, the regularisation constants for junk inputs are automatically inferred to be large, preventing those inputs from causing significant overfitting. Please summarise all the given information.

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

Above are papers related to the following paper: [Paper_ID] Paper #1132443. 	[Title] The Observer-Observation Dilemma in Neuro-Forecasting: Reliable Models From Unreliable Data Through CLEARNING [Abstract] This paper introduces the idea of clearning, of simultaneously cleaning data and learning the underlying structure. The cleaning step can be viewed as top-down processing (the model modifies the data), and the learning step can be viewed as bottom-up processing (where the data modifies the model). After discussing the statistical foundation of the proposed method from a maximum likelihood perspective, we apply clearning to a notoriously hard problem where benchmark performances are very well known: the prediction of foreign exchange rates. On the difficult 1993-1994 test period, clearning in conjunction with pruning yields an annualized return between 35 and 40% (out-of-sample), significantly better than an otherwise identical network trained without cleaning. The network was started with 69 inputs and 15 hidden units and ended up with only 39 non-zero weights between inputs and hidden units. The resulting ultra-sparse final architectures obtained with clearning and pruning are immune against overfitting, even on very noisy problems since the cleaned data allow for a simpler model. Apart from the very competitive performance, clearning gives insight into the data: we show how to estimate the overall signal-to-noise ratio of each input variable, and we show that error estimates for each pattern can be used to detect and remove outliers, and to replace missing or corrupted data by cleaned values. Clearning can be used in any nonlinear regression or classification problem. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #124828. 	[Title] Ensemble Training: Some Recent Experiments with Postal Zip Data [Abstract] Recent findings suggest that a classification scheme based on an ensemble of networks is an effective way to address overfitting. We study optimal methods for training an ensemble of networks. Some recent experiments on Postal Zip-code character data suggest that weight decay may not be an optimal method for controlling the variance of a classifier. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #288. 	[Title] Memory Based Stochastic Optimization for Validation and Tuning of Function Approximators [Abstract] This paper focuses on the optimization of hyper-parameters for function approximators. We describe a kind of racing algorithm for continuous optimization problems that spends less time evaluating poor parameter settings and more time honing its estimates in the most promising regions of the parameter space. The algorithm is able to automatically optimize the parameters of a function approximator with less computation time. We demonstrate the algorithm on the problem of finding good parameters for a memory based learner and show the tradeoffs involved in choosing the right amount of computation to spend on each evaluation. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #92065. 	[Title] ADAPTIVE REGULARIZATION [Abstract] Regularization, e.g., in the form of weight decay, is important for training and optimization of neural network architectures. In this work we provide a tool based on asymptotic sampling theory, for iterative estimation of weight decay parameters. The basic idea is to do a gradient descent in the estimated generalization error with respect to the regularization parameters. The scheme is implemented in our Designer Net framework for network training and pruning, i.e., is based on the diagonal Hessian approximation. The scheme does not require essential computational overhead in addition to what is needed for training and pruning. The viability of the approach is demonstrated in an experiment concerning prediction of the chaotic Mackey-Glass series. We find that the optimized weight decays are relatively large for densely connected networks in the initial pruning phase, while they decrease as pruning proceeds. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #671269. 	[Title] Predicting Conditional Probability Distributions: A Connectionist Approach [Abstract] Most traditional prediction techniques deliver the mean of the probability distribution (a single point). For multimodal processes, instead of predicting the mean of the probability distribution, it is important to predict the full distribution. This article presents a new connectionist method to predict the conditional probability distribution in response to an input. The main idea is to transform the problem from a regression to a classification problem. The conditional probability distribution network can perform both direct predictions and iterated predictions, a task which is specific for time series problems. We compare our method to fuzzy logic and discuss important differences, and also demonstrate the architecture on two time series. The first is the benchmark laser series used in the Santa Fe competition, a deterministic chaotic system. The second is a time series from a Markov process which exhibits structure on two time scales. The network produces multimodal predictions for this series. We compare the predictions of the network with a nearest-neighbor predictor and find that the conditional probability network is more than twice as likely a model. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1153703. 	[Title]  [Abstract] Instance-based learning methods explicitly remember all the data that they receive. They usually have no training phase, and only at prediction time do they perform computation. Then, they take a query, search the database for similar datapoints and build an on-line local model (such as a local average or local regression) with which to predict an output value. In this paper we review the advantages of instance based methods for autonomous systems, but we also note the ensuing cost: hopelessly slow computation as the database grows large. We present and evaluate a new way of structuring a database and a new algorithm for accessing it that maintains the advantages of instance-based learning. Earlier attempts to combat the cost of instance-based learning have sacrificed the explicit retention of all data, or been applicable only to instance-based predictions based on a small number of near neighbors or have had to re-introduce an explicit training phase in the form of an interpolative data structure. Our approach builds a multiresolution data structure to summarize the database of experiences at all resolutions of interest simultaneously. This permits us to query the database with the same exibility as a conventional linear search, but at greatly reduced computational cost. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #2354. 	[Title] A Statistical Approach to Solving the EBL Utility Problem [Abstract] Many "learning from experience" systems use information extracted from problem solving experiences to modify a performance element PE, forming a new element PE 0 that can solve these and similar problems more efficiently. However, as transformations that improve performance on one set of problems can degrade performance on other sets, the new PE 0 is not always better than the original PE; this depends on the distribution of problems. We therefore seek the performance element whose expected performance, over this distribution, is optimal. Unfortunately, the actual distribution, which is needed to determine which element is optimal, is usually not known. Moreover, the task of finding the optimal element, even knowing the distribution, is intractable for most interesting spaces of elements. This paper presents a method, palo, that side-steps these problems by using a set of samples to estimate the unknown distribution, and by using a set of transformations to hill-climb to a local optimum. This process is based on a mathematically rigorous form of utility analysis: in particular, it uses statistical techniques to determine whether the result of a proposed transformation will be better than the original system. We also present an efficient way of implementing this learning system in the context of a general class of performance elements, and include empirical evidence that this approach can work effectively. fl Much of this work was performed at the University of Toronto, where it was supported by the Institute for Robotics and Intelligent Systems and by an operating grant from the National Science and Engineering Research Council of Canada. We also gratefully acknowledge receiving many helpful comments from William Cohen, Dave Mitchell, Dale Schuurmans and the anonymous referees. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1152307. 	[Title]  [Abstract] Instance-based learning methods explicitly remember all the data that they receive. They usually have no training phase, and only at prediction time do they perform computation. Then, they take a query, search the database for similar datapoints and build an on-line local model (such as a local average or local regression) with which to predict an output value. In this paper we review the advantages of instance based methods for autonomous systems, but we also note the ensuing cost: hopelessly slow computation as the database grows large. We present and evaluate a new way of structuring a database and a new algorithm for accessing it that maintains the advantages of instance-based learning. Earlier attempts to combat the cost of instance-based learning have sacrificed the explicit retention of all data, or been applicable only to instance-based predictions based on a small number of near neighbors or have had to re-introduce an explicit training phase in the form of an interpolative data structure. Our approach builds a multiresolution data structure to summarize the database of experiences at all resolutions of interest simultaneously. This permits us to query the database with the same exibility as a conventional linear search, but at greatly reduced computational cost. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #641976. 	[Title] A comparison of some error estimates for neural network models  Summary [Abstract] We discuss a number of methods for estimating the standard error of predicted values from a multi-layer perceptron. These methods include the delta method based on the Hessian, bootstrap estimators, and the "sandwich" estimator. The methods are described and compared in a number of examples. We find that the bootstrap methods perform best, partly because they capture variability due to the choice of starting weights. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #239800. 	[Title] Ensemble Learning and Evidence Maximization [Abstract] Ensemble learning by variational free energy minimization is a tool introduced to neural networks by Hinton and van Camp in which learning is described in terms of the optimization of an ensemble of parameter vectors. The optimized ensemble is an approximation to the posterior probability distribution of the parameters. This tool has now been applied to a variety of statistical inference problems. In this paper I study a linear regression model with both parameters and hyper-parameters. I demonstrate that the evidence approximation for the optimization of regularization constants can be derived in detail from a free energy minimization viewpoint. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #65212. 	[Title] Bayesian Training of Backpropagation Networks by the Hybrid Monte Carlo Method [Abstract] It is shown that Bayesian training of backpropagation neural networks can feasibly be performed by the "Hybrid Monte Carlo" method. This approach allows the true predictive distribution for a test case given a set of training cases to be approximated arbitrarily closely, in contrast to previous approaches which approximate the posterior weight distribution by a Gaussian. In this work, the Hybrid Monte Carlo method is implemented in conjunction with simulated annealing, in order to speed relaxation to a good region of parameter space. The method has been applied to a test problem, demonstrating that it can produce good predictions, as well as an indication of the uncertainty of these predictions. Appropriate weight scaling factors are found automatically. By applying known techniques for calculation of "free energy" differences, it should also be possible to compare the merits of different network architectures. The work described here should also be applicable to a wide variety of statistical models other than neural networks. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #63549. 	[Title] A Practical Monte Carlo Implementation of Bayesian Learning [Abstract]  Please summarise all the given information.

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

Above are papers related to the following paper: [Paper_ID] Paper #1105344. 	[Title] In Advances in Neural Information Processing Systems 8  Gaussian Processes for Regression [Abstract] The Bayesian analysis of neural networks is difficult because a simple prior over weights implies a complex prior distribution over functions. In this paper we investigate the use of Gaussian process priors over functions, which permit the predictive Bayesian analysis for fixed values of hyperparameters to be carried out exactly using matrix operations. Two methods, using optimization and averaging (via Hybrid Monte Carlo) over hyperparameters have been tested on a number of challenging problems and have produced excellent results. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1104449. 	[Title] Using Neural Networks for Descriptive Statistical Analysis of Educational Data [Abstract] In this paper we discuss the methodological issues of using a class of neural networks called Mixture Density Networks (MDN) for discriminant analysis. MDN models have the advantage of having a rigorous probabilistic interpretation, and they have proven to be a viable alternative as a classification procedure in discrete domains. We will address both the classification and interpretive aspects of discriminant analysis, and compare the approach to the traditional method of linear discrimin- ants as implemented in standard statistical packages. We show that the MDN approach adopted performs well in both aspects. Many of the observations made are not restricted to the particular case at hand, and are applicable to most applications of discriminant analysis in educational research. fl URL: http://www.cs.Helsinki.FI/research/cosco/ Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1152194. 	[Title]  [Abstract] Draft A Brief Introduction to Neural Networks Richard D. De Veaux Lyle H. Ungar Williams College University of Pennsylvania Abstract Artificial neural networks are being used with increasing frequency for high dimensional problems of regression or classification. This article provides a tutorial overview of neural networks, focusing on back propagation networks as a method for approximating nonlinear multivariable functions. We explain, from a statistician's vantage point, why neural networks might be attractive and how they compare to other modern regression techniques. KEYWORDS: nonparametric regression; function approximation; backpropagation. 1 Introduction Networks that mimic the way the brain works; computer programs that actually LEARN patterns; forecasting without having to know statistics. These are just some of the many claims and attractions of artificial neural networks. Neural networks (we will henceforth drop the term artificial, unless we need to distinguish them from biological neural networks) seem to be everywhere these days, and at least in their advertising, are able to do all that statistics can do without all the fuss and bother of having to do anything except buy a piece of software. Neural networks have been successfully used for many different applications including robotics, chemical process control, speech recognition, optical character recognition, credit card fraud detection, interpretation of chemical spectra and vision for autonomous navigation of vehicles. (Pointers to the literature are given at the end of this article.) In this article we will attempt to explain how one particular type of neural network, feedforward networks with sigmoidal activation functions ("backpropagation networks") actually works, how it is "trained", and how it compares with some more well known statistical techniques. As an example of why someone would want to use a neural network, consider the problem of recognizing hand written ZIP codes on letters. This is a classification problem, where the 1 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1106370. 	[Title] The Effective Size of a Neural Network: A Principal Component Approach [Abstract] Often when learning from data, one attaches a penalty term to a standard error term in an attempt to prefer simple models and prevent overfitting. Current penalty terms for neural networks, however, often do not take into account weight interaction. This is a critical drawback since the effective number of parameters in a network usually differs dramatically from the total number of possible parameters. In this paper, we present a penalty term that uses Principal Component Analysis to help detect functional redundancy in a neural network. Results show that our new algorithm gives a much more accurate estimate of network complexity than do standard approaches. As a result, our new term should be able to improve techniques that make use of a penalty term, such as weight decay, weight pruning, feature selection, Bayesian, and prediction-risk tech niques. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1152448. 	[Title]  [Abstract] Instance-based learning methods explicitly remember all the data that they receive. They usually have no training phase, and only at prediction time do they perform computation. Then, they take a query, search the database for similar datapoints and build an on-line local model (such as a local average or local regression) with which to predict an output value. In this paper we review the advantages of instance based methods for autonomous systems, but we also note the ensuing cost: hopelessly slow computation as the database grows large. We present and evaluate a new way of structuring a database and a new algorithm for accessing it that maintains the advantages of instance-based learning. Earlier attempts to combat the cost of instance-based learning have sacrificed the explicit retention of all data, or been applicable only to instance-based predictions based on a small number of near neighbors or have had to re-introduce an explicit training phase in the form of an interpolative data structure. Our approach builds a multiresolution data structure to summarize the database of experiences at all resolutions of interest simultaneously. This permits us to query the database with the same exibility as a conventional linear search, but at greatly reduced computational cost. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #79809. 	[Title] MDL and MML Similarities and Differences (Introduction to Minimum Encoding Inference Part III) [Abstract] Tech Report 207 Department of Computer Science, Monash University, Clayton, Vic. 3168, Australia Abstract: This paper continues the introduction to minimum encoding inductive inference given by Oliver and Hand. This series of papers was written with the objective of providing an introduction to this area for statisticians. We describe the message length estimates used in Wallace's Minimum Message Length (MML) inference and Rissanen's Minimum Description Length (MDL) inference. The differences in the message length estimates of the two approaches are explained. The implications of these differences for applications are discussed. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #672070. 	[Title] Evaluating Neural Network Predictors by Bootstrapping [Abstract] We present a new method, inspired by the bootstrap, whose goal it is to determine the quality and reliability of a neural network predictor. Our method leads to more robust forecasting along with a large amount of statistical information on forecast performance that we exploit. We exhibit the method in the context of multi-variate time series prediction on financial data from the New York Stock Exchange. It turns out that the variation due to different resamplings (i.e., splits between training, cross-validation, and test sets) is significantly larger than the variation due to different network conditions (such as architecture and initial weights). Furthermore, this method allows us to forecast a probability distribution, as opposed to the traditional case of just a single value at each time step. We demonstrate this on a strictly held-out test set that includes the 1987 stock market crash. We also compare the performance of the class of neural networks to identically bootstrapped linear models. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #672071. 	[Title] Predictions with Confidence Intervals (Local Error Bars) [Abstract] We present a new method for obtaining local error bars, i.e., estimates of the confidence in the predicted value that depend on the input. We approach this problem of nonlinear regression in a maximum likelihood framework. We demonstrate our technique first on computer generated data with locally varying, normally distributed target noise. We then apply it to the laser data from the Santa Fe Time Series Competition. Finally, we extend the technique to estimate error bars for iterated predictions, and apply it to the exact competition task where it gives the best performance to date. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #197452. 	[Title] Best-First Model Merging for Dynamic Learning and Recognition [Abstract] Best-first model merging is a general technique for dynamically choosing the structure of a neural or related architecture while avoiding overfitting. It is applicable to both learning and recognition tasks and often generalizes significantly better than fixed structures. We demonstrate the approach applied to the tasks of choosing radial basis functions for function learning, choosing local affine models for curve and constraint surface modelling, and choosing the structure of a balltree or bumptree to maximize efficiency of access. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #23116. 	[Title] Bayesian Methods for Adaptive Models [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1152975. 	[Title]  [Abstract] Instance-based learning methods explicitly remember all the data that they receive. They usually have no training phase, and only at prediction time do they perform computation. Then, they take a query, search the database for similar datapoints and build an on-line local model (such as a local average or local regression) with which to predict an output value. In this paper we review the advantages of instance based methods for autonomous systems, but we also note the ensuing cost: hopelessly slow computation as the database grows large. We present and evaluate a new way of structuring a database and a new algorithm for accessing it that maintains the advantages of instance-based learning. Earlier attempts to combat the cost of instance-based learning have sacrificed the explicit retention of all data, or been applicable only to instance-based predictions based on a small number of near neighbors or have had to re-introduce an explicit training phase in the form of an interpolative data structure. Our approach builds a multiresolution data structure to summarize the database of experiences at all resolutions of interest simultaneously. This permits us to query the database with the same exibility as a conventional linear search, but at greatly reduced computational cost. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #40151. 	[Title] Hoeffding Races: Accelerating Model Selection Search for Classification and Function Approximation [Abstract] Selecting a good model of a set of input points by cross validation is a computationally intensive process, especially if the number of possible models or the number of training points is high. Techniques such as gradient descent are helpful in searching through the space of models, but problems such as local minima, and more importantly, lack of a distance metric between various models reduce the applicability of these search methods. Hoeffding Races is a technique for finding a good model for the data by quickly discarding bad models, and concentrating the computational effort at differentiating between the better ones. This paper focuses on the special case of leave-one-out cross validation applied to memory-based learning algorithms, but we also argue that it is applicable to any class of model selection problems. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #131042. 	[Title] Efficient Implementation of Gaussian Processes [Abstract] Neural networks and Bayesian inference provide a useful framework within which to solve regression problems. However their parameterization means that the Bayesian analysis of neural networks can be difficult. In this paper, we investigate a method for regression using Gaussian process priors which allows exact Bayesian analysis using matrix manipulations. We discuss the workings of the method in detail. We will also detail a range of mathematical and numerical techniques that are useful in applying Gaussian processes to general problems including efficient approximate matrix inversion methods developed by Skilling. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #95719. 	[Title] Choice of Basis for Laplace Approximation [Abstract] Maximum a posteriori optimization of parameters and the Laplace approximation for the marginal likelihood are both basis-dependent methods. This note compares two choices of basis for models parameterized by probabilities, showing that it is possible to improve on the traditional choice, the probability simplex, by transforming to the `softmax' basis. Please summarise all the given information.

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

Above are papers related to the following paper: [Paper_ID] Paper #145134. 	[Title] Brief Papers Computing Second Derivatives in Feed-Forward Networks: A Review [Abstract] The calculation of second derivatives is required by recent training and analysis techniques of connectionist networks, such as the elimination of superfluous weights, and the estimation of confidence intervals both for weights and network outputs. We here review and develop exact and approximate algorithms for calculating second derivatives. For networks with jwj weights, simply writing the full matrix of second derivatives requires O(jwj 2 ) operations. For networks of radial basis units or sigmoid units, exact calculation of the necessary intermediate terms requires of the order of 2h + 2 backward/forward-propagation passes where h is the number of hidden units in the network. We also review and compare three approximations (ignoring some components of the second derivative, numerical differentiation, and scoring). Our algorithms apply to arbitrary activation functions, networks, and error functions (for instance, with connections that skip layers, or radial basis functions, or cross-entropy error and Softmax units, etc.). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1106671. 	[Title] Bayesian Learning in Feed Forward Neural Networks [Abstract] Bayesian methods are applicable to complex modeling tasks. In this review, the principles of Bayesian inference are presented and applied to neural network models. Several approximate implementations are discussed, and their advantages over conventional fre-quentist model training and selection are outlined. It is argued that Bayesian methods are preferable to traditional approaches, although empirical evidence for this is still sparse. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #19697. 	[Title] Keeping Neural Networks Simple by Minimizing the Description Length of the Weights [Abstract] Supervised neural networks generalize well if there is much less information in the weights than there is in the output vectors of the training cases. So during learning, it is important to keep the weights simple by penalizing the amount of information they contain. The amount of information in a weight can be controlled by adding Gaussian noise and the noise level can be adapted during learning to optimize the trade-off between the expected squared error of the network and the amount of information in the weights. We describe a method of computing the derivatives of the expected squared error and of the amount of information in the noisy weights in a network that contains a layer of non-linear hidden units. Provided the output units are linear, the exact derivatives can be computed efficiently without time-consuming Monte Carlo simulations. The idea of minimizing the amount of information that is required to communicate the weights of a neural network leads to a number of interesting schemes for encoding the weights. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #131318. 	[Title] FLAT MINIMA Neural Computation 9(1):1-42 (1997) [Abstract] We present a new algorithm for finding low complexity neural networks with high generalization capability. The algorithm searches for a "flat" minimum of the error function. A flat minimum is a large connected region in weight-space where the error remains approximately constant. An MDL-based, Bayesian argument suggests that flat minima correspond to "simple" networks and low expected overfitting. The argument is based on a Gibbs algorithm variant and a novel way of splitting generalization error into underfitting and overfitting error. Unlike many previous approaches, ours does not require Gaussian assumptions and does not depend on a "good" weight prior instead we have a prior over input/output functions, thus taking into account net architecture and training set. Although our algorithm requires the computation of second order derivatives, it has backprop's order of complexity. Automatically, it effectively prunes units, weights, and input lines. Various experiments with feedforward and recurrent nets are described. In an application to stock market prediction, flat minimum search outperforms (1) conventional backprop, (2) weight decay, (3) "optimal brain surgeon" / "optimal brain damage". We also provide pseudo code of the algorithm (omitted from the NC-version). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1123576. 	[Title] Density Networks and their Application to Protein Modelling [Abstract] I define a latent variable model in the form of a neural network for which only target outputs are specified; the inputs are unspecified. Although the inputs are missing, it is still possible to train this model by placing a simple probability distribution on the unknown inputs and maximizing the probability of the data given the parameters. The model can then discover for itself a description of the data in terms of an underlying latent variable space of lower dimensionality. I present preliminary results of the application of these models to protein data. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1154042. 	[Title] 5 Bayesian estimation 5.1 Introduction [Abstract] This chapter takes a different standpoint to address the problem of learning. We will here reason only in terms of probability, and make extensive use of the chain rule known as "Bayes' rule". A fast definition of the basics in probability is provided in appendix A for quick reference. Most of this chapter is a review of the methods of Bayesian learning applied to our modelling purposes. Some original analyses and comments are also provided in section 5.8, 5.11 and 5.12. There is a latent rivalry between "Bayesian" and "Orthodox" statistics. It is by no means our intention to enter this kind of controversy. We are perfectly willing to accept orthodox as well as unorthodox methods, as long as they are scientifically sound and provide good results when applied to learning tasks. The same disclaimer applies to the two frameworks presented here. They have been the object of heated controversy in the past 3 years in the neural networks community. We will not take side, but only present both frameworks, with their strong points and their weaknesses. In the context of this work, the "Bayesian frameworks" are especially interesting as the provide some continuous update rules that can be used during regularised cost minimisation to yield an automatic selection of the regularisation level. Unlike the methods presented in chapter 3, it is not necessary to try several regularisation levels and perform as many optimisations. The Bayesian framework is the only one in which training is achieved through a one-pass optimisation procedure. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #49660. 	[Title] Feature Subset Selection as Search with Probabilistic Estimates [Abstract] Irrelevant features and weakly relevant features may reduce the comprehensibility and accuracy of concepts induced by supervised learning algorithms. We formulate the search for a feature subset as an abstract search problem with probabilistic estimates. Searching a space using an evaluation function that is a random variable requires trading off accuracy of estimates for increased state exploration. We show how recent feature subset selection algorithms in the machine learning literature fit into this search problem as simple hill climbing approaches, and conduct a small experiment using a best-first search technique. Please summarise all the given information.

Paper #671293 has the title `Selecting Input Variables Using Mutual Information and Nonparametric Density Estimation  
` and the abstract `In learning problems where a connectionist network is trained with a finite sized training set, better generalization performance is often obtained when unneeded weights in the network are eliminated. One source of unneeded weights comes from the inclusion of input variables that provide little information about the output variables. We propose a method for identifying and eliminating these input variables. The method first determines the relationship between input and output variables using nonparametric density estimation and then measures the relevance of input variables using the information theoretic concept of mutual information. We present results from our method on a simple toy problem and a nonlinear time series.
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Question: Which category should Paper #671293 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #671293 has the title `Selecting Input Variables Using Mutual Information and Nonparametric Density Estimation  
` and the abstract `In learning problems where a connectionist network is trained with a finite sized training set, better generalization performance is often obtained when unneeded weights in the network are eliminated. One source of unneeded weights comes from the inclusion of input variables that provide little information about the output variables. We propose a method for identifying and eliminating these input variables. The method first determines the relationship between input and output variables using nonparametric density estimation and then measures the relevance of input variables using the information theoretic concept of mutual information. We present results from our method on a simple toy problem and a nonlinear time series.
`.
Question: Which category should Paper #671293 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: Probabilistic_Methods