Above are papers related to the following paper: [Paper_ID] Paper #24974. 	[Title] EVALUATION OF GAUSSIAN PROCESSES AND OTHER METHODS FOR NON-LINEAR REGRESSION [Abstract]  Please summarise all the given information.

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

Above are papers related to the following paper: [Paper_ID] Paper #1104258. 	[Title] Regression with Input-dependent Noise: A Gaussian Process Treatment [Abstract] Technical Report NCRG/98/002, available from http://www.ncrg.aston.ac.uk/ To appear in Advances in Neural Information Processing Systems 10 eds. M. I. Jordan, M. J. Kearns and S. A. Solla. Lawrence Erlbaum (1998). Abstract Gaussian processes provide natural non-parametric prior distributions over regression functions. In this paper we consider regression problems where there is noise on the output, and the variance of the noise depends on the inputs. If we assume that the noise is a smooth function of the inputs, then it is natural to model the noise variance using a second Gaussian process, in addition to the Gaussian process governing the noise-free output value. We show that prior uncertainty about the parameters controlling both processes can be handled and that the posterior distribution of the noise rate can be sampled from using Markov chain Monte Carlo methods. Our results on a synthetic data set give a posterior noise variance that well-approximates the true variance. 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 #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 #34315. 	[Title] Gaussian Processes for Bayesian Classification via Hybrid Monte Carlo [Abstract] The full Bayesian method for applying neural networks to a prediction problem is to set up the prior/hyperprior structure for the net and then perform the necessary integrals. However, these integrals are not tractable analytically, and Markov Chain Monte Carlo (MCMC) methods are slow, especially if the parameter space is high-dimensional. Using Gaussian processes we can approximate the weight space integral analytically, so that only a small number of hyperparameters need be integrated over by MCMC methods. We have applied this idea to classification problems, obtaining ex cellent results on the real-world problems investigated so far. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1103979. 	[Title] Prior Information and Generalized Questions [Abstract] This report describes research done within the Center for Biological and Computational Learning in the Department of Brain and Cognitive Sciences at the Massachusetts Institute of Technology. This research is sponsored by a grant from National Science Foundation under contract ASC-9217041 and a grant from ONR/ARPA under contract N00014-92-J-1879. The author was supported by a Postdoctoral Fellowship (Le 1014/1-1) from the Deutsche Forschungsgemeinschaft and a NSF/CISE Postdoctoral Fellowship. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #910. 	[Title] Learning networks for face analysis and synthesis [Abstract] This paper presents an overview of the face-related projects in our group. The unifying theme underlying our work is the use of example-based learning methods for both analyzing and synthesizing face images. We label the example face images (and for the problem of face detection, "near miss" faces as well) with descriptive parameters for pose, expression, identity, and face vs. non-face. Then, by using example-based learning techniques, we develop networks for performing analysis tasks such as pose and expression estimation, face recognition, and face detection in cluttered scenes. In addition to these analysis applications, we show how the example-based technique can also be used as a novel method for image synthesis that is for computer graphics. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1999. 	[Title] WRAPPERS FOR PERFORMANCE ENHANCEMENT AND OBLIVIOUS DECISION GRAPHS [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #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 #32083. 	[Title] Back Propagation is Sensitive to Initial Conditions [Abstract] This paper explores the effect of initial weight selection on feed-forward networks learning simple functions with the back-propagation technique. We first demonstrate, through the use of Monte Carlo techniques, that the magnitude of the initial condition vector (in weight space) is a very significant parameter in convergence time variability. In order to further understand this result, additional deterministic experiments were performed. The results of these experiments demonstrate the extreme sensitivity of back propagation to initial weight configuration. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #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 #1112723. 	[Title] Interpolation Models with Multiple [Abstract] A traditional interpolation model is characterized by the choice of reg-ularizer applied to the interpolant, and the choice of noise model. Typically, the regularizer has a single regularization constant ff, and the noise model has a single parameter fi. The ratio ff=fi alone is responsible for determining globally all these attributes of the interpolant: its `complexity', `flexibility', `smoothness', `characteristic scale length', and `characteristic amplitude'. We suggest that interpolation models should be able to capture more than just one flavour of simplicity and complexity. We describe Bayesian models in which the interpolant has a smoothness that varies spatially. We emphasize the importance, in practical implementation, of the concept of `conditional convexity' when designing models with many hyperparameters. We apply the new models to the interpolation of neuronal spike data and demonstrate a substantial improvement in generalization error. 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 #141596. 	[Title] Variational Gaussian Process Classifiers [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #40125. 	[Title] Monte Carlo Implementation of Gaussian Process Models for Bayesian Regression and Classification [Abstract] Technical Report No. 9702, Department of Statistics, University of Toronto Abstract. Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an observed response, a Gaussian process model can easily be implemented using matrix computations that are feasible for datasets of up to about a thousand cases. Hyperparameters that define the covariance function of the Gaussian process can be sampled using Markov chain methods. Regression models where the noise has a t distribution and logistic or probit models for classification applications can be implemented by sampling as well for latent values underlying the observations. Software is now available that implements these methods using covariance functions with hierarchical parameterizations. Models defined in this way can discover high-level properties of the data, such as which inputs are relevant to predicting the response. Please summarise all the given information.

Paper #24974 has the title `EVALUATION OF GAUSSIAN PROCESSES AND OTHER METHODS FOR NON-LINEAR REGRESSION  
` and the abstract `nan`.
Question: Which category should Paper #24974 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #24974 has the title `EVALUATION OF GAUSSIAN PROCESSES AND OTHER METHODS FOR NON-LINEAR REGRESSION  
` and the abstract `nan`.
Question: Which category should Paper #24974 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