Above are papers related to the following paper: [Paper_ID] Paper #1131150. 	[Title] Penalisation multiple adaptative un nouvel algorithme de regression, la penalisation multiple adapta-tive. Cet algorithme represente [Abstract] Chaque parametre du modele est penalise individuellement. Le reglage de ces penalisations se fait automatiquement a partir de la definition d'un hyperparametre de regularisation globale. Cet hyperparametre, qui controle la complexite du regresseur, peut ^etre estime par des techniques de reechantillonnage. Nous montrons experimentalement les performances et la stabilite de la penalisation multiple adaptative dans le cadre de la regression lineaire. Nous avons choisi des problemes pour lesquels le probleme du controle de la complexite est particulierement crucial, comme dans le cadre plus general de l'estimation fonctionnelle. Les comparaisons avec les moindres carres regularises et la selection de variables nous permettent de deduire les conditions d'application de chaque algorithme de penalisation. Lors des simulations, nous testons egalement plusieurs techniques de reechantillonnage. Ces techniques sont utilisees pour selectionner la complexite optimale des estimateurs de la fonction de regression. Nous comparons les pertes occasionnees par chacune d'entre elles lors de la selection de modeles sous-optimaux. Nous regardons egalement si elles permettent de determiner l'estimateur de la fonction de regression minimisant l'erreur en generalisation parmi les differentes methodes de penalisation en competition. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #641956. 	[Title] Adaptive Noise Injection for Input Variables Relevance Determination [Abstract] In this paper we consider the application of training with noise in multi-layer perceptron to input variables relevance determination. Noise injection is modified in order to penalize irrelevant features. The proposed algorithm is attractive as it requires the tuning of a single parameter. This parameter controls the penalization of the inputs together with the complexity of the model. After the presentation of the method, experimental evidences are given on simulated data sets. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #74821. 	[Title] Regression shrinkage and selection via the lasso [Abstract] We propose a new method for estimation in linear models. The "lasso" minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactly zero and hence gives interpretable models. Our simulation studies suggest that the lasso enjoys some of the favourable properties of both subset selection and ridge regression. It produces interpretable models like subset selection and exhibits the stability of ridge regression. There is also an interesting relationship with recent work in adaptive function estimation by Donoho and Johnstone. The lasso idea is quite general and can be applied in a variety of statistical models: extensions to generalized regression models and tree-based models are briefly described. 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 #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 #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 #25772. 	[Title] Flexible Metric Nearest Neighbor Classiflcation [Abstract] The K-nearest-neighbor decision rule assigns an object of unknown class to the plurality class among the K labeled "training" objects that are closest to it. Closeness is usually deflned in terms of a metric distance on the Euclidean space with the input measurement variables as axes. The metric chosen to deflne this distance can strongly efiect performance. An optimal choice depends on the problem at hand as characterized by the respective class distributions on the input measurement space, and within a given problem, on the location of the unknown object in that space. In this paper new types of K-nearest-neighbor procedures are described that estimate the local relevance of each input variable, or their linear combinations, for each individual point to be classifled. This information is then used to separately customize the metric used to deflne distance from that object in flnding its nearest neighbors. These procedures are a hybrid between regular K-nearest-neighbor methods and treestructured recursive partitioning techniques popular in statistics and machine learning. 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 #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 #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 #1120252. 	[Title] A proposal for variable selection in the Cox model [Abstract] We propose a new method for variable selection and estimation in Cox's proportional hazards model. Our proposal minimizes the log partial likelihood subject to the sum of the absolute values of the parameters being bounded by a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactly zero and hence gives interpretable models. The method is a variation of the "lasso" proposal of Tibshirani (1994), designed for the linear regression context. Simulations indicate that the lasso can be more accurate than stepwise selection in this setting. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3229. 	[Title] Book Review  Introduction to the Theory of Neural Computation Reviewed by: 2 [Abstract] Neural computation, also called connectionism, parallel distributed processing, neural network modeling or brain-style computation, has grown rapidly in the last decade. Despite this explosion, and ultimately because of impressive applications, there has been a dire need for a concise introduction from a theoretical perspective, analyzing the strengths and weaknesses of connectionist approaches and establishing links to other disciplines, such as statistics or control theory. The Introduction to the Theory of Neural Computation by Hertz, Krogh and Palmer (subsequently referred to as HKP) is written from the perspective of physics, the home discipline of the authors. The book fulfills its mission as an introduction for neural network novices, provided that they have some background in calculus, linear algebra, and statistics. It covers a number of models that are often viewed as disjoint. Critical analyses and fruitful comparisons between these models Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #370366. 	[Title] From Data Distributions to Regularization in Invariant Learning [Abstract] Ideally pattern recognition machines provide constant output when the inputs are transformed under a group G of desired invariances. These invariances can be achieved by enhancing the training data to include examples of inputs transformed by elements of G, while leaving the corresponding targets unchanged. Alternatively the cost function for training can include a regularization term that penalizes changes in the output when the input is transformed under the group. This paper relates the two approaches, showing precisely the sense in which the regularized cost function approximates the result of adding transformed (or distorted) examples to the training data. The cost function for the enhanced training set is equivalent to the sum of the original cost function plus a regularizer. For unbiased models, the regularizer reduces to the intuitively obvious choice - a term that penalizes changes in the output when the inputs are transformed under the group. For infinitesimal transformations, the coefficient of the regularization term reduces to the variance of the distortions introduced into the training data. This correspondence provides a simple bridge between the two approaches. Please summarise all the given information.

Paper #1131150 has the title `Penalisation multiple adaptative un nouvel algorithme de regression, la penalisation multiple adapta-tive. Cet algorithme represente
` and the abstract `Chaque parametre du modele est penalise individuellement. Le reglage de ces penalisations se fait automatiquement a partir de la definition d'un hyperparametre de regularisation globale. Cet hyperparametre, qui controle la complexite du regresseur, peut ^etre estime par des techniques de reechantillonnage. Nous montrons experimentalement les performances et la stabilite de la penalisation multiple adaptative dans le cadre de la regression lineaire. Nous avons choisi des problemes pour lesquels le probleme du controle de la complexite est particulierement crucial, comme dans le cadre plus general de l'estimation fonctionnelle. Les comparaisons avec les moindres carres regularises et la selection de variables nous permettent de deduire les conditions d'application de chaque algorithme de penalisation. Lors des simulations, nous testons egalement plusieurs techniques de reechantillonnage. Ces techniques sont utilisees pour selectionner la complexite optimale des estimateurs de la fonction de regression. Nous comparons les pertes occasionnees par chacune d'entre elles lors de la selection de modeles sous-optimaux. Nous regardons egalement si elles permettent de determiner l'estimateur de la fonction de regression minimisant l'erreur en generalisation parmi les differentes methodes de penalisation en competition. 
`.
Question: Which category should Paper #1131150 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1131150 has the title `Penalisation multiple adaptative un nouvel algorithme de regression, la penalisation multiple adapta-tive. Cet algorithme represente
` and the abstract `Chaque parametre du modele est penalise individuellement. Le reglage de ces penalisations se fait automatiquement a partir de la definition d'un hyperparametre de regularisation globale. Cet hyperparametre, qui controle la complexite du regresseur, peut ^etre estime par des techniques de reechantillonnage. Nous montrons experimentalement les performances et la stabilite de la penalisation multiple adaptative dans le cadre de la regression lineaire. Nous avons choisi des problemes pour lesquels le probleme du controle de la complexite est particulierement crucial, comme dans le cadre plus general de l'estimation fonctionnelle. Les comparaisons avec les moindres carres regularises et la selection de variables nous permettent de deduire les conditions d'application de chaque algorithme de penalisation. Lors des simulations, nous testons egalement plusieurs techniques de reechantillonnage. Ces techniques sont utilisees pour selectionner la complexite optimale des estimateurs de la fonction de regression. Nous comparons les pertes occasionnees par chacune d'entre elles lors de la selection de modeles sous-optimaux. Nous regardons egalement si elles permettent de determiner l'estimateur de la fonction de regression minimisant l'erreur en generalisation parmi les differentes methodes de penalisation en competition. 
`.
Question: Which category should Paper #1131150 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