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 #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 #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 #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 #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.

Paper #74821 has the title `Regression shrinkage and selection via the lasso  
` and the 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. 
`.
Question: Which category should Paper #74821 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #74821 has the title `Regression shrinkage and selection via the lasso  
` and the 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. 
`.
Question: Which category should Paper #74821 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