Above are papers related to the following paper: [Paper_ID] Paper #1133028. 	[Title] An Efficient Method To Estimate Bagging's Generalization Error [Abstract] In bagging [Bre94a] one uses bootstrap replicates of the training set [Efr79, ET93] to try to improve a learning algorithm's performance. The computational requirements for estimating the resultant generalization error on a test set by means of cross-validation are often prohibitive; for leave-one-out cross-validation one needs to train the underlying algorithm on the order of m- times, where m is the size of the training set and is the number of replicates. This paper presents several techniques for exploiting the bias-variance decomposition [GBD92, Wol96] to estimate the generalization error of a bagged learning algorithm without invoking yet more training of the underlying learning algorithm. The best of our estimators exploits stacking [Wol92]. In a set of experiments reported here, it was found to be more accurate than both the alternative cross-validation-based estimator of the bagged algorithm's error and the cross-validation-based estimator of the underlying algorithm's error. This improvement was particularly pronounced for small test sets. This suggests a novel justification for using bagging| im proved estimation of generalization error. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #154982. 	[Title] Bias, variance and prediction error for classification rules [Abstract] We study the notions of bias and variance for classification rules. Following Efron (1978) we develop a decomposition of prediction error into its natural components. Then we derive bootstrap estimates of these components and illustrate how they can be used to describe the error behaviour of a classifier in practice. In the process we also obtain a bootstrap estimate of the error of a "bagged" classifier. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #129897. 	[Title] The out-of-bootstrap method for model averaging and selection [Abstract] We propose a bootstrap-based method for model averaging and selection that focuses on training points that are left out of individual bootstrap samples. This information can be used to estimate optimal weighting factors for combining estimates from different bootstrap samples, and also for finding the best subsets the linear model setting. These proposals provide alternatives to Bayesian approaches to model averaging and selection, requiring less computation and fewer subjective choices. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1121867. 	[Title] MAJORITY VOTE CLASSIFIERS: THEORY AND APPLICATIONS [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1997. 	[Title] Cross-Validation and the Bootstrap: Estimating the Error Rate of a Prediction Rule [Abstract] A training set of data has been used to construct a rule for predicting future responses. What is the error rate of this rule? The traditional answer to this question is given by cross-validation. The cross-validation estimate of prediction error is nearly unbiased, but can be highly variable. This article discusses bootstrap estimates of prediction error, which can be thought of as smoothed versions of cross-validation. A particular bootstrap method, the 632+ rule, is shown to substantially outperform cross-validation in a catalog of 24 simulation experiments. Besides providing point estimates, we also consider estimating the variability of an error rate estimate. All of the results here are nonparametric, and apply to any possible prediction rule: however we only study classification problems with 0-1 loss in detail. Our simulations include "smooth" prediction rules like Fisher's Linear Discriminant Function, and unsmooth ones like Nearest Neighbors. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #8079. 	[Title] Bias Plus Variance Decomposition for Zero-One Loss Functions [Abstract] We present a bias-variance decomposition of expected misclassification rate, the most commonly used loss function in supervised classification learning. The bias-variance decomposition for quadratic loss functions is well known and serves as an important tool for analyzing learning algorithms, yet no decomposition was offered for the more commonly used zero-one (misclassification) loss functions until the recent work of Kong & Dietterich (1995) and Breiman (1996). Their decomposition suffers from some major shortcomings though (e.g., potentially negative variance), which our decomposition avoids. We show that, in practice, the naive frequency-based estimation of the decomposition terms is by itself biased and show how to correct for this bias. We illustrate the decomposition on various algorithms and datasets from the UCI repository. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1130927. 	[Title] Parametric regression 1.1 Learning problem model f bw b w in turn is an estimator [Abstract] Let us present briefly the learning problem we will address in this chapter and the following. The ultimate goal is the modelling of a mapping f : x 7! y from multidimensional input x to output y. The output can be multi-dimensional, but we will mostly address situations where it is a one dimensional real value. Furthermore, we should take into account the fact that we scarcely ever observe the actual true mapping y = f (x). This is due to perturbations such as e.g. observational noise. We will rather have a joint probability p (x; y). We expect this probability to be peaked for values of x and y corresponding to the mapping. We focus on automatic learning by example. A set D = of data sampled from the joint distribution p (x; y) = p (yjx) p (x) is collected. With the help of this set, we try to identify a model of the data, parameterised by a set of 1.2 Learning and optimisation The fit of the model to the system in a given point x is measured using a criterion representing the distance from the model prediction b y to the system, e (y; f w (x)). This is the local risk . The performance of the model is measured by the expected This quantity represents the ability to yield good performance for all the possible situations (i.e. (x; y) pairs) and is thus called generalisation error . The optimal set 1 parameters w: f w : x 7! b y. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1130931. 	[Title] TH presentee par STATISTICAL LEARNING AND REGULARISATION FOR REGRESSION Application to system identification and time [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1130934. 	[Title] 82 Lag-space estimation in time-series modelling keep track of cases where the estimation of P [Abstract] When m = 0 (no delays), we set A 0 (ffi) = f(j; k) ; j 6= kg, such that P m (*jffi) depends only on *. The estimated probabilities above become quite noisy when the number of elements in set A m and B m are small. For this reason, we estimate the standard deviation of P m (*jffi). Notice that this estimate is the empirical average of a binomial variable (either a given couple satisfied the conditions on ffi and *, or it does not). The standard deviation is then estimated easily by: Generally speaking, P m (*jffi) increases with * (laxer output test), and when ffi approaches 0 (stricter input condition). Let us now define by P m (*) the maximum over ffi of P m (*jffi): P m (*) = max ffi&gt;0 P m (*jffi). The dependability index is defined as: P 0 (*) represents how much data passes the continuity test when no input information is available. This dependability index measures how much of the remaining continuity information is associated with involving input i m . This index is then averaged over * with respect to the probability (1 P 0 (*)): m (*) (1 P 0 (*)) d* (4.8) It is clear that m (*), and therefore its average, should be positive quantities. Furthermore, if the system is deterministic, the dependability is zero after a certain number of inputs, so the sum of averages saturates. If the system is also noise-free, they sum up to 1. For any m greater than the embedding dimension: refers to results obtained using this method. 4.6 Statistical variable selection Statistical variable selection (or feature selection) encompasses a number of techniques aimed at choosing a relevant subset of input variables in a regression or a classification problem. As in the rest of this document, we will limit ourselves to considerations related to the regression problem, even though most methods discussed below apply to classification as well. Variable selection can be seen as a part of the data analysis problem: the selection (or discard) of a variable tells us about the relevance of the associated measurement to the modelled system. In a general setting, this is a purely combinatorial problem: given V possible variables, there is 2 V possible subsets (including the empty set and the full set) of these variables. Given a performance measure, such as prediction error, the only optimal scheme is to test all these subset and choose the one that gives the best performance. It is easy to see that such an extensive scheme is only viable when the number of variables is rather low. Identifying 2 V models when we have more than a few variables requires too much computation. A number of techniques have been devised to overcome this combinatorial limit. Some of them use an iterative, locally optimal technique to construct an estimate of the relevant subset in a number of steps. We will refer to them as stepwise selection methods, not to be con fused with stepwise regression, a subset of these methods that we will address below. In forward selection, we start with an empty set of variables. At each step, we select a candidate variable using a selection criteria, check whether this variable should be added to the set, and iterate until a given stop condition is reached. On the contrary, backward elimination methods start with the full set of all input variables. At each step, the least significant variable is selected according to a selection criteria. If this variable is irrelevant, it is removed and the process is iterated until a stop condition is reached. It is easy to devise examples where the inclusion of a variable causes a previously included variable to become irrelevant. It thus seems appropriate to consider running a backward elimination each time a new variable is added by forward selection. This combination of both ap proaches is known as stepwise regression in the linear regression con Please summarise all the given information.

Paper #1133028 has the title `An Efficient Method To Estimate Bagging's Generalization Error  
` and the abstract `In bagging [Bre94a] one uses bootstrap replicates of the training set [Efr79, ET93] to try to improve a learning algorithm's performance. The computational requirements for estimating the resultant generalization error on a test set by means of cross-validation are often prohibitive; for leave-one-out cross-validation one needs to train the underlying algorithm on the order of m- times, where m is the size of the training set and is the number of replicates. This paper presents several techniques for exploiting the bias-variance decomposition [GBD92, Wol96] to estimate the generalization error of a bagged learning algorithm without invoking yet more training of the underlying learning algorithm. The best of our estimators exploits stacking [Wol92]. In a set of experiments reported here, it was found to be more accurate than both the alternative cross-validation-based estimator of the bagged algorithm's error and the cross-validation-based estimator of the underlying algorithm's error. This improvement was particularly pronounced for small test sets. This suggests a novel justification for using bagging| im proved estimation of generalization error.
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Question: Which category should Paper #1133028 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1133028 has the title `An Efficient Method To Estimate Bagging's Generalization Error  
` and the abstract `In bagging [Bre94a] one uses bootstrap replicates of the training set [Efr79, ET93] to try to improve a learning algorithm's performance. The computational requirements for estimating the resultant generalization error on a test set by means of cross-validation are often prohibitive; for leave-one-out cross-validation one needs to train the underlying algorithm on the order of m- times, where m is the size of the training set and is the number of replicates. This paper presents several techniques for exploiting the bias-variance decomposition [GBD92, Wol96] to estimate the generalization error of a bagged learning algorithm without invoking yet more training of the underlying learning algorithm. The best of our estimators exploits stacking [Wol92]. In a set of experiments reported here, it was found to be more accurate than both the alternative cross-validation-based estimator of the bagged algorithm's error and the cross-validation-based estimator of the underlying algorithm's error. This improvement was particularly pronounced for small test sets. This suggests a novel justification for using bagging| im proved estimation of generalization error.
`.
Question: Which category should Paper #1133028 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: Theory