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97
Irrelevant Features and the Subset Selection Problem
 MACHINE LEARNING: PROCEEDINGS OF THE ELEVENTH INTERNATIONAL
, 1994
"... We address the problem of finding a subset of features that allows a supervised induction algorithm to induce small highaccuracy concepts. We examine notions of relevance and irrelevance, and show that the definitions used in the machine learning literature do not adequately partition the features ..."
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Cited by 594 (23 self)
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We address the problem of finding a subset of features that allows a supervised induction algorithm to induce small highaccuracy concepts. We examine notions of relevance and irrelevance, and show that the definitions used in the machine learning literature do not adequately partition the features into useful categories of relevance. We present definitions for irrelevance and for two degrees of relevance. These definitions improve our understanding of the behavior of previous subset selection algorithms, and help define the subset of features that should be sought. The features selected should depend not only on the features and the target concept, but also on the induction algorithm. We describe a method for feature subset selection using crossvalidation that is applicable to any induction algorithm, and discuss experiments conducted with ID3 and C4.5 on artificial and real datasets.
Model Selection and the Principle of Minimum Description Length
 Journal of the American Statistical Association
, 1998
"... This paper reviews the principle of Minimum Description Length (MDL) for problems of model selection. By viewing statistical modeling as a means of generating descriptions of observed data, the MDL framework discriminates between competing models based on the complexity of each description. This ..."
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Cited by 145 (5 self)
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This paper reviews the principle of Minimum Description Length (MDL) for problems of model selection. By viewing statistical modeling as a means of generating descriptions of observed data, the MDL framework discriminates between competing models based on the complexity of each description. This approach began with Kolmogorov's theory of algorithmic complexity, matured in the literature on information theory, and has recently received renewed interest within the statistics community. In the pages that follow, we review both the practical as well as the theoretical aspects of MDL as a tool for model selection, emphasizing the rich connections between information theory and statistics. At the boundary between these two disciplines, we find many interesting interpretations of popular frequentist and Bayesian procedures. As we will see, MDL provides an objective umbrella under which rather disparate approaches to statistical modeling can coexist and be compared. We illustrate th...
Smoothing by Local Regression: Principles and Methods
"... this paper we describe two adaptive procedures, one based on C p and the other based on crossvalidation. Still, when we have a final adaptive fit in hand, it is critical to subject it to graphical diagnostics to study its performance. The important implication of these statements is that the above c ..."
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Cited by 88 (1 self)
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this paper we describe two adaptive procedures, one based on C p and the other based on crossvalidation. Still, when we have a final adaptive fit in hand, it is critical to subject it to graphical diagnostics to study its performance. The important implication of these statements is that the above choices must be tailored to each data set in practice; that is, the choices represent a modeling of the data. It is widely accepted that in global parametric regression there are a variety of choices that must be made  for example, the parametric family to be fitted and the form of the distribution of the response  and that we must rely on our knowledge of the mechanism generating the data, on model selection diagnostics, and on graphical diagnostic methods to make the choices. The same is true for smoothing. Cleveland (1993) presents many examples of this modeling process. For example, in one application, oxides of nitrogen from an automobile engine are fitted to the equivalence ratio, E, of the fuel and the compression ratio, C, of the engine. Coplots show that it is reasonable to use quadratics as the local parametric family but with the added assumption that given E the fitted f
Smoothing Spline ANOVA for Exponential Families, with Application to the Wisconsin Epidemiological Study of Diabetic Retinopathy
 ANN. STATIST
, 1995
"... Let y i ; i = 1; \Delta \Delta \Delta ; n be independent observations with the density of y i of the form h(y i ; f i ) = exp[y i f i \Gammab(f i )+c(y i )], where b and c are given functions and b is twice continuously differentiable and bounded away from 0. Let f i = f(t(i)), where t = (t 1 ; \De ..."
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Cited by 83 (44 self)
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Let y i ; i = 1; \Delta \Delta \Delta ; n be independent observations with the density of y i of the form h(y i ; f i ) = exp[y i f i \Gammab(f i )+c(y i )], where b and c are given functions and b is twice continuously differentiable and bounded away from 0. Let f i = f(t(i)), where t = (t 1 ; \Delta \Delta \Delta ; t d ) 2 T (1)\Omega \Delta \Delta \Delta\Omega T (d) = T , the T (ff) are measureable spaces of rather general form, and f is an unknown function on T with some assumed `smoothness' properties. Given fy i ; t(i); i = 1; \Delta \Delta \Delta ; ng, it is desired to estimate f(t) for t in some region of interest contained in T . We develop the fitting of smoothing spline ANOVA models to this data of the form f(t) = C + P ff f ff (t ff ) + P ff!fi f fffi (t ff ; t fi ) + \Delta \Delta \Delta. The components of the decomposition satisfy side conditions which generalize the usual side conditions for parametric ANOVA. The estimate of f is obtained as the minimizer...
Predicting risk of software changes
 Bell Labs Technical Journal
, 2000
"... Reducing the number of software failures is one of the most challenging problems of software production. We assume that software development proceeds as a series of changes and model the probability that a change to software will cause a failure. We use predictors based on the properties of a change ..."
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Cited by 81 (25 self)
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Reducing the number of software failures is one of the most challenging problems of software production. We assume that software development proceeds as a series of changes and model the probability that a change to software will cause a failure. We use predictors based on the properties of a change itself. Such predictors include size in lines of code added, deleted, and unmodified; diffusion of the change and its component subchanges, as reflected in the number of files, modules, and subsystems touched, or changed; several measures of developer experience; and the type of change and its subchanges (fault fixes or new code). The model is built on historic information and is used to predict the risk of new changes. In this paper we apply the model to 5ESS ® software updates and find that change diffusion and developer experience are essential to predicting failures. The predictive model is implemented as a Webbased tool to allow timely prediction of change quality. The ability to predict the quality of change enables us to make appropriate decisions regarding inspection, testing, and delivery. Historic information on software changes is recorded in many commercial software projects, suggesting that our results can be easily and widely applied in practice.
The estimation of prediction error: Covariance penalties and crossvalidation
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2004
"... Having constructed a databased estimation rule, perhaps a logistic regression or a classification tree, the statistician would like to know its performance as a predictor of future cases. There are two main theories concerning prediction error: (1) penalty methods such as Cp, AIC, and SURE that dep ..."
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Cited by 46 (4 self)
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Having constructed a databased estimation rule, perhaps a logistic regression or a classification tree, the statistician would like to know its performance as a predictor of future cases. There are two main theories concerning prediction error: (1) penalty methods such as Cp, AIC, and SURE that depend on the covariance between data points and their corresponding predictions; (2) Crossvalidation and related nonparametric bootstrap techniques. This paper concerns the connection between the two theories. A RaoBlackwell type of relation is derived, in which nonparametric methods like crossvalidation are seen to be randomized versions of their covariance penalty counterparts. The modelbased penalty methods offer substantially better accuracy, assuming that the model is believable.
Smoothing spline ANOVA models for large data sets with Bernoulli observations and the randomized GACV
 Ann. Statist
"... (ranGACV) method for choosing multiple smoothing parameters in penalized likelihood estimates for Bernoulli data. The method is intended for application with penalized likelihood smoothing spline ANOVA models. In addition we propose a class of approximate numerical methods for solving the penalized ..."
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Cited by 41 (19 self)
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(ranGACV) method for choosing multiple smoothing parameters in penalized likelihood estimates for Bernoulli data. The method is intended for application with penalized likelihood smoothing spline ANOVA models. In addition we propose a class of approximate numerical methods for solving the penalized likelihood variational problem which, in conjunction with the ranGACV method allows the application of smoothing spline ANOVA models with Bernoulli data to much larger data sets than previously possible. These methods are based on choosing an approximating subset of the natural (representer) basis functions for the variational problem. Simulation studies with synthetic data, including synthetic data mimicking demographic risk factor data sets is used to examine the properties of the method and to compare the approach with the GRKPACK code of Wang (1997c). Bayesian “confidence intervals ” are obtained for the fits and are shown in the simulation studies to have the “across the function ” property usually claimed for these confidence intervals. Finally the method is applied
The variable selection problem
 Journal of the American Statistical Association
, 2000
"... The problem of variable selection is one of the most pervasive model selection problems in statistical applications. Often referred to as the problem of subset selection, it arises when one wants to model the relationship between a variable of interest and a subset of potential explanatory variables ..."
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Cited by 39 (2 self)
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The problem of variable selection is one of the most pervasive model selection problems in statistical applications. Often referred to as the problem of subset selection, it arises when one wants to model the relationship between a variable of interest and a subset of potential explanatory variables or predictors, but there is uncertainty about which subset to use. This vignette reviews some of the key developments which have led to the wide variety of approaches for this problem. 1
Variable selection in data mining: Building a predictive model for bankruptcy
 Journal of the American Statistical Association
, 2004
"... We predict the onset of personal bankruptcy using least squares regression. Although well publicized, only 2,244 bankruptcies occur in our data set of 2.9 million months of creditcard activity. We use stepwise selection to find predictors from a mix of payment history, debt load, demographics, and ..."
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Cited by 34 (9 self)
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We predict the onset of personal bankruptcy using least squares regression. Although well publicized, only 2,244 bankruptcies occur in our data set of 2.9 million months of creditcard activity. We use stepwise selection to find predictors from a mix of payment history, debt load, demographics, and their interactions. This combination of rare responses and over 67,000 possible predictors leads to a challenging modeling question: How does one separate coincidental from useful predictors? We show that three modifications turn stepwise regression into an effective methodology for predicting bankruptcy. Our version of stepwise regression (1) organizes calculations to accommodate interactions, (2) exploits modern decision theoretic criteria to choose predictors, and (3) conservatively estimates pvalues to handle sparse data and a binary response. Omitting any one of these leads to poor performance. A final step in our procedure calibrates regression predictions. With these modifications, stepwise regression predicts bankruptcy as well, if not better, than recently developed datamining tools. When sorted, the largest 14,000 resulting predictions hold 1000 of the 1800 bankruptcies hidden in a validation sample of 2.3 million observations. If the cost of missing a bankruptcy is 200 times that of a false positive, our predictions incur less than 2/3 of the costs of classification errors produced by the treebased classifier C4.5. Key Phrases: AIC, Cp, Bonferroni, calibration, hard thresholding, risk inflation criterion (RIC),