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634
Regularization and variable selection via the Elastic Net
 Journal of the Royal Statistical Society, Series B
, 2005
"... Summary. We propose the elastic net, a new regularization and variable selection method. Real world data and a simulation study show that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation. In addition, the elastic net encourages a grouping effect, where ..."
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Cited by 922 (13 self)
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Summary. We propose the elastic net, a new regularization and variable selection method. Real world data and a simulation study show that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation. In addition, the elastic net encourages a grouping effect, where strongly correlated predictors tend to be in or out of the model together.The elastic net is particularly useful when the number of predictors (p) is much bigger than the number of observations (n). By contrast, the lasso is not a very satisfactory variable selection method in the p n case. An algorithm called LARSEN is proposed for computing elastic net regularization paths efficiently, much like algorithm LARS does for the lasso.
Bug Isolation via Remote Program Sampling
 In Proceedings of the ACM SIGPLAN 2003 Conference on Programming Language Design and Implementation
, 2003
"... We propose a lowoverhead sampling infrastructure for gathering information from the executions experienced by a program 's user community. Several example applications illustrate ways to use sampled instrumentation to isolate bugs. Assertiondense code can be transformed to share the cost of a ..."
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Cited by 327 (16 self)
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We propose a lowoverhead sampling infrastructure for gathering information from the executions experienced by a program 's user community. Several example applications illustrate ways to use sampled instrumentation to isolate bugs. Assertiondense code can be transformed to share the cost of assertions among many users. Lacking assertions, broad guesses can be made about predicates that predict program errors and a process of elimination used to whittle these down to the true bug. Finally, even for nondeterministic bugs such as memory corruption, statistical modeling based on logistic regression allows us to identify program behaviors that are strongly correlated with failure and are therefore likely places to look for the error.
Sparsity and smoothness via the fused lasso
 Journal of the Royal Statistical Society Series B
, 2005
"... The lasso (Tibshirani 1996) penalizes a least squares regression by the sum of the absolute values (L1 norm) of the coefficients. The form of this penalty encourages sparse solutions, that is, having many coefficients equal to zero. Here we propose the “fused lasso”, a generalization of the lasso de ..."
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Cited by 322 (17 self)
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The lasso (Tibshirani 1996) penalizes a least squares regression by the sum of the absolute values (L1 norm) of the coefficients. The form of this penalty encourages sparse solutions, that is, having many coefficients equal to zero. Here we propose the “fused lasso”, a generalization of the lasso designed for problems with features that can be ordered in some meaningful way. The fused lasso penalizes both the L1 norm of the coefficients and their successive differences. Thus it encourages both sparsity
Sure independence screening for ultrahigh dimensional feature space
, 2006
"... Variable selection plays an important role in high dimensional statistical modeling which nowadays appears in many areas and is key to various scientific discoveries. For problems of large scale or dimensionality p, estimation accuracy and computational cost are two top concerns. In a recent paper, ..."
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Cited by 279 (27 self)
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Variable selection plays an important role in high dimensional statistical modeling which nowadays appears in many areas and is key to various scientific discoveries. For problems of large scale or dimensionality p, estimation accuracy and computational cost are two top concerns. In a recent paper, Candes and Tao (2007) propose the Dantzig selector using L1 regularization and show that it achieves the ideal risk up to a logarithmic factor log p. Their innovative procedure and remarkable result are challenged when the dimensionality is ultra high as the factor log p can be large and their uniform uncertainty principle can fail. Motivated by these concerns, we introduce the concept of sure screening and propose a sure screening method based on a correlation learning, called the Sure Independence Screening (SIS), to reduce dimensionality from high to a moderate scale that is below sample size. In a fairly general asymptotic framework, the SIS is shown to have the sure screening property for even exponentially growing dimensionality. As a methodological extension, an iterative SIS (ISIS) is also proposed to enhance its finite sample performance. With dimension reduced accurately from high to below sample size, variable selection can be improved on both speed and accuracy, and can then be ac
A Shrinkage Approach to LargeScale Covariance Matrix Estimation and Implications for Functional Genomics
, 2005
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Sparse Principal Component Analysis
 Journal of Computational and Graphical Statistics
, 2004
"... Principal component analysis (PCA) is widely used in data processing and dimensionality reduction. However, PCA su#ers from the fact that each principal component is a linear combination of all the original variables, thus it is often di#cult to interpret the results. We introduce a new method ca ..."
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Cited by 270 (6 self)
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Principal component analysis (PCA) is widely used in data processing and dimensionality reduction. However, PCA su#ers from the fact that each principal component is a linear combination of all the original variables, thus it is often di#cult to interpret the results. We introduce a new method called sparse principal component analysis (SPCA) using the lasso (elastic net) to produce modified principal components with sparse loadings. We show that PCA can be formulated as a regressiontype optimization problem, then sparse loadings are obtained by imposing the lasso (elastic net) constraint on the regression coe#cients. E#cient algorithms are proposed to realize SPCA for both regular multivariate data and gene expression arrays. We also give a new formula to compute the total variance of modified principal components. As illustrations, SPCA is applied to real and simulated data, and the results are encouraging.
Penalized Discriminant Analysis
 Annals of Statistics
, 1995
"... Fisher's linear discriminant analysis (LDA) is a popular dataanalytic tool for studying the relationship between a set of predictors and a categorical response. In this paper we describe a penalized version of LDA. It is designed for situations in which there are many highly correlated predict ..."
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Cited by 225 (9 self)
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Fisher's linear discriminant analysis (LDA) is a popular dataanalytic tool for studying the relationship between a set of predictors and a categorical response. In this paper we describe a penalized version of LDA. It is designed for situations in which there are many highly correlated predictors, such as those obtained by discretizing a function, or the greyscale values of the pixels in a series of images. In cases such as these it is natural, efficient, and sometimes essential to impose a spatial smoothness constraint on the coefficients, both for improved prediction performance and interpretability. We cast the classification problem into a regression framework via optimal scoring. Using this, our proposal facilitates the use of any penalized regression technique in the classification setting. The technique is illustrated with examples in speech recognition and handwritten character recognition. AMS 1991 Classifications: Primary 62H30, Secondary 62G07 1 Introduction Linear discrim...
BagBoosting for tumor classification with gene expression data
 Bioinformatics
, 2004
"... Motivation: Microarray experiments are expected to contribute significantly to the progress in cancer treatment by enabling a precise and early diagnosis. They create a need for class prediction tools, which can deal with a large number of highly correlated input variables, perform feature selection ..."
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Cited by 192 (2 self)
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Motivation: Microarray experiments are expected to contribute significantly to the progress in cancer treatment by enabling a precise and early diagnosis. They create a need for class prediction tools, which can deal with a large number of highly correlated input variables, perform feature selection and provide class probability estimates that serve as a quantification of the predictive uncertainty. A very promising solution is to combine the two ensemble schemes bagging and boosting to a novel algorithm called BagBoosting.
Results: When bagging is used as a module in boosting, the resulting classifier consistently improves the predictive performance and the probability estimates of both bagging and boosting on real and simulated gene expression data. This quasiguaranteed improvement can be obtained by simply making a bigger computing effort. The advantageous predictive potential is also confirmed by comparing BagBoosting to several established class prediction tools for microarray data.
On testing the significance of sets of genes
 Annals of Applied Statistics
"... This paper discusses the problem of identifying differentially expressed groups of genes from a microarray experiment. The groups of genes are externally defined, for example, sets of gene pathways derived from biological databases. Our starting point is the interesting Gene Set Enrichment Analysis ..."
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Cited by 164 (3 self)
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This paper discusses the problem of identifying differentially expressed groups of genes from a microarray experiment. The groups of genes are externally defined, for example, sets of gene pathways derived from biological databases. Our starting point is the interesting Gene Set Enrichment Analysis (GSEA) procedure of Subramanian et al. (2005). We study the problem in some generality and propose two potential improvements to GSEA: the maxmean statistic for summarizing genesets, and restandardization for more accurate inferences. We discuss a variety of examples and extensions, including the use of geneset scores for class predictions. We also describe a new R language package GSA that implements our ideas. 1
MicroRNA gene expression deregulation in human breast cancer. Cancer Res
, 2005
"... Access the most recent version of this article at: doi: 10.1158/00085472.CAN051783 Access the most recent supplemental material at: ..."
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Cited by 127 (5 self)
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Access the most recent version of this article at: doi: 10.1158/00085472.CAN051783 Access the most recent supplemental material at: