In generalized linear regression problems with an abundant number of features, lasso-type regularization which imposes an `-constraint on the regression coefficients has become a widely established technique. Crucial deficiencies of the lasso were unmasked when Zhou and Hastie (2005) introduced the elastic net. In this paper, we propose to extend the elastic net by admitting general nonnegative...

In view of its ongoing importance for a variety of practical applications, feature selection via `1-regularization methods like the lasso has been subject to extensive theoretical as well empirical investigations. Despite its popularity, mere `1-regularization has been criticized for being inadequate or ineffective, notably in situations in which additional structural knowledge about the predic...

MOTIVATION There has been an increasing interest in expressing a survival phenotype (e.g. time to cancer recurrence or death) or its distribution in terms of a subset of the expression data of a subset of genes. Due to high dimensionality of gene expression data, however, there is a serious problem of collinearity in fitting a prediction model, e.g. Cox's proportional hazards model. To avoid th...

Generalized Additive Models (GAMs) have been popularized by the work of Hastie and Tibshirani (1990) and the availability of user friendly GAM software in Splus. However, whilst it is flexible and efficient, the GAM framework based on backfitting with linear smoothers presents some difficulties when it comes to model selection and inference. On the other hand, the mathematically elegant work of...

Abduction, or inference to the best explanation, is a form of inference that goes from data describing something to a hypothesis that best explains or accounts for the data. Thus abduction is a kind of theory-forming or interpretive inference. The philosopher and logician Charles Sanders Peirce (1839-1914) contended that there occurs in science and in everyday life a distinctive pattern of reas...

The method of sparse principal component analysis (S-PCA) proposed by Zou, Hastie, and Tibshirani (2006) is an attractive approach to obtain sparse loadings in principal component analysis (PCA). S-PCA was motivated by reformulating PCA as a least-squares problem so that a lasso penalty on the loading coefficients can be applied. In this article, we propose new estimates to improve S-PCA in the...

Texts can be distinguished in terms of their content, function, structure or layout (Brinker, ; Bateman et al., ; Joachims, ; Power et al., ). These reference points do not open necessarily orthogonal perspectives on text classification. As part of explorative data analysis, text classification aims at automatically dividing sets of textual objects into classes of maximum intern...

As an alternative to the local partial likelihood method of Tibshirani and Hastie and Fan, Gijbels, and King, a global partial likelihood method is proposed to estimate the covariate effect in a nonparametric proportional hazards model, λ(t|x) = exp{ψ(x)}λ(0)(t). The estimator, ψ̂(x), reduces to the Cox partial likelihood estimator if the covariate is discrete. The estimator is shown to be consi...

The primary goal of fMRI analysis is the identification of brain locations, or image voxels, associated with cognitive tasks of interest. Predictive modeling techniques have become widely used in such analysis and sparse modeling techniques have become especially attractive due to their ability to identify relevant locations in a multivariate manner. However, many sparse methods may be too cons...

A linear stability theory of non-ideal MHD ballooning modes is investigated using a two fluid model for arbitrary three-dimensional electron-ion plasmas. Resistive-inertia ballooning mode (RIBM) eigenvalues and eigenfunctions are calculated for a variety of equilibria including axisymmetric shifted circular geometry (ŝ−α model) as well as for three dimensional configurations of interest relevan...