We employ Lasso shrinkage within the context of sufficient dimension reduction to obtain a shrinkage sliced inverse regression estimator, which provides easier interpretations and better prediction accuracy without assuming a parametric model. The shrinkage sliced inverse regression approach can be employed for both single-index and multiple-index models. Simulation studies suggest that the new...

BACKGROUND The study of circulating biomarkers and their association with disease outcomes has become progressively complex due to advances in the measurement of these biomarkers through multiplex technologies. The Least Absolute Shrinkage and Selection Operator (LASSO) is a data analysis method that may be utilized for biomarker selection in these high dimensional data. However, it is unclear ...

In this paper we study the problem of variable selection for the proportional odds model, which is a useful alternative to the proportional hazards model and might be appropriate when the proportional hazards assumption is not satisfied. We propose to fit the proportional odds model by maximizing the marginal likelihood subject to a shrinkage-type penalty, which encourages sparse solutions and ...

The learning of dependencies in microarray data is challenging. Here, we will give a review of estimation methods based on Stein-type shrinkage. At their core lies a regularized estimation of the covariance matrix of the data. Subsequently, genetic networks from both, static and time-series data, can be inferred. The algorithms described exhibit a high accuracy, are computationally efficient, a...

Algorithms for simultaneous shrinkage and selection in regression and classification provide attractive solutions to knotty old statistical challenges. Nevertheless, as far as we can tell, Tibshirani’s Lasso algorithm has had little impact on statistical practice. Two particular reasons for this may be the relative inefficiency of the original Lasso algorithm and the relative complexity of more...

In statistics, the least absolute shrinkage and selection operator (Lasso) is a regression method that performs both variable regularization. There lot of literature available, discussing statistical properties coefficients estimated by Lasso method. However, there lacks comprehensive review algorithms to solve optimization problem in Lasso. this review, we summarize five representative optimiz...

We establish the Stein phenomenon in the context of two-step, monotone incomplete data drawn from Np+q(μ,Σ), a (p+ q)-dimensional multivariate normal population with mean μ and covariance matrix Σ. On the basis of data consisting of n observations on all p+q characteristics and an additional N − n observations on the last q characteristics, where all observations are mutually independent, denot...

The “least absolute shrinkage and selection operator” (Lasso) method has been adapted recently for network-structured datasets. In particular, this network Lasso method allows to learn graph signals from a small number of noisy signal samples by using the total variation of a graph signal for regularization. While efficient and scalable implementations of the network Lasso are available, only l...

In this paper, we are concerned with regression problems where covariates can be grouped in nonoverlapping blocks, and where only a few of them are assumed to be active. In such a situation, the group Lasso is an attractive method for variable selection since it promotes sparsity of the groups. We study the sensitivity of any group Lasso solution to the observations and provide its precise loca...