We propose a new method of learning a sparse nonnegative-definite target matrix. Our primary example of the target matrix is the inverse of a population covariance or correlation matrix. The algorithm first estimates each column of the target matrix by the scaled Lasso and then adjusts the matrix estimator to be symmetric. The penalty level of the scaled Lasso for each column is completely dete...

Binary logistic regression with a sparsity constraint on the solution plays a vital role in many high dimensional machine learning applications. In some cases, the features can be grouped together, so that entire subsets of features can be selected or zeroed out. In many applications, however, this can be very restrictive. In this paper, we are interested in a less restrictive form of structure...

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 ...

Eigenphone-based speaker adaptation outperforms conventional maximum likelihood linear regression (MLLR) and eigenvoice methods when there is sufficient adaptation data. However, it suffers from severe over-fitting when only a few seconds of adaptation data are provided. In this paper, various regularization methods are investigated to obtain a more robust speaker-dependent eigenphone matrix es...

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 mor...

I briefly report on some unexpected results that I obtained when optimizing the model parameters of the Lasso. In simulations with varying observations-to-variables ratio n/p, I typically observe a strong peak in the test error curve at the transition point n/p = 1. This peaking phenomenon is well-documented in scenarios that involve the inversion of the sample covariance matrix, and as I illus...

We consider a linear regression problem in a high dimensional setting where the number of covariates p can be much larger than the sample size n. In such a situation, one often assumes sparsity of the regression vector, i.e., the regression vector contains many zero components. We propose a Lasso-type estimator β̂ (where ‘Quad’ stands for quadratic) which is based on two penalty terms. The first...

Geographic information systems (GIS) organize spatial data in multiple two-dimensional arrays called layers. In many applications, a response of interest is observed on a set of sites in the landscape, and it is of interest to build a regression model from the GIS layers to predict the response at unsampled sites. Model selection in this context then consists not only of selecting appropriate l...

Group LASSO is widely used to enforce the structural sparsity, which achieves the sparsity at the inter-group level. In this paper, we propose a new formulation called “exclusive group LASSO”, which brings out sparsity at intra-group level in the context of feature selection. The proposed exclusive group LASSO is applicable on any feature structures, regardless of their overlapping or non-overl...

Previous genome-wide association study (GWAS) focused on low-order interactions between pairwise single-nucleotide polymorphisms (SNPs) with significant main effects. Little is known how high-order interactions effect, especially one among the SNPs without main effects regulates quantitative traits.Within the frameworks of linear model and generalized linear model, the LASSO with coordinate des...