We discuss the behavior of penalized robust regression estimators in high-dimension and compare our theoretical predictions to simulations. Our results show the importance of the geometry of the dataset and shed light on the theoretical behavior of LASSO and much more involved methods.

The conserved threonine (Thr) residue in the penultimate position of the leader peptide of lasso peptides microcin J25 and capistruin can be effectively replaced by several amino acids close in size and shape to Thr. These findings suggest a model for lasso peptide biosynthesis in which the Thr sidechain is a recognition element for the lasso peptide maturation machinery.

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...