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We consider the group lasso penalty for the linear model. We note that the standard algorithm for solving the problem assumes that the model matrices in each group are orthonormal. Here we consider a ...
In ordinary regression, imposition of a lasso penalty makes continuous model selection straightforward. Lasso penalized regression is particularly advantageous when the number of predictors far exceed...
We consider rules for discarding predictors in lasso regression and related problems, for computational efficiency. El Ghaoui et al. (2010) propose “SAFE” rules, based on univariate inner products bet...
The graphical lasso [5] is an algorithm for learning the structure in an undirected Gaussian graphical model, using ℓ1 regularization to control the number of zeros in the precision matrix Θ = Σ...
We propose several methods for estimating edge-sparse and nodesparse graphical models based on lasso and grouped lasso penalties.We develop efficient algorithms for fitting these models when the numbe...
We consider the sparse inverse covariance regularization problem or graphical lasso with regularization parameter λ. Suppose the sample covariance graph formed by thresholding the entries of the sampl...
We develop a new method for frequentist multiple testing with Bayesian prior information. Our procedure nds a new set of optimal p-value weights called the Bayes weights. Prior information is relev...
In this paper we study a bootstrap strategy for estimating the variance of a mean taken over large multifactor crossed random e ects data sets. We apply bootstrap reweighting independently to the lev...
Suppose we have observations yi = si +zi, i = 1; :::; n, where (si) is signal and (zi) is i.i.d. Gaussian white noise. Suppose we have available a library L of orthogonal bases, such as the Wavelet ...
With ideal spatial adaptation, an oracle furnishes information about how best to adapt a spatially variable estimator, whether piecewise constant, piecewise polynomial, variable knot spline, or vari...
Consider estimating the mean vector  from data Nn(; 2I ) with lq norm loss, q  1, when  is known to lie in an n-dimensional lp ball, p 2 (0; 1). For large n, the ratio of minimax linear risk to...
Mallows has conjectured that among distributions which are Gaussian but for occasional contamination by additive noise, the one having least Fisher information has (two-sided) geometric contaminatio...
Pinsker(1980) gave a precise asymptotic evaluation of the minimax mean squared error of estimation of a signal in Gaussian noise when the signal is known a priori to lie in a compact ellipsoid in Hi...
Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. Contemporary data sets of...
This paper explores a class of empirical Bayes methods for levedependent threshold selection in wavelet shrinkage. The prior considered for each wavelet coefficient is a mixture of an atom of p...

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