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Sparse inverse covariance estimation with the lasso
Sparse inverse covariance estimation the lasso
2015/8/21
We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm— the ...
WAVELET SHRINKAGE FOR CORRELATED DATA AND INVERSE PROBLEMS: ADAPTIVITY RESULTS
Adaptation correlated data fractional brownian motion
2015/8/20
Johnstone and Silverman (1997) described a level-dependent thresholding
method for extracting signals from correlated noise. The thresholds were chosen
to minimize a data based unbiased risk criteri...
Bayesian inverse problems with non-conjugate priors
Rate of contraction posterior distribution nonparametric hypothesis testing.
2012/11/23
We investigate the frequentist posterior contraction rate of nonparametric Bayesian procedures in linear inverse problems in both the mildly and severely ill-posed cases. A theorem is proved in a gene...
Bayes procedures for adaptive inference in nonparametric inverse problems
Bayes procedures adaptive inference nonparametric inverse problems
2012/11/22
We study empirical and hierarchical Bayes approaches to the problem of estimating an infinite-dimensional parameter in mildly ill-posed inverse problems. We consider a class of prior distributions ind...
An Inverse Power Method for Nonlinear Eigenproblems with Applications in 1-Spectral Clustering and Sparse PCA
Inverse Power Method Nonlinear Eigenproblems
2011/1/4
Many problems in machine learning and statistics can be formulated as (generalized) eigenproblems. In terms of the associated optimization problem, computing linear eigenvectors amounts to finding cri...
In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimensi...
Two-Point Vorticity Statistics in the Inverse Turbulent Cascade
Two-Point Vorticity Statistics Inverse Turbulent Cascade
2010/12/28
We present a statistical analysis of the two-point vorticity probability density of the vorticity eld generated in the inverse cascade of stationary two-dimensional turbulence.
Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss
Sequential estimation Point estimator Inverse binomial sampling
2010/12/3
Sequential estimation of the success probability p in inverse binomial sam-pling is considered in this paper. For any estimator ˆp, its quality is measured by the risk associated with normalized ...