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On Model Selection Consistency of Lasso
It is proved that a single condition, which is called the Irrepresentable Condition, is almost necessary and sufficient for Lasso to select the true model both in the classical fixed p setting and in the large p setting as the sample size n gets large.
Adaptive wavelet thresholding for image denoising and compression
- S. Chang, Bin Yu, M. Vetterli
- Computer Science, EngineeringIEEE Trans. Image Process.
- 1 September 2000
An adaptive, data-driven threshold for image denoising via wavelet soft-thresholding derived in a Bayesian framework, and the prior used on the wavelet coefficients is the generalized Gaussian distribution widely used in image processing applications.
A unified framework for high-dimensional analysis of $M$-estimators with decomposable regularizers
- S. Negahban, Pradeep Ravikumar, M. Wainwright, Bin Yu
- Computer Science, MathematicsNIPS
- 7 December 2009
A unified framework for establishing consistency and convergence rates for regularized M-estimators under high-dimensional scaling is provided and one main theorem is state and shown how it can be used to re-derive several existing results, and also to obtain several new results.
High-dimensional covariance estimation by minimizing ℓ1-penalized log-determinant divergence
The first result establishes consistency of the estimate b � in the elementwise maximum-norm, which allows us to derive convergence rates in Frobenius and spectral norms, and shows good correspondences between the theoretical predictions and behavior in simulations.
Boosting with the L2-loss: regression and classification
The Minimum Description Length Principle in Coding and Modeling
The normalized maximized likelihood, mixture, and predictive codings are each shown to achieve the stochastic complexity to within asymptotically vanishing terms.
Spectral clustering and the high-dimensional stochastic blockmodel
The asymptotic results in th is paper are the first clustering results that allow the number of clusters in the model to grow with theNumber of nodes, hence the name high-dimensional.
Statistical guarantees for the EM algorithm: From population to sample-based analysis
A general framework for proving rigorous guarantees on the performance of the EM algorithm and a variant known as gradient EM and consequences of the general theory for three canonical examples of incomplete-data problems are developed.
LASSO-TYPE RECOVERY OF SPARSE REPRESENTATIONS FOR HIGH-DIMENSIONAL DATA
Even though the Lasso cannot recover the correct sparsity pattern, the estimator is still consistent in the ‘2-norm sense for fixed designs under conditions on (a) the number sn of non-zero components of the vector n and (b) the minimal singular values of the design matrices that are induced by selecting of order sn variables.
This work formalizes the notion of instability and derive theoretical results to analyze the variance reduction effect of bagging (or variants thereof) in mainly hard decision problems, which include estimation after testing in regression and decision trees for regression functions and classifiers.