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Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs
Sparse graphical model Reversible Markov chain Markov equivalence class
2016/1/25
Graphical models are popular statistical tools which are used to represent dependent or causal complex systems. Statistically equivalent causal or directed graphical models are said to belong to a Mar...
Bayesian and L1 Approaches to Sparse Unsupervised Learning
Bayesian L1 Approaches Sparse Unsupervised Learning
2011/7/6
The use of L1 regularisation for sparse learning has generated immense research interest, with successful application in such diverse areas as signal acquisition, image coding, genomics and collaborat...
High Dimensional Sparse Econometric Models: An Introduction
High Dimensional Sparse Econometric Models An Introduction
2011/7/6
In this chapter we discuss conceptually high dimensional sparse econometric models as well as estimation of these models using L1-penalization and post-L1-penalization methods.
Sparse Bayesian Methods for Low-Rank Matrix Estimation
Low-Rank Matrix Estimation Sparse Bayesian Methods
2011/3/24
Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesti...
Submodular meets Spectral: Greedy Algorithms for Subset Selection, Sparse Approximation and Dictionary Selection
Greedy Algorithms Subset Selection Dictionary Selection
2011/3/22
We study the problem of selecting a subset of k random variables from a large set, in order to obtain the best linear prediction of another variable of interest. This problem can be viewed in the cont...
Adaptive Thresholding for Sparse Covariance Matrix Estimation
constrained ℓ 1 minimization covariance matrix Frobenius norm Gaus-sian graphical model rate of convergence precision matrix spectral norm
2011/3/21
In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven...
A Constrained L1 Minimization Approach to Sparse Precision Matrix Estimation
constrained ℓ 1 minimization covariance matrix Frobenius norm Gaus-sian graphical model rate of convergence precision matrix spectral norm
2011/3/21
A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy ...