On the convergence of the coordinate descent method for convex differentiable minimization
Journal of Optimization Theory and Applications
Determinant Maximization with Linear Matrix Inequality Constraints
SIAM Journal on Matrix Analysis and Applications
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Covariance selection for nonchordal graphs via chordal embedding
Optimization Methods & Software - Mathematical programming in data mining and machine learning
Log-determinant relaxation for approximate inference in discrete Markov random fields
IEEE Transactions on Signal Processing - Part I
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Sparse Gaussian graphical models with unknown block structure
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Decomposable principal component analysis
IEEE Transactions on Signal Processing
The Nonparanormal: Semiparametric Estimation of High Dimensional Undirected Graphs
The Journal of Machine Learning Research
Covariance estimation in decomposable Gaussian graphical models
IEEE Transactions on Signal Processing
Robust graphical modeling with t-distributions
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Group sparse priors for covariance estimation
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Grafting-light: fast, incremental feature selection and structure learning of Markov random fields
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Semi-supervised sparse metric learning using alternating linearization optimization
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
High Dimensional Inverse Covariance Matrix Estimation via Linear Programming
The Journal of Machine Learning Research
Learning an L1-regularized Gaussian Bayesian network in the equivalence class space
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Learning sparse Gaussian Markov networks using a greedy coordinate ascent approach
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part III
ICONIP'10 Proceedings of the 17th international conference on Neural information processing: theory and algorithms - Volume Part I
Topology Selection in Graphical Models of Autoregressive Processes
The Journal of Machine Learning Research
Regularized parameter estimation in high-dimensional gaussian mixture models
Neural Computation
Network-scale traffic modeling and forecasting with graphical lasso
ISNN'11 Proceedings of the 8th international conference on Advances in neural networks - Volume Part II
The Journal of Machine Learning Research
Common substructure learning of multiple graphical Gaussian models
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part II
Inferring multiple graphical structures
Statistics and Computing
High-dimensional Covariance Estimation Based On Gaussian Graphical Models
The Journal of Machine Learning Research
Solving Log-Determinant Optimization Problems by a Newton-CG Primal Proximal Point Algorithm
SIAM Journal on Optimization
Theory and Applications of Robust Optimization
SIAM Review
Missing values: sparse inverse covariance estimation and an extension to sparse regression
Statistics and Computing
Model selection and estimation in the matrix normal graphical model
Journal of Multivariate Analysis
Foundations and Trends® in Machine Learning
Exact covariance thresholding into connected components for large-scale graphical lasso
The Journal of Machine Learning Research
Alternating Direction Method for Covariance Selection Models
Journal of Scientific Computing
Fitting very large sparse Gaussian graphical models
Computational Statistics & Data Analysis
Journal of Multivariate Analysis
Numerical methods for A-optimal designs with a sparsity constraint for ill-posed inverse problems
Computational Optimization and Applications
A unifying probabilistic perspective for spectral dimensionality reduction: insights and new models
The Journal of Machine Learning Research
Short communication: A note on the lack of symmetry in the graphical lasso
Computational Statistics & Data Analysis
Sparse methods for biomedical data
ACM SIGKDD Explorations Newsletter
Multiple Response Regression for Gaussian Mixture Models with Known Labels
Statistical Analysis and Data Mining
Group sparse inverse covariance selection with a dual augmented lagrangian method
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part III
Monitoring the covariance matrix with fewer observations than variables
Computational Statistics & Data Analysis
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Robust methods for inferring sparse network structures
Computational Statistics & Data Analysis
Learning a factor model via regularized PCA
Machine Learning
Journal of Multivariate Analysis
Sparse matrix inversion with scaled Lasso
The Journal of Machine Learning Research
A joint convex penalty for inverse covariance matrix estimation
Computational Statistics & Data Analysis
Hi-index | 0.01 |
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l1-norm penalty term. The problem as formulated is convex but the memory requirements and complexity of existing interior point methods are prohibitive for problems with more than tens of nodes. We present two new algorithms for solving problems with at least a thousand nodes in the Gaussian case. Our first algorithm uses block coordinate descent, and can be interpreted as recursive l1-norm penalized regression. Our second algorithm, based on Nesterov's first order method, yields a complexity estimate with a better dependence on problem size than existing interior point methods. Using a log determinant relaxation of the log partition function (Wainwright and Jordan, 2006), we show that these same algorithms can be used to solve an approximate sparse maximum likelihood problem for the binary case. We test our algorithms on synthetic data, as well as on gene expression and senate voting records data.