Learning the Structure of Mixed Graphical Models

Journal of Computational and Graphical Statistics

Volumn 24, Issue 1, 2015, Pages 230-253

  Lee, Jason D ^a   Hastie, Trevor J ^b  

^a Stanford University   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Group lasso; Lasso; Structure learning

Indexed keywords

EID: 84926139290     PISSN: 10618600     EISSN: 15372715     Source Type: Journal    
DOI: 10.1080/10618600.2014.900500     Document Type: Article

References (38)

1. Bach, F., Jenatton, R., Mairal, J., Obozinski, G. (2011), Optimization With Sparsity-Inducing Penalties, Foundations and Trends in Machine Learning, 4, 1–106. Available at http://dx.doi.org/doi:10.1561/2200000015.
2. Banerjee, O., Ghaoui, L., d’Aspremont, A. (2008), Model Selection Through Sparse Maximum Likelihood Estimation for Multivariate Gaussian or Binary Data, The Journal of Machine Learning Research, 9, 485–516.
3. Beck, A., Teboulle, M. (2010), Gradient-Based Algorithms With Applications to Signal Recovery Problems, in Convex Optimization in Signal Processing and Communications, eds. D. Palomar and Y. Eldar, 42–88, Cambridge: Cambridge University Press.
4. Becker, S.R., Candès, E.J., Grant, M.C. (2011), Templates for Convex Cone Problems With Applications to Sparse Signal Recovery, Mathematical Programming Computation, 3, 165–218.
5. Besag, J. (1974), Spatial Interaction and the Statistical Analysis of Lattice Systems, Journal of the Royal Statistical Society, Series B, 36, 192–236.
6. (1975), Statistical Analysis of Non-Lattice Data, The Statistician, 179–195.
7. Cheng, J., Levina, E., Zhu, J. (2013), High-Dimensional Mixed Graphical Models, arXiv preprint arXiv:1304.2810.
8. Combettes, P.L., Pesquet, J.C. (2011), Proximal Splitting Methods in Signal Processing, in Fixed-Point Algorithms for Inverse Problems in Science and Engineering, eds. H. H. Bauschke et al.,,. New York: Springer, pp. 185–212.
9. Edwards, D. (2000), Introduction to Graphical Modelling, New York: Springer.
10. Friedman, J., Hastie, T., Höfling, H., Tibshirani, R. (2007), Pathwise Coordinate Optimization, The Annals of Applied Statistics, 1, 302–332.
11. Friedman, J., Hastie, T., Tibshirani, R. (2008), Sparse Inverse Covariance Estimation With the Graphical Lasso, Biostatistics, 9, 432–441.
12. ——— (2010), “Applications of the Lasso and Grouped Lasso to the Estimation of Sparse Graphical Models,” Technical Report, Stanford University.
13. Guo, J., Levina, E., Michailidis, G., Zhu, J. (2010), Joint Structure Estimation for Categorical Markov Networks, available at http://www.stat.lsa.umich.edu/~elevina.
14. Höfling, H., Tibshirani, R. (2009), Estimation of Sparse Binary Pairwise Markov Networks Using Pseudo-Likelihoods, The Journal of Machine Learning Research, 10, 883–906.
15. Jalali, A., Ravikumar, P., Vasuki, V., Sanghavi, S., ECE, UT, and CS, UT (2011), “On Learning Discrete Graphical Models Using Group-Sparse Regularization,” in Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS).
16. Kim, S., Sohn, K.-A., Xing, E.P. (2009), A Multivariate Regression Approach to Association Analysis of a Quantitative Trait Network, Bioinformatics, 25, i204–i212.
17. Koller, D., and Friedman, N. (2009), Probabilistic Graphical Models: Principles and Techniques, CambridgeMA: The MIT Press.
18. Lafferty, J., McCallum, A., Pereira, F. C.N. (2001), Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data.” Departmental Papers (CIS), Paper 159, available at http://repository.upenn.edu/cis_papers/159
19. Lauritzen, S.L. (1996), Graphical Models (Vol. 17), Oxford: Clarendon Press.
20. Lee, J.D., Sun, Y., Saunders, M.A. (2012), Proximal Newton-Type Methods for Minimizing Convex Objective Functions in Composite Form, arXiv preprint arXiv:1206.1623.
21. Lee, J.D., Sun, Y., Taylor, J. (2013), On Model Selection Consistency of M-estimators With Geometrically Decomposable Penalties, arXiv preprint arXiv:1305.7477.
22. Lee, S.I., Ganapathi, V., Koller, D. (2006), Efficient Structure Learning of Markov Networks Using L1 regularization, in Advances in Neural Information Processing Systems, 817–827.
23. Liang, P., and Jordan, M.I. (2008), “An Asymptotic Analysis of Generative, Discriminative, and Pseudolikelihood Estimators,” in Proceedings of the 25th International Conference on Machine Learning, ACM, pp. 584–591.
24. Liu, Q., and Ihler, A. (2011), “Learning Scale Free Networks by Reweighted l1 Regularization,” in Proceedings of the 14th International Conference on Artificial Intelligence and Statistics (AISTATS).
25. ——— (2012), “Distributed Parameter Estimation via Pseudo-Likelihood,” in Proceedings of the International Conference on Machine Learning (ICML).
26. Meinshausen, N., Bühlmann, P. (2006), High-Dimensional Graphs and Variable Selection With the Lasso, The Annals of Statistics, 34, 1436–1462.
27. Peng, J., Wang, P., Zhou, N., Zhu, J. (2009), Partial Correlation Estimation by Joint Sparse Regression Models, Journal of the American Statistical Association, 104, 735–746.
28. Ravikumar, P., Wainwright, M.J., Lafferty, J.D. (2010), High-Dimensional Ising Model Selection Using l1-Regularized Logistic Regression, The Annals of Statistics, 38, 1287–1319.
29. Rothman, A.J., Levina, E., Zhu, J. (2010), Sparse Multivariate Regression With Covariance Estimation, Journal of Computational and Graphical Statistics, 19, 947–962.
30. Schmidt, M. (2010), Graphical Model Structure Learning With l1-Regularization, PhD thesis, University of British Columbia.
31. Schmidt, M., Kim, D., Sra, S. (2011), Projected Newton-Type Methods in Machine Learning, in Optimization for Machine Learning, Cambridge, MA: MIT Press.
32. Schmidt, M., Murphy, K., Fung, G., Rosales, R. (2008), Structure Learning in Random Fields for Heart Motion Abnormality Detection, CVPR, IEEE Computer Society.
33. Tur, I., Castelo, R. (2012), Learning Mixed Graphical Models From Data With p Larger Than n, arXiv preprint arXiv:1202.3765.
34. Witten, D.M., Tibshirani, R. (2009), Covariance-Regularized Regression and Classification for High Dimensional Problems, Journal of the Royal Statistical Society, Series B, 71, 615–636.
35. Wright, S.J., Nowak, R.D., Figueiredo, M. A.T. (2009), Sparse Reconstruction by Separable Approximation, IEEE Transactions on Signal Processing, 57, 2479–2493.
36. Yang, E., Ravikumar, P., Allen, G. I., and Liu, Z. (2012), “Graphical Models via Generalized Linear Models,” in Advances in Neural Information Processing Systems25, 1367–1375.
37. (2013), On Graphical Models via Univariate Exponential Family Distributions, arXiv preprint arXiv:1301.4183.
38. Yuan, M., Lin, Y. (2006), Model Selection and Estimation in Regression With Grouped Variables, Journal of the Royal Statistical Society, Series B, 68, 49–67.