1,957
Views
4
CrossRef citations to date
0
Altmetric
Theory and Methods

On High-Dimensional Constrained Maximum Likelihood Inference

, &
Pages 217-230 | Received 13 Aug 2017, Accepted 21 Oct 2018, Published online: 11 Apr 2019

References

  • Alizadeh, F., Haeberly, J. A., and Overton, M. L. (1998), “Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Numerical Results,” SIAM Journal on Optimization, 8, 746–768. DOI: 10.1137/S1052623496304700.
  • Alzheimer’s Association (2016). “Changing the Trajectory of Alzheimer’s Disease: How a Treatment by 2025 Saves Lives and Dollars,”
  • Boyd, S., Parikh, N., Chu, E., Peleato, B., and Eckstein, J. (2011), “Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers,” Foundations and Trends in Machine Learning, 3, 1–122. DOI: 10.1561/2200000016.
  • Brown, L. D. (1986), Fundamentals of Statistical Exponential Families With Applications in Statistical Decision Theory (Lecture Notes-Monograph Series), Durham, NC: Duke University Press, pp. 1–279.
  • Desikan, R. S., Ségonne, F., Fischl, B., Quinn, B. T., Dickerson, B. C., Blacker, D., Buckner, R. L., Dale, A. M., Maguire, R. P., and Hyman, B. T. (2006), “An Automated Labeling System for Subdividing the Human Cerebral Cortex on MRI Scans Into Gyral Based Regions of Interest,” Neuroimage, 31, 968–980. DOI: 10.1016/j.neuroimage.2006.01.021.
  • Fan, J., Feng, Y., and Wu, Y. (2009), “Network Exploration via the Adaptive LASSO and SCAD Penalties,” The Annals of Applied Statistics, 3, 521–541. DOI: 10.1214/08-AOAS215SUPP.
  • Fan, J., and Li, R. (2001), “Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties,” Journal of the American Statistical Association, 96, 1348–1360. DOI: 10.1198/016214501753382273.
  • Friedman, J., Hastie, T., and Tibshirani, R. (2008), “Sparse Inverse Covariance Estimation With the Graphical Lasso,” Biostatistics, 9, 432–441. DOI: 10.1093/biostatistics/kxm045.
  • Greicius, M. D., Srivastava, G., Reiss, A. L., and Menon, V. (2004), “Default-Mode Network Activity Distinguishes Alzheimer’s Disease From Healthy Aging: Evidence From Functional MRI,” Proceedings of the National Academy of Sciences of the United States of America, 101, 4637–4642. DOI: 10.1073/pnas.0308627101.
  • He, Y., Chen, Z., and Evans, A. (2008), “Structural Insights Into Aberrant Topological Patterns of Large-Scale Cortical Networks in Alzheimer’s Disease,” The Journal of Neuroscience, 28, 4756–4766. DOI: 10.1523/JNEUROSCI.0141-08.2008.
  • Janková, J., and Van de Geer, S. (2017), “Honest Confidence Regions and Optimality in High-Dimensional Precision Matrix Estimation,” TEST, 26, 143–162. DOI: 10.1007/s11749-016-0503-5.
  • Javanmard, A., and Montanari, A. (2014), “Confidence Intervals and Hypothesis Testing for High-Dimensional Regression,” Journal of Machine Learning Research, 15, 2869–2909.
  • Li, B., Chun, H., and Zhao, H. (2012), “Sparse Estimation of Conditional Graphical Models With Application to Gene Networks,” Journal of the American Statistical Association, 107, 152–167. DOI: 10.1080/01621459.2011.644498.
  • Lin, Z., Wang, T., Yang, C., and Zhao, H. (2017), “On Joint Estimation of Gaussian Graphical Models for Spatial and Temporal Data,” Biometrics, 73, 769–779. DOI: 10.1111/biom.12650.
  • Liu, J., and Ye, J. (2009), “Efficient Euclidean Projections in Linear Time,” in Proceedings of the 26th Annual International Conference on Machine Learning, pp. 657–664, ACM.
  • Meinshausen, N., and Bühlmann, P. (2006), “High-Dimensional Graphs and Variable Selection With the Lasso,” The Annals of Statistics, 34, 1436–1462. DOI: 10.1214/009053606000000281.
  • Montembeault, M., Rouleau, I., Provost, J. S., and Brambati, S. M. (2015), “Altered Gray Matter Structural Covariance Networks in Early Stages of Alzheimer’s Disease,” Cerebral Cortex, 26, 2650–2662. DOI: 10.1093/cercor/bhv105.
  • Portnoy, S. (1988), “Asymptotic Behavior of Likelihood Methods for Exponential Families When the Number of Parameters Tends to Infinity”, The Annals of Statistics, 16, 356–366. DOI: 10.1214/aos/1176350710.
  • Rothman, A., Bickel, P., Levina, E., and Zhu, J. (2008), “Sparse Permutation Invariant Covariance Estimation,” Electronic Journal of Statistics, 2, 494–515. DOI: 10.1214/08-EJS176.
  • Shen, X. (1997), “On Methods of Sieves and Penalization,” The Annals of Statistics, 25, 2555–2591. DOI: 10.1214/aos/1030741085.
  • Shen, X., Pan, W., and Zhu, Y. (2012), “Likelihood-Based Selection and Sharp Parameter Estimation,” Journal of American Statistical Association, 107, 223–232. DOI: 10.1080/01621459.2011.645783.
  • Shen, X., Pan, W., Zhu, Y., and Zhou, H.(2013), “On Constrained and Regularized High-Dimensional Regression,” Annals of the Institute of Statistical Mathematics, 65, 807–832. DOI: 10.1007/s10463-012-0396-3.
  • Tibshirani, R. (1996), “Regression Shrinkage and Selection Via the Lasso,” Journal of the Royal Statistical Society, Series B, 58, 267–288. DOI: 10.1111/j.2517-6161.1996.tb02080.x.
  • Van de Geer, S., Bühlmann, P., Ritov, Y., and Dezeure, R. (2014), “On Asymptotically Optimal Confidence Regions and Tests for High-Dimensional Models,” The Annals of Statistics, 42, 1166–1202. DOI: 10.1214/14-AOS1221.
  • Yin, J., and Li, H. (2013), “Adjusting for High-Dimensional Covariates in Sparse Precision Matrix Estimation by 1-Penalization,” Journal of Multivariate Analysis, 116, 365–381. DOI: 10.1016/j.jmva.2013.01.005.
  • Yuan, M., and Lin, Y. (2007), “Model Selection and Estimation in the Gaussian Graphical Model,” Biometrika, 94, 19–35. DOI: 10.1093/biomet/asm018.
  • Zhang, C. (2010), “Nearly Unbiased Variable Selection Under Minimax Concave Penalty,” The Annals of Statistics, 38, 894–942. DOI: 10.1214/09-AOS729.
  • Zhang, C., and Zhang, S. (2014), “Confidence Intervals for Low Dimensional Parameters in High Dimensional Linear Models,” Journal of the Royal Statistical Society, Series B, 76, 217–242. DOI: 10.1111/rssb.12026.
  • Zhang, X., and Cheng, G. (2017), “Simultaneous Inference for High-Dimensional Linear Models,” Journal of the American Statistical Association, 112, 757–768. DOI: 10.1080/01621459.2016.1166114.
  • Zhu, Y. (2017), “An Augmented ADMM Algorithm With Application to the Generalized Lasso Problem,” Journal of Computational and Graphical Statistics, 26, 195–204. DOI: 10.1080/10618600.2015.1114491.
  • Zhu, Y., Shen, X., and Pan, W. (2014), “Structural Pursuit Over Multiple Undirected Graphs,” Journal of the American Statistical Association, 109, 1683–1696. DOI: 10.1080/01621459.2014.921182.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.