Markov Neighborhood Regression for High-Dimensional Inference

References

• Aliferis, C., Statnikov, A., Tsamardinos, I., Mani, S., and Koutsoukos, X. D. (2010), “Local Causal and Markov Blanket Induction for Causal Discovery and Feature Selection for Classification, Part I: Algorithms and Empirical Evaluation,” Journal of Machine Learning Research, 11, 171–234.
   Web of Science ®Google Scholar
• Barretina, J., Caponigro, G., Stransky, N., Venkatesan, K., Margolin, A. A., Kim, S., Wilson, C. J., Lehár, J., Kryukov, G. V., Sonkin, D., Reddy, A., Liu, M., Murray, L., Berger, M. F., Monahan, J. E., Morais, P., Meltzer, J., Korejwa, A., Jané-Valbuena, J., Mapa, F. A., Thibault, J., Bric-Furlong, E., Raman, P., Shipwayn, A., Engels, I. H., Cheng, J., Yu, G. K., Yu, J., Aspesi, P., de Silva, M., Jagtap, K., Jones, M. D., Wang, L., Hatton, C., Palescandolo, E., Gupta, S., Mahan, S., Sougnez, C., Onofrio, R. C., Liefeld, T., MacConaill, L., Winckler, W., Reich, M., Li, N., Mesirov, J. P., Gabriel, S. B., Getz, G., Ardlie, K., Chan, V., Myer, V. E., Weber, B. L., Porter, J., Warmuth, M., Finan, P., Harris, J. L., Meyerson, M., Golub, T. R., Morrissey, M. P., Sellers, W. R., Schlegel, R., and Garraway, L. A. (2012), “The Cancer Cell Line Encyclopedia Enables Predictive Modeling of Anticancer Drug Sensitivity,” Nature, 483, 603–607. DOI: 10.1038/nature11003.
   PubMed Web of Science ®Google Scholar
• Belloni, A., Chernozhukov, V., and Kato, K. (2015), “Uniform Post-Selection Inference for Least Absolute Deviation Regression and Other Z-Estimation Problems,” Biometrika, 102, 77–94. DOI: 10.1093/biomet/asu056.
   Web of Science ®Google Scholar
• Berk, R., Brown, L., Buja, A., Zhang, K., and Zhao, L. (2013), “Valid Post-Selection Inference,” The Annals of Statistics, 41, 802–837. DOI: 10.1214/12-AOS1077.
   Web of Science ®Google Scholar
• Bowman, E., Campbell, J., Druey, K., Scheschonka, A., Kehrl, J., and Butcher, E. (1998), “Regulation of Chemotactic and Proadhesive Responses to Chemoattractant Receptors by RGS (Regulator of G-Protein Signaling) Family Members,” Journal of Biological Chemistry, 273, 28040–28048. DOI: 10.1074/jbc.273.43.28040.
   PubMed Web of Science ®Google Scholar
• Bühlmann, P. (2013), “Statistical Significance in High-Dimensional Linear Models,” Bernoulli, 19, 1212–1242. DOI: 10.3150/12-BEJSP11.
   Web of Science ®Google Scholar
• Bühlmann, P., Kalisch, M., and Maathuis, M. (2010), “Variable Selection in High-Dimensional Linear Models: Partially Faithful Distributions and the PC-Simple Algorithm,” Biometrika, 97, 261–278. DOI: 10.1093/biomet/asq008.
   Web of Science ®Google Scholar
• Bühlmann, P., and van de Geer, S. (2011), Statistics for High-Dimensional Data: Methods, Theory and Applications, New York: Springer.
   Google Scholar
• Buzdar, A. (2009), “Role of Biologic Therapy and Chemotherapy in Hormone Receptor and HER2-Positive Breast Cancer,” The Annals of Oncology, 20, 993–999. DOI: 10.1093/annonc/mdn739.
   PubMed Web of Science ®Google Scholar
• Chatterjee, A., and Lahiri, S. (2013), “Rates of Convergence of the Adaptive LASSO Estimators to the Oracle Distribution and Higher Order Refinements by the Bootstrap,” The Annals of Statistics, 41, 1232–1259. DOI: 10.1214/13-AOS1106.
   Web of Science ®Google Scholar
• Cox, D. (1975), “Partial Likelihood,” Biometrika, 62, 269–276. DOI: 10.1093/biomet/62.2.269.
   Web of Science ®Google Scholar
• Dezeure, R., Bühlmann, P., Meier, L., and Meinshausen, N. (2015), “High-Dimensional Inference: Confidence Intervals, p-Values and R-Software hdi,” Statistical Science, 30, 533–558. DOI: 10.1214/15-STS527.
   Web of Science ®Google Scholar
• Dobra, A. (2009), “Variable Selection and Dependency Networks for Genomewide Data,” Biostatistics, 10, 621–639. DOI: 10.1093/biostatistics/kxp018.
   PubMed Web of Science ®Google Scholar
• Dorman, S., Baranova, K., Knoll, J., Urquhart, B., Mariani, G., Carcangiu, M., and Rogan, P. (2016), “Genomic Signatures for Paclitaxel and Gemcitabine Resistance in Breast Cancer Derived by Machine Learning,” Molecular Oncology, 10, 85–100. DOI: 10.1016/j.molonc.2015.07.006.
   PubMed Web of Science ®Google Scholar
• Fan, J., Guo, S., and Hao, N. (2012), “Variance Estimation Using Refitted Cross-Validation in Ultrahigh Dimensional Regression,” Journal of the Royal Statistical Society, Series B, 74, 37–65. DOI: 10.1111/j.1467-9868.2011.01005.x.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• Fan, J., and Lv, J. (2008), “Sure Independence Screening for Ultrahigh Dimensional Feature Space” (with discussion), Journal of the Royal Statistical Society, Series B, 70, 849–911. DOI: 10.1111/j.1467-9868.2008.00674.x.
   PubMed Web of Science ®Google Scholar
• Fan, J., and Peng, H. (2004), “Nonconcave Penalized Likelihood With a Diverging Number of Parameters,” The Annals of Statistics, 32, 928–961. DOI: 10.1214/009053604000000256.
   Web of Science ®Google Scholar
• Fan, J., and Song, R. (2010), “Sure Independence Screening in Generalized Linear Model With NP-Dimensionality,” The Annals of Statistics, 38, 3567–3604. DOI: 10.1214/10-AOS798.
   Web of Science ®Google Scholar
• Fithian, W., Sun, D., and Taylor, J. (2014), “Optimal Inference After Model Selection,” arXiv no. 1410.2597.
   Google Scholar
• 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.
   PubMed Web of Science ®Google Scholar
• Gaither, A., Porter, D., Yao, Y., Borawski, J., Yang, G., Donovan, J., Sage, D., Slisz, J., Tran, M., Straub, C., Ramsey, T., Iourgenko, V., Huang, A., Chen, Y., Schlegel, R., Labow, M., Fawell, S., Sellers, W., and Zawel, L. (2007), “A Smac Mimetic Rescue Screen Reveals Roles for Inhibitor of Apoptosis Proteins in Tumor Necrosis Factor-Alpha Signaling,” Cancer Research, 67, 11493–11498. DOI: 10.1158/0008-5472.CAN-07-5173.
   PubMed Web of Science ®Google Scholar
• Grünwald, V., and Hidalgo, M. (2003), “Developing Inhibitors of the Epidermal Growth Factor Receptor for Cancer Treatment,” Journal of the National Cancer Institute, 95, 851–867. DOI: 10.1093/jnci/95.12.851.
   PubMed Web of Science ®Google Scholar
• Hadley, K., and Hendricks, D. (2014), “Use of NQO1 Status as a Selective Biomarker for Oesophageal Squamous Cell Carcinomas With Greater Sensitivity to 17-AAG,” BMC Cancer, 14, 1–8. DOI: 10.1186/1471-2407-14-334.
   PubMed Web of Science ®Google Scholar
• Hans, C., Dobra, A., and West, M. (2007), “Shotgun Stochastic Search for Regression With Many Candidate Predictors,” Journal of the American Statistical Association, 102, 507–516. DOI: 10.1198/016214507000000121.
   Web of Science ®Google Scholar
• Holm, S. (1979), “A Simple Sequentially Rejective Multiple Test Procedure,” Scandinavian Journal of Statistics, 6, 65–70.
   Web of Science ®Google Scholar
• Javanmard, A., and Montanari, A. (2014), “Confidence Intervals and Hypothesis Testing for High-Dimensional Regression,” Journal of Machine Learning Research, 15, 2869–2909.
   Web of Science ®Google Scholar
• Jia, B., Liang, F., Shi, R., and Xu, S. (2018), “equSA: Estimate Directed and Undirected Graphical Models and Construct Networks,” R Package Version 1.1.5, available at https://CRAN.R-project.org/package=equSA.
   Google Scholar
• Lauritzen, S. (1996), Graphical Models, Oxford: Oxford University Press.
   Google Scholar
• Lawrence, R., and Salgia, R. (2010), “MET Molecular Mechanisms and Therapiesin Lung Cancer,” Cell Adhesion & Migration, 4, 146–152.
   PubMed Web of Science ®Google Scholar
• Lee, H., Hanibuchi, M., Lim, S.-J., Yu, H., Kim, M., He, J., Langley, R., Lehembre, F., Regenass, U., and Fidler, I. (2016), “Treatment of Experimental Human Breast Cancer and Lung Cancer Brain Metastases in Mice by Macitentan, a Dual Antagonist of Endothelin Receptors, Combined With Paclitaxel,” NeuroOncology, 18, 486–496. DOI: 10.1093/neuonc/now037.
   PubMed Web of Science ®Google Scholar
• Lee, J. D., and Hastie, T. J. (2015), “Learning the Structure of Mixed Graphical Models,” Journal of Computational and Graphical Statistics, 24, 230–253. DOI: 10.1080/10618600.2014.900500.
   PubMed Web of Science ®Google Scholar
• Lee, J. D., Sun, D. L., Sun, Y., and Taylor, J. E. (2016), “Exact Post-Selection Inference, With Application to the Lasso,” The Annals of Statistics, 44, 907–927. DOI: 10.1214/15-AOS1371.
   Web of Science ®Google Scholar
• Liang, F., Song, Q., and Qiu, P. (2015), “An Equivalent Measure of Partial Correlation Coefficients for High Dimensional Gaussian Graphical Models,” Journal of the American Statistical Association, 110, 1248–1265. DOI: 10.1080/01621459.2015.1012391.
   Web of Science ®Google Scholar
• Liang, F., Song, Q., and Yu, K. (2013), “Bayesian Subset Modeling for High Dimensional Generalized Linear Models,” Journal of the American Statistical Association, 108, 589–606. DOI: 10.1080/01621459.2012.761942.
   Web of Science ®Google Scholar
• Liang, F., and Zhang, J. (2008), “Estimating FDR Under General Dependence Using Stochastic Approximation,” Biometrika, 95, 961–977. DOI: 10.1093/biomet/asn036.
   Web of Science ®Google Scholar
• Liu, Y., and Yu, B. (2013), “Asymptotic Properties of Lasso + mLS and Lasso + Ridge in Sparse High-Dimensional Linear Regression,” Electronic Journal of Statistics, 7, 3124–3169.
   Web of Science ®Google Scholar
• Lockhart, R., Taylor, J., Tibshirani, R., and Tibshirani, B. (2014), “A Significant Test for the Lasso,” The Annals of Statistics, 42, 413–468. DOI: 10.1214/13-AOS1175.
   PubMed Web of Science ®Google Scholar
• McCullagh, P., and Nelder, J. A. (1989), Generalized Linear Models (2nd ed.), London: Chapman & Hall.
   Google Scholar
• Meek, C. (1995), “Causal Inference and Causal Explanation With Background Knowledge,” in Proceedings of the 11th Conference on Uncertainty in Artificial Intelligence, pp. 403–410.
   Google Scholar
• Meier, L., Dezeure, R., Meinshausen, N., Maechler, M., and Buehlmann, P. (2016), “High-Dimensional Inference,” available at https://cran.r-project.org/.
   Google Scholar
• Meinshausen, N. (2007), “Relaxed Lasso,” Computational Statistics & Data Analysis, 52, 374–393.
   Web of Science ®Google Scholar
• Meinshausen, N. (2015), “Group Bound: Confidence Intervals for Groups of Variables in Sparse High Dimensional Regression Without Assumptions on the Design,” Journal of the Royal Statistical Society, Series B, 77, 923–945.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• Meinshausen, N., Meier, L., and Bühlmann, P. (2009), “p-Values for High-Dimensional Regression,” Journal of the American Statistical Association, 104, 1671–1681. DOI: 10.1198/jasa.2009.tm08647.
   Web of Science ®Google Scholar
• Moriwaki, K., Bertin, J., Gough, P., Orlowski, G., and Chan, F. (2015), “Differential Roles of RIPK1 and RIPK3 in TNF-Induced Necroptosis and Chemotherapeutic Agent-Induced Cell Death,” Cell Death & Disease, 6, e1636.
   PubMed Web of Science ®Google Scholar
• Ooe, A., Kato, K., and Noguchi, S. (2007), “Possible Involvement of CCT5, RGS3, and YKT6 Genes Up-Regulated in p53-Mutated Tumors in Resistance to Docetaxel in Human Breast Cancers,” Breast Cancer Research and Treatment, 101, 305–315. DOI: 10.1007/s10549-006-9293-x.
   PubMed Web of Science ®Google Scholar
• Pellet, J.-P., and Elisseeff, A. (2008), “Using Markov Blankets for Causal Structure Learning,” Journal of Machine Learning Research, 9, 1295–1342.
   Web of Science ®Google Scholar
• Saldana, D., and Feng, Y. (2018), “SIS: An R Package for Sure Independence Screening in Ultrahigh-dimensional Statistical Models,” Journal of Statistical Software, 83, 1–25. DOI: 10.18637/jss.v083.i02.
   Web of Science ®Google Scholar
• Song, Q., and Liang, F. (2015a), “High Dimensional Variable Selection With Reciprocal L1-Regularization,” Journal of the American Statistical Association, 110, 1607–1620. DOI: 10.1080/01621459.2014.984812.
   Web of Science ®Google Scholar
• Song, Q., and Liang, F. (2015b), “A Split-and-Merge Bayesian Variable Selection Approach for Ultra-high Dimensional Regression,” Journal of the Royal Statistical Society, Series B, 77, 947–972.
   Google Scholar
• Spirtes, P., Glymour, C., and Scheines, R. (2000), Causation, Prediction, and Search, Boston: MIT Press.
   Google Scholar
• Storey, J. (2002), “A Direct Approach to False Discovery Rates,” Journal of the Royal Statistical Society, Series B, 64, 479–498. DOI: 10.1111/1467-9868.00346.
   Google Scholar
• 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.
   Google Scholar
• Tibshirani, R. J., Taylor, J., Lockhart, R., and Tibshirani, R. (2016), “Exact Post-Selection Inference for Sequential Regression Procedures,” Journal of the American Statistical Association, 111, 600–620. DOI: 10.1080/01621459.2015.1108848.
   Web of Science ®Google Scholar
• van de Geer, S., and Bühlmann, P. (2009), “On the Conditions Used to Prove Oracle Results for the Lasso,” Electronic Journal of Statistics, 3, 1360–1392. DOI: 10.1214/09-EJS506.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Wasserman, L., and Roeder, K. (2009), “High-Dimensional Variable Selection,” The Annals of Statistics, 37, 2178–2201. DOI: 10.1214/08-aos646.
   PubMed Web of Science ®Google Scholar
• Witten, D., Friedman, J., and Simon, N. (2011), “New Insights and Faster Computations for the Graphical Lasso,” Journal of Computational and Graphical Statistics, 20, 892–900. DOI: 10.1198/jcgs.2011.11051a.
   Web of Science ®Google Scholar
• Xu, S., Jia, B., and Liang, F. (2019), “Learning Moral Graphs in Construction of High-Dimensional Bayesian Networks for Mixed Data,” Neural Computation, 31, 1183–1214. DOI: 10.1162/neco_a_01190.
   PubMed Web of Science ®Google Scholar
• Xue, J., and Liang, F. (2017), “A Robust Model-Free Feature Screening Method for Ultrahigh Dimensional Data,” Journal of Computational and Graphical Statistics, 26, 803–818. DOI: 10.1080/10618600.2017.1328364.
   PubMed Web of Science ®Google Scholar
• Yang, Y. (2017), “Statistical Inference for High Dimensional Regression via Constrained Lasso,” arXiv no. 1704.05098v1.
   Google Scholar
• Yuan, M., and Lin, Y. (2007), “Model Selection and Estimation in the Gaussian Graphical Model,” Biometrika, 95, 19–35. DOI: 10.1093/biomet/asm018.
   Web of Science ®Google Scholar
• Zhang, C.-H. (2010), “Nearly Unbiased Variable Selection Under Minimax Concave Penalty,” The Annals of Statistics, 38, 894–942. DOI: 10.1214/09-AOS729.
   Web of Science ®Google Scholar
• Zhang, C.-H., and Zhang, S. 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.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Zoppoli, G., Regairaz, M., Leo, E., Reinhold, W., Varma, S., Ballestrero, A., Doroshow, J., and Pommier, Y. (2012), “Putative DNA/RNA Helicase Schlafenl1 (SLFN11) Sensitizes Cancer Cells to DNA-Damaging Agents,” Proceedings of the National Academy of Sciences of the United States of America, 109, 15030–15035. DOI: 10.1073/pnas.1205943109.
   PubMed Web of Science ®Google Scholar
• Zou, H. (2006), “The Adaptive Lasso and Its Oracle Properties,” The Annals of Statistics, 38, 894–942.
   Google Scholar