Estimation and Inference for High-Dimensional Generalized Linear Models with Knowledge Transfer

References

• Agarwal, A., Negahban, S., and Wainwright, M. J. (2012), “Noisy Matrix Decomposition via Convex Relaxation: Optimal Rates in High Dimensions,” The Annals of Statistics, 40, 1171–1197. DOI: 10.1214/12-AOS1000.
   Web of Science ®Google Scholar
• Bastani, H. (2018), “Predicting with Proxies: Transfer Learning in High Dimension,” arXiv: 1812.11097.
   Google Scholar
• Baxter, N. T., Zackular, J. P., Chen, G. Y., and Schloss, P. D. (2014), “Structure of the Gut Microbiome Following Colonization with Human Feces Determines Colonic Tumor Burden,” Microbiome, 2, 1–11. DOI: 10.1186/2049-2618-2-20.
   PubMed Web of Science ®Google Scholar
• Bradic, J., Claeskens, G., and Gueuning, T. (2020), “Fixed Effects Testing in High-Dimensional Linear Mixed Models,” Journal of the American Statistical Association, 115, 1835–1850. DOI: 10.1080/01621459.2019.1660172.
   Web of Science ®Google Scholar
• Cai, T. T., and Guo, Z. (2017), “Confidence Intervals for High-Dimensional Linear Regression: Minimax Rates and Adaptivity,” The Annals of Statistics, 45, 615–646.
   Web of Science ®Google Scholar
• Cai, T. T., Guo, Z., and Ma, R. (in press), “Statistical Inference for High-Dimensional Generalized Linear Models with Binary Outcomes,” Journal of the American Statistical Association.
   Web of Science ®Google Scholar
• Cai, T. T., Wang, Y., and Zhang, L. (2020), “The Cost of Privacy in Generalized Linear Models: Algorithms and Minimax Lower Bounds,” arXiv:2011.03900.
   Google Scholar
• Cai, T. T., Wang, Y., and Zhang, L. (2021), “The Cost of Privacy: Optimal Rates of Convergence for Parameter Estimation with Differential Privacy,” Annals of Statistics, 49, 2825–2850.
   Web of Science ®Google Scholar
• Cai, T. T., and Wei, H. (2021), “Transfer Learning for Nonparametric Classification: Minimax Rate and Adaptive Classifier,” The Annals of Statistics, 49, 100–128. DOI: 10.1214/20-AOS1949.
   Web of Science ®Google Scholar
• Campbell, P. T., Lin, Y., Bien, S. A., Figueiredo, J. C., Harrison, T. A., Guinter, M. A., Berndt, S. I., Brenner, H., Chan, A. T., Chang-Claude, J., et al. (2021), “Association of Body Mass Index with Colorectal Cancer Risk by Genome-Wide Variants,” JNCI: Journal of the National Cancer Institute, 113, 38–47. DOI: 10.1093/jnci/djaa058.
   PubMedGoogle Scholar
• Chen, X., Kim, S., Lin, Q., Carbonell, J. G., and Xing, E. P. (2010), “Graph-Structured Multi-Task Regression and an Efficient Optimization Method for General Fused Lasso,” arXiv:1005.3579.
   Google Scholar
• Dai, D., Rigollet, P., and Zhang, T. (2012), “Deviation Optimal Learning Using Greedy q-Aggregation,” The Annals of Statistics, 40, 1878–1905. DOI: 10.1214/12-AOS1025.
   Web of Science ®Google Scholar
• Danaher, P., Wang, P., and Witten, D. M. (2014), “The Joint Graphical Lasso for Inverse Covariance Estimation Across Multiple Classes,” Journal of the Royal Statistical Society, Series B, 76, 373–397. DOI: 10.1111/rssb.12033.
   Google Scholar
• Dezeure, R., Bühlmann, P., and Zhang, C.-H. (2017), “High-Dimensional Simultaneous Inference with the Bootstrap,” Test, 26, 685–719. DOI: 10.1007/s11749-017-0554-2.
   Web of Science ®Google Scholar
• Dondelinger, F., Mukherjee, S., and The Alzheimer’s Disease Neuroimaging Initiative (2020), “The Joint Lasso: High-Dimensional Regression for Group Structured Data,” Biostatistics, 21, 219–235. DOI: 10.1093/biostatistics/kxy035.
   PubMed Web of Science ®Google Scholar
• Duvallet, C., Gibbons, S. M., Gurry, T., Irizarry, R. A., and Alm, E. J. (2017), “Meta-Analysis of Gut Microbiome Studies Identifies Disease-Specific and Shared Responses,” Nature Communications, 8, 1–10. DOI: 10.1038/s41467-017-01973-8.
   PubMed Web of Science ®Google Scholar
• Dwork, C., and Roth, A. (2014), “The Algorithmic Foundations of Differential Privacy,” Foundations and Trends[textregistered] in Theoretical Computer Science, 9, 211–407. DOI: 10.1561/0400000042.
   Google Scholar
• Fang, E. X., Ning, Y., and Liu, H. (2017), “Testing and Confidence Intervals for High Dimensional Proportional Hazards Models,” Journal of the Royal Statistical Society, Series B, 79, 1415–1437. DOI: 10.1111/rssb.12224.
   Google Scholar
• Hanneke, S., and Kpotufe, S. (2020), “A No-Free-Lunch Theorem for Multitask Learning,” arXiv:2006.15785.
   Google Scholar
• Hastie, T., Tibshirani, R., and Friedman, J. (2009), The Elements of Statistical Learning: Data Mining, Inference, and Prediction, New York: Springer.
   Google Scholar
• Hosny, K. M., Kassem, M. A., and Foaud, M. M. (2018), “Skin Cancer Classification Using Deep Learning and Transfer Learning,” in 2018 9th Cairo International Biomedical Engineering Conference (CIBEC), pp. 90–93. IEEE. DOI: 10.1109/CIBEC.2018.8641762.
   Google Scholar
• Huang, J., and Zhang, C.-H. (2012), “Estimation and Selection via Absolute Penalized Convex Minimization and its Multistage Adaptive Applications,” The Journal of Machine Learning Research, 13, 1839–1864.
   PubMed Web of Science ®Google Scholar
• Javanmard, A., and Javadi, H. (2019), “False Discovery Rate Control via Debiased Lasso,” Electronic Journal of Statistics, 13, 1212–1253. DOI: 10.1214/19-EJS1554.
   Web of Science ®Google Scholar
• Javanmard, A., and Montanari, A. (2014), “Confidence Intervals and Hypothesis Testing for High-Dimensional Regression,” The Journal of Machine Learning Research, 15, 2869–2909.
   Web of Science ®Google Scholar
• Jiang, Y., He, Y., and Zhang, H. (2016), “Variable Selection with Prior Information for Generalized Linear Models via the Prior Lasso Method,” Journal of the American Statistical Association, 111, 355–376. DOI: 10.1080/01621459.2015.1008363.
   PubMed Web of Science ®Google Scholar
• Li, S. (2020), “Debiasing the Debiased Lasso with Bootstrap,” Electronic Journal of Statistics, 14, 2298–2337. DOI: 10.1214/20-EJS1713.
   Web of Science ®Google Scholar
• Li, S., Cai, T. T., and Li, H. (2020), “Inference for High-Dimensional Linear Mixed-Effects Models: A Quasi-Likelihood Approach,” Journal of the American Statistical Association, 117, 1835–1846. DOI: 10.1080/01621459.2021.1888740.
   Web of Science ®Google Scholar
• Li, S., Cai, T. T., and Li, H. (in press-a), “Transfer Learning for High-Dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality,” Journal of the Royal Statistical Society, Series B.
   Google Scholar
• Li, S., Cai, T. T., and Li, H. (in press-b), “Transfer Learning in Large-Scale Gaussian Graphical Models with False Discovery Rate Control,” Journal of the American Statistical Association, DOI: 10.1080/01621459.2022.2044333.
   Web of Science ®Google Scholar
• Li, S., Zhang, L., Cai, T. T., and Li, H. (2021), “Supplements to “Estimation and Inference in High-Dimensional Generalized Linear Models with Knowledge Transfer”.”
   Google Scholar
• Liang, M., Zhong, X., and Park, J. (2020), “Learning a High-Dimensional Classification Rule Using Auxiliary Outcomes,” arXiv:2011.05493.
   Google Scholar
• Ma, R., Tony Cai, T., and Li, H. (2020), “Global and Simultaneous Hypothesis Testing for High-Dimensional Logistic Regression Models,” Journal of the American Statistical Association, 116, 984–998. DOI: 10.1080/01621459.2019.1699421.
   PubMed Web of Science ®Google Scholar
• Negahban, S. N., Ravikumar, P., Wainwright, M. J., and Yu, B. (2012), “A Unified Framework for High-Dimensional Analysis of m-estimators with Decomposable Regularizers,” Statistical Science, 27, 538–557. DOI: 10.1214/12-STS400.
   Web of Science ®Google Scholar
• Pan, S. J., and Yang, Q. (2009), “A Survey on Transfer Learning,” IEEE Transactions on Knowledge and Data Engineering, 22, 1345–1359. DOI: 10.1109/TKDE.2009.191.
   Web of Science ®Google Scholar
• Rigollet, P., and Tsybakov, A. (2011), “Exponential Screening and Optimal Rates of Sparse Estimation,” The Annals of Statistics, 39, 731–771. DOI: 10.1214/10-AOS854.
   Web of Science ®Google Scholar
• Sevakula, R. K., Singh, V., Verma, N. K., Kumar, C., and Cui, Y. (2018), “Transfer Learning for Molecular Cancer Classification using Deep Neural Networks,” IEEE/ACM Transactions on Computational Biology and Bioinformatics, 16, 2089–2100. DOI: 10.1109/TCBB.2018.2822803.
   PubMed Web of Science ®Google Scholar
• Takada, M., and Fujisawa, H. (2020), “Transfer Learning via l1 Regularization,” in Advances in Neural Information Processing Systems (Vol. 33), pp. 14266–14277.
   Google Scholar
• Tian, Y., and Feng, Y. (2022), “Transfer Learning under High-Dimensional Generalized Linear Models,” Journal of the American Statistical Association, 1–30 (just-accepted), DOI: 10.1080/01621459.2022.2071278.
   PubMed Web of Science ®Google Scholar
• Torrey, L., and Shavlik, J. (2010), “Transfer Learning,” in Handbook of Research on Machine Learning Applications and Trends: Algorithms, Methods, and Techniques, pp. 242–264, Hershey, PA: IGI Global.
   Google Scholar
• Tripuraneni, N., Jin, C., and Jordan, M. I. (2020), “Provable Meta-Learning of Linear Representations,” arXiv:2002.11684.
   Google Scholar
• Tripuraneni, N., Jordan, M. I., and Jin, C. (2020), “On the Theory of Transfer Learning: The Importance of Task Diversity,” arXiv:2006.11650.
   Google Scholar
• Turki, T., Wei, Z., and Wang, J. T. (2017), “Transfer Learning Approaches to Improve Drug Sensitivity Prediction in Multiple Myeloma Patients,” IEEE Access, 5, 7381–7393. DOI: 10.1109/ACCESS.2017.2696523.
   Web of Science ®Google Scholar
• van de Geer, S., Bühlmann, P., Ritov, Y. (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
• Van de Geer, S. A. (2008), “High-Dimensional Generalized Linear Models and the Lasso,” The Annals of Statistics, 36, 614–645. DOI: 10.1214/009053607000000929.
   Web of Science ®Google Scholar
• Yurdakul, D., Yazgan-Karataş, A., and Şahin, F. (2015), “Enterobacter Strains Might Promote Colon Cancer,” Current Microbiology, 71, 403–411. DOI: 10.1007/s00284-015-0867-x.
   PubMed 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
• Zhang, Y., Liu, M., Neykov, M., and Cai, T. (2020), “Prior Adaptive Semi-supervised Learning with Application to EHR Phenotyping,” arXiv preprint arXiv:2003.11744.
   Google Scholar
• Zhang, Y., and Yang, Q. (2017), “A Survey on Multi-Task Learning,” arXiv:1707.08114.
   Google Scholar
• Zheng, R., Du, M., Zhang, B., Xin, J., Chu, H., Ni, M., Zhang, Z., Gu, D., and Wang, M. (2018), “Body Mass Index (BMI) Trajectories and Risk of Colorectal Cancer in the PLCO Cohort,” British Journal of Cancer, 119, 130–132. DOI: 10.1038/s41416-018-0121-y.
   PubMed Web of Science ®Google Scholar
• Zhu, Y., and Bradic, J. (2018), “Significance Testing in Non-sparse High-dimensional Linear Models,” Electronic Journal of Statistics, 12, 3312–3364. DOI: 10.1214/18-EJS1443.
   Web of Science ®Google Scholar