Spatial Homogeneity Pursuit of Regression Coefficients for Large Datasets

References

• Arnold, T. B., and Tibshirani, R. J. (2016), “Efficient Implementations of the Generalized Lasso Dual Path Algorithm,” Journal of Computational and Graphical Statistics, 25, 1–27. DOI: 10.1080/10618600.2015.1008638.
   Web of Science ®Google Scholar
• Banerjee, S., Gelfand, A. E., Finley, A. O., and Sang, H. (2008), “Gaussian Predictive Process Models for Large Spatial Data Sets,” Journal of the Royal Statistical Society, Series B, 70, 825–848. DOI: 10.1111/j.1467-9868.2008.00663.x.
   Google Scholar
• Basu, S., and Michailidis, G. (2015), “Regularized Estimation in Sparse High-dimensional Time Series Models,” Annals of Statistics 43, 1535–1567. DOI: 10.1214/15-AOS1315.
   Web of Science ®Google Scholar
• Boyd, S. (2011). “Alternating Direction Method of Multipliers,” in Talk at NIPS Workshop on Optimization and Machine Learning. DOI: 10.1561/2200000016.
   Google Scholar
• Braunstein, L. A., Wu, Z., Chen, Y., Buldyrev, S. V., Kalisky, T., Sreenivasan, S., Cohen, R., López, E., Havlin, S., and Stanley, H. E. (2007), “Optimal Path and Minimal Spanning Trees in Random Weighted Networks,” International Journal of Bifurcation and Chaos, 17, 2215–2255. DOI: 10.1142/S0218127407018361.
   Web of Science ®Google Scholar
• Came, R. E., Oppo, D. W., Curry, W. B., and Lynch-Stieglitz, J. (2008), “Deglacial Variability in the Surface Return Flow of the Atlantic Meridional Overturning Circulation,” Paleoceanography, 23 (1), PA1217.
   Google Scholar
• Chen, J., and Chen, Z. (2008), “Extended Bayesian Information Criteria for Model Selection With Large Model Spaces,” Biometrika, 95, 759–771. DOI: 10.1093/biomet/asn034.
   Web of Science ®Google Scholar
• Chen, J., and Chen, Z. (2012), “Extended Bic for Small-n-Large-p Sparse GLM,” Statistica Sinica, 22, 555–574.
   Google Scholar
• Cressie, N. (1993), “Statistics for Spatial Data. New York: Wiley.
   Google Scholar
• Diggle, P. J., Tawn, J., and Moyeed, R. (1998), “Model-Based Geostatistics,” Journal of the Royal Statistical Society, Series C, 47 (3), 299–350. DOI: 10.1111/1467-9876.00113.
   Web of Science ®Google Scholar
• Dobriban, E., and Fan, J. (2016), “Regularity Properties for Sparse Regression,” Communications in Mathematics and Statistics, 4, 1–19. DOI: 10.1007/s40304-015-0078-6.
   PubMed Web of Science ®Google Scholar
• Dobrin, R., and Duxbury, P. (2001), “Minimum Spanning Trees on Random Networks,” Physical Review Letters, 86, 5076–5079. DOI: 10.1103/PhysRevLett.86.5076.
   PubMed Web of Science ®Google Scholar
• Dolan, J., Weiss, R., and Smith, J. M. (1991), “Minimal Length Tree Networks on the Unit Sphere,” Annals of Operations Research, 33, 501–535. DOI: 10.1007/BF02067239.
   Google Scholar
• Efron, B., Hastie, T., Johnstone, I., and Tibshirani, R. (2004), “Least Angle Regression,” Annals of Statistics, 32, 407–499. DOI: 10.1214/009053604000000067.
   Web of Science ®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
• Finley, A. O. (2011), “Comparing Spatially-Varying Coefficients Models for Analysis of Ecological Data with Non-Stationary and Anisotropic Residual Dependence,” Methods in Ecology and Evolution, 2, 143–154. DOI: 10.1111/j.2041-210X.2010.00060.x.
   Web of Science ®Google Scholar
• Fotheringham, A. S., Brunsdon, C., and Charlton, M. (2003), Geographically Weighted Regression, Chichester: Wiley.
   Google Scholar
• Foygel, R., and Drton, M. (2010), “Extended Bayesian Information Criteria for Gaussian Graphical Models,” in Advances in Neural Information Processing Systems, eds. J. D. Lafferty, C. K. I. Williams, J. Shawe-Taylor, R. S. Zemel, and A. Culotta, Vancouver, British Columbia, Canada: Curran Associates, Inc, pp. 604–612.
   Google Scholar
• Frandi, E., R. Ñanculef, S. Lodi, C. Sartori, and J. A. Suykens (2016), “Fast and Scalable Lasso Via Stochastic Frank–Wolfe Methods With a Convergence Guarantee,” Machine Learning, 104, 195–221. DOI: 10.1007/s10994-016-5578-4.
   Web of Science ®Google Scholar
• Friedman, J., Hastie, T., and Tibshirani, R. (2010), “Regularization Paths for Generalized Linear Models Via Coordinate Descent,” Journal of Statistical Software, 33, 1–22.
   PubMed Web of Science ®Google Scholar
• Gelfand, A. E., Kim, H.-J., Sirmans, C., and Banerjee, S. (2003), “Spatial Modeling With Spatially Varying Coefficient Processes,” Journal of the American Statistical Association, 98, 387–396. DOI: 10.1198/016214503000170.
   Web of Science ®Google Scholar
• Golub, G. H., Heath, M., and Wahba, G. (1979), “Generalized Cross-validation as a Method for Choosing a Good Ridge Parameter,” Technometrics, 21, 215–223. DOI: 10.1080/00401706.1979.10489751.
   Web of Science ®Google Scholar
• Grygorash, O., Zhou, Y., and Jorgensen, Z.(2006), “Minimum Spanning Tree Based Clustering Algorithms,” in Tools with Artificial Intelligence, 18th IEEE International Conference on 2006 (ICTAI’06), pp. 73–81. Arlington, VA: IEEE.
   Google Scholar
• Ke, Z. T., Fan, J., and Wu, Y. (2015), “Homogeneity Pursuit,” Journal of the American Statistical Association, 110, 175–194. DOI: 10.1080/01621459.2014.892882.
   PubMed Web of Science ®Google Scholar
• LeSage, J. P. (2004). “A Family of Geographically Weighted Regression Models,” in Advances in Spatial Econometrics, eds. J. G. M. Raymond and S. J. Rey, pp. 241–264.
   Google Scholar
• Lindgren, F., Rue, H., and Lindström, J. (2011), “An Explicit Link Between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach,” Journal of the Royal Statistical Society, Series B, 73, 423–498. DOI: 10.1111/j.1467-9868.2011.00777.x.
   Google Scholar
• Locarnini, R., Mishonov, A., Antonov, J., Boyer, T., Garcia, H., Baranova, O., Zweng, M., Paver, C., Reagan, J., Johnson, D., et al. (2013), World ocean atlas 2013, volume 1: Temperature. Boulder, CO: NOAA Atlas NESDIS.
   Google Scholar
• March, W. B., Ram, P., and Gray, A. G. (2010), “Fast Euclidean Minimum Spanning Tree: Algorithm, Analysis, and Applications,” in Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 603–612. Washington, DC: ACM.
   Google Scholar
• Oppo, D., and Curry, W. (2012), “Deep Atlantic Circulation During the Last Glacial Maximum and Deglaciation,” Nature Education Knowledge, 3, 1.
   Google Scholar
• Sabine, C. L., Feely, R. A., Gruber, N., Key, R. M., Lee, K., Bullister, J. L., Wanninkhof, R., Wong, C., Wallace, D. W., Tilbrook, B., et al. (2004), “The Oceanic Sink for Anthropogenic CO2 ,” Science, 305, 367–371. DOI: 10.1126/science.1097403.
   PubMed Web of Science ®Google Scholar
• Schwarz, G. et al. (1978), “Estimating the Dimension of a Model,” Annals of Statistics, 6, 461–464. DOI: 10.1214/aos/1176344136.
   Web of Science ®Google Scholar
• Shen, X., and Huang, H.-C. (2010), “Grouping Pursuit Through a Regularization Solution Surface,” Journal of the American Statistical Association, 105, 727–739. DOI: 10.1198/jasa.2010.tm09380.
   PubMed Web of Science ®Google Scholar
• Simmonds, J. G. (2012), A Brief on Tensor Analysis, New York: Springer Science & Business Media.
   Google Scholar
• Song, Q., and Liang, F. (2015), “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
• Sun, Y., Wang, H. J., and Fuentes, M. (2016), “Fused Adaptive Lasso for Spatial and Temporal Quantile Function Estimation,” Technometrics, 58, 127–137. DOI: 10.1080/00401706.2015.1017115.
   Web of Science ®Google Scholar
• Talley, L. D. (2011), Descriptive Physical Oceanography: An Introduction, London: Academic Press.
   Google Scholar
• Tang, L., and Song, P. X. (2016), “Fused Lasso Approach in Regression Coefficients Clustering–Learning Parameter Heterogeneity in Data Integration,” Journal of Machine Learning Research, 17, 1–23.
   Web of Science ®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., Saunders, M., Rosset, S., Zhu, J., and Knight, K. (2005), “Sparsity and Smoothness Via the Fused Lasso,” Journal of the Royal Statistical Society, Series B, 67, 91–108. DOI: 10.1111/j.1467-9868.2005.00490.x.
   Google Scholar
• Tibshirani, R., Wainwright, M., and Hastie, T. (2015), Statistical Learning With Sparsity: The Lasso and Generalizations, Boca Raton, FL: Chapman and Hall/CRC.
   Google Scholar
• Vallis, G. K. (2006), Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-scale Circulation. Cambridge: Cambridge University Press.
   Google Scholar
• Wheeler, D. C., and Calder, C. A. (2007), “An Assessment of Coefficient Accuracy in Linear Regression Models With Spatially Varying Coefficients,” Journal of Geographical Systems, 9, 145–166. DOI: 10.1007/s10109-006-0040-y.
   Web of Science ®Google Scholar
• Xie, R. C., Marcantonio, F., and Schmidt, M. W. (2012), “Deglacial Variability of Antarctic Intermediate Water Penetration Into the North Atlantic From Authigenic Neodymium Isotope Ratios,” Paleoceanography, 27, PA3221.
   Google Scholar
• Zhang, C. -H. (2010), “Nearly Unbiased Variable Selection Under Minimax Concave Penalty,” Annals of Statistics, 38, 894–942. DOI: 10.1214/09-AOS729.
   Web of Science ®Google Scholar
• Zhu, J., Huang, H.-C., and Reyes, P. E. (2010), “On Selection of Spatial Linear Models for Lattice Data,” Journal of the Royal Statistical Society, Series B, 72, 389–402. DOI: 10.1111/j.1467-9868.2010.00739.x.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• Zou, H. (2006), “The Adaptive Lasso and Its Oracle Properties,” Journal of the American Statistical Association, 101, 1418–1429. DOI: 10.1198/016214506000000735.
   Web of Science ®Google Scholar
• Zweng, M., Reagan, J., Antonov, J., Locarnini, R., Mishonov, A., Boyer, T., Garcia, H., Baranova, O., Johnson, D., Seidov, D., and M. M. Biddle. (2013), World Ocean Atlas 2013, Vol. 2: Salinity, Boulder, CO: NOAA Atlas NESDIS Berlin, Heidelberg: Springer.
   Google Scholar