Akaike, Hirotogu. 1973. “Information Theory and an Extension of the Maximum Likelihood Principle.”
In Proceeding of the Second International Symposium on Information Theory
, edited by Petrovand F Caski, 199–213. Budapest: Akademiai Kiado.
Azizyan, Martin, Akshay Krishnamurthy, and Aarti Singh. 2015. “Extreme Compressive Sampling for Covariance Estimation.” arXiv:1506.00898 [Cs, Math, Stat]
Banerjee, Arindam, Sheng Chen, Farideh Fazayeli, and Vidyashankar Sivakumar. 2014. “Estimation with Norm Regularization.”
In Advances in Neural Information Processing Systems 27
, edited by Z. Ghahramani, M. Welling, C. Cortes, N. D. Lawrence, and K. Q. Weinberger, 1556–64. Curran Associates, Inc.
Barron, Andrew R., Cong Huang, Jonathan Q. Li, and Xi Luo. 2008. “MDL, Penalized Likelihood, and Statistical Risk.”
In Information Theory Workshop, 2008. ITW’08. IEEE
, 247–57. IEEE.
Bellec, Pierre C., and Alexandre B. Tsybakov. 2016. “Bounds on the Prediction Error of Penalized Least Squares Estimators with Convex Penalty.” arXiv:1609.06675 [Math, Stat]
Bickel, Peter J., Bo Li, Alexandre B. Tsybakov, Sara A. van de Geer, Bin Yu, Teófilo Valdés, Carlos Rivero, Jianqing Fan, and Aad van der Vaart. 2006. “Regularization in Statistics.” Test
15 (2): 271–344.
Bühlmann, Peter, and Sara van de Geer. 2011. “Additive Models and Many Smooth Univariate Functions.”
In Statistics for High-Dimensional Data
, 77–97. Springer Series in Statistics. Springer Berlin Heidelberg.
Candès, Emmanuel J., and Carlos Fernandez-Granda. 2013. “Super-Resolution from Noisy Data.” Journal of Fourier Analysis and Applications
19 (6): 1229–54.
Candès, Emmanuel J., and Y. Plan. 2010. “Matrix Completion With Noise.” Proceedings of the IEEE
98 (6): 925–36.
Chernozhukov, Victor, Christian Hansen, and Martin Spindler. 2015. “Valid Post-Selection and Post-Regularization Inference: An Elementary, General Approach.” Annual Review of Economics
7 (1): 649–88.
Efron, Bradley. 2004. “The Estimation of Prediction Error.” Journal of the American Statistical Association
99 (467): 619–32.
Efron, Bradley, Trevor Hastie, Iain Johnstone, and Robert Tibshirani. 2004. “Least Angle Regression.” The Annals of Statistics
32 (2): 407–99.
Flynn, Cheryl J., Clifford M. Hurvich, and Jeffrey S. Simonoff. 2013. “Efficiency for Regularization Parameter Selection in Penalized Likelihood Estimation of Misspecified Models.” arXiv:1302.2068 [Stat]
Friedman, Jerome, Trevor Hastie, and Rob Tibshirani. 2010. “Regularization Paths for Generalized Linear Models via Coordinate Descent.” Journal of Statistical Software
33 (1): 1–22.
Fuglstad, Geir-Arne, Daniel Simpson, Finn Lindgren, and Håvard Rue. 2019. “Constructing Priors That Penalize the Complexity of Gaussian Random Fields.” Journal of the American Statistical Association
114 (525): 445–52.
Geer, Sara van de. 2014a. “Weakly Decomposable Regularization Penalties and Structured Sparsity.” Scandinavian Journal of Statistics
41 (1): 72–86.
———. 2014b. “Statistical Theory for High-Dimensional Models.” arXiv:1409.8557 [Math, Stat]
Giryes, Raja, Guillermo Sapiro, and Alex M. Bronstein. 2014. “On the Stability of Deep Networks.” arXiv:1412.5896 [Cs, Math, Stat]
Golub, Gene H., Michael Heath, and Grace Wahba. 1979. “Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter.” Technometrics
21 (2): 215–23.
Golubev, Grigori K., and Michael Nussbaum. 1990. “A Risk Bound in Sobolev Class Regression.” The Annals of Statistics
18 (2): 758–78.
Green, Peter J. 1990. “On Use of the EM for Penalized Likelihood Estimation.” Journal of the Royal Statistical Society. Series B (Methodological)
52 (3): 443–52.
Gu, Chong. 1993. “Smoothing Spline Density Estimation: A Dimensionless Automatic Algorithm.” Journal of the American Statistical Association
88 (422): 495–504.
Hastie, Trevor J., and Robert J. Tibshirani. 1990. Generalized Additive Models
. Vol. 43. CRC Press.
Hastie, Trevor J., Tibshirani, Rob, and Martin J. Wainwright. 2015. Statistical Learning with Sparsity: The Lasso and Generalizations
. Boca Raton: Chapman and Hall/CRC.
Hawe, S., M. Kleinsteuber, and K. Diepold. 2013. “Analysis Operator Learning and Its Application to Image Reconstruction.” IEEE Transactions on Image Processing
22 (6): 2138–50.
Hegde, Chinmay, Piotr Indyk, and Ludwig Schmidt. 2015. “A Nearly-Linear Time Framework for Graph-Structured Sparsity.”
In Proceedings of the 32nd International Conference on Machine Learning (ICML-15)
Hoerl, Arthur E., and Robert W. Kennard. 1970. “Ridge Regression: Biased Estimation for Nonorthogonal Problems.” Technometrics
12 (1): 55–67.
Huang, Jianhua Z., Naiping Liu, Mohsen Pourahmadi, and Linxu Liu. 2006. “Covariance Matrix Selection and Estimation via Penalised Normal Likelihood.” Biometrika
93 (1): 85–98.
James, William, and Charles Stein. 1961. “Estimation with Quadratic Loss.”
In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability
, 1:361–79. University of California Press.
Janson, Lucas, William Fithian, and Trevor J. Hastie. 2015. “Effective Degrees of Freedom: A Flawed Metaphor.” Biometrika
102 (2): 479–85.
Javanmard, Adel, and Andrea Montanari. 2014. “Confidence Intervals and Hypothesis Testing for High-Dimensional Regression.” Journal of Machine Learning Research
15 (1): 2869–909.
Kloft, Marius, Ulrich Rückert, and Peter L. Bartlett. 2010. “A Unifying View of Multiple Kernel Learning.”
In Machine Learning and Knowledge Discovery in Databases
, edited by José Luis Balcázar, Francesco Bonchi, Aristides Gionis, and Michèle Sebag, 66–81. Lecture Notes in Computer Science. Springer Berlin Heidelberg.
Koenker, Roger, and Ivan Mizera. 2006. “Density Estimation by Total Variation Regularization.” Advances in Statistical Modeling and Inference
Konishi, Sadanori, and G. Kitagawa. 2008. Information Criteria and Statistical Modeling. Springer Series in Statistics. New York: Springer.
Konishi, Sadanori, and Genshiro Kitagawa. 1996. “Generalised Information Criteria in Model Selection.” Biometrika
83 (4): 875–90.
Lange, K. 1990. “Convergence of EM image reconstruction algorithms with Gibbs smoothing.” IEEE transactions on medical imaging
9 (4): 439–46.
Liu, Han, Kathryn Roeder, and Larry Wasserman. 2010. “Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models.”
In Advances in Neural Information Processing Systems 23
, edited by J. D. Lafferty, C. K. I. Williams, J. Shawe-Taylor, R. S. Zemel, and A. Culotta, 1432–40. Curran Associates, Inc.
Meinshausen, Nicolai, and Peter Bühlmann. 2010. “Stability Selection.” Journal of the Royal Statistical Society: Series B (Statistical Methodology)
72 (4): 417–73.
Meyer, Mary C. 2008. “Inference Using Shape-Restricted Regression Splines.” The Annals of Applied Statistics
2 (3): 1013–33.
Miller, David L., Richard Glennie, and Andrew E. Seaton. 2020. “Understanding the Stochastic Partial Differential Equation Approach to Smoothing.” Journal of Agricultural, Biological and Environmental Statistics
25 (1): 1–16.
Montanari, Andrea. 2012. “Graphical Models Concepts in Compressed Sensing.” Compressed Sensing: Theory and Applications
Needell, D., and J. A. Tropp. 2008. “CoSaMP: Iterative Signal Recovery from Incomplete and Inaccurate Samples.” arXiv:0803.2392 [Cs, Math]
Rahimi, Ali, and Benjamin Recht. 2009. “Weighted Sums of Random Kitchen Sinks: Replacing Minimization with Randomization in Learning.”
In Advances in Neural Information Processing Systems
, 1313–20. Curran Associates, Inc.
Rezende, Danilo Jimenez, Shakir Mohamed, and Daan Wierstra. 2015. “Stochastic Backpropagation and Approximate Inference in Deep Generative Models.”
In Proceedings of ICML
Shen, Xiaotong, and Hsin-Cheng Huang. 2006. “Optimal Model Assessment, Selection, and Combination.” Journal of the American Statistical Association
101 (474): 554–68.
Shen, Xiaotong, Hsin-Cheng Huang, and Jimmy Ye. 2004. “Adaptive Model Selection and Assessment for Exponential Family Distributions.” Technometrics
46 (3): 306–17.
Shen, Xiaotong, and Jianming Ye. 2002. “Adaptive Model Selection.” Journal of the American Statistical Association
97 (457): 210–21.
———. 1984. “Spline Smoothing: The Equivalent Variable Kernel Method.” The Annals of Statistics
12 (3): 898–916.
Simon, Noah, Jerome Friedman, Trevor Hastie, and Rob Tibshirani. 2011. “Regularization Paths for Cox’s Proportional Hazards Model via Coordinate Descent.” Journal of Statistical Software
Smola, Alex J., Bernhard Schölkopf, and Klaus-Robert Müller. 1998. “The Connection Between Regularization Operators and Support Vector Kernels.” Neural Networks
11 (4): 637–49.
Somekh-Baruch, Anelia, Amir Leshem, and Venkatesh Saligrama. 2016. “On the Non-Existence of Unbiased Estimators in Constrained Estimation Problems.” arXiv:1609.07415 [Cs, Math, Stat]
Stein, Charles M. 1981. “Estimation of the Mean of a Multivariate Normal Distribution.” The Annals of Statistics
9 (6): 1135–51.
Tansey, Wesley, Oluwasanmi Koyejo, Russell A. Poldrack, and James G. Scott. 2014. “False Discovery Rate Smoothing.” arXiv:1411.6144 [Stat]
Tikhonov, A. N., and V. B. Glasko. 1965. “Use of the Regularization Method in Non-Linear Problems.” USSR Computational Mathematics and Mathematical Physics
5 (3): 93–107.
Wahba, Grace. 1990. Spline Models for Observational Data. SIAM.
Wood, S. N. 2000. “Modelling and Smoothing Parameter Estimation with Multiple Quadratic Penalties.” Journal of the Royal Statistical Society: Series B (Statistical Methodology)
62 (2): 413–28.
Wood, Simon N. 2008. “Fast Stable Direct Fitting and Smoothness Selection for Generalized Additive Models.” Journal of the Royal Statistical Society: Series B (Statistical Methodology)
70 (3): 495–518.
Wu, Tong Tong, and Kenneth Lange. 2008. “Coordinate Descent Algorithms for Lasso Penalized Regression.” The Annals of Applied Statistics
2 (1): 224–44.
Xie, Bo, Yingyu Liang, and Le Song. 2016. “Diversity Leads to Generalization in Neural Networks.” arXiv:1611.03131 [Cs, Stat]
Ye, Jianming. 1998. “On Measuring and Correcting the Effects of Data Mining and Model Selection.” Journal of the American Statistical Association
93 (441): 120–31.
Zhang, Cun-Hui, and Stephanie S. Zhang. 2014. “Confidence Intervals for Low Dimensional Parameters in High Dimensional Linear Models.” Journal of the Royal Statistical Society: Series B (Statistical Methodology)
76 (1): 217–42.
Zhang, Yiyun, Runze Li, and Chih-Ling Tsai. 2010. “Regularization Parameter Selections via Generalized Information Criterion.” Journal of the American Statistical Association
105 (489): 312–23.
Zou, Hui, and Trevor Hastie. 2005. “Regularization and Variable Selection via the Elastic Net.” Journal of the Royal Statistical Society: Series B (Statistical Methodology)
67 (2): 301–20.
Zou, Hui, Trevor Hastie, and Robert Tibshirani. 2007. “On the ‘Degrees of Freedom’ of the Lasso.” The Annals of Statistics
35 (5): 2173–92.