STAT 695 (Spring 2007)
Dimension Reduction and Variable Selection
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Information Theory and An Extension of the Maximum Likelihood Principle, Akaike, (1973)
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Model Selection and Akaike's Information Criterion (AIC): The General Theory and Its Analytical Extensions, Bozdogan, H., Psychometrika, (1987), Vol 52, Page345-370.
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Estimating the dimension of a model. Schwarz, (1978),
Annals of Statistics 6(2):461-464.
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Some comments on Cp. Mallows, (1973),
Technometrics, 42(1):87-94.
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=More comments on Cp. Mallows, (1995),
Technometrics, 37(4):362-372.
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Mean square error of prediction as a criterion for selecting variable, Allen,
(1971), Technometrics, 13(3): 469-475.
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Cross-validatory choice and assessment of statistical prediction, Stone,
(1974), JRSSB, 36: 111-147.
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The predictive sample reuse method with applications, Geisser,
(1975), JASA, 70: 320-328.
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=An Optimal Selection of Regression Variables, Shibata (1981), Biometrika,
68:45-54.
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=Approximate Efficiency of a selection procedure for the number of regression
variables, Shibata (1984), Biometrika,
71:43-49.
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=Asymptotic Properties of Criteria for Selection of Variables in Multiple
Regression, Nishii (1984), Annals, 12:758-765.
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=A Strongly Consistent Procedure for Model Selection in a Regression Problem,
Rao and Wu (1989), Biometrika 76:369-374.
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=Asymptotic Optimality for Cp, CL, Cross Validation and Generalized Cross
Validation: Discrete Index Set, Li (1987), Annals 15: 958-975.
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=Model Selection via Multifold Cross Validation, Zhang (1993),
Annals, 21:299-313.
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An Asymptotic Theory for Linear Model Selection, Shao (1997), Sinica,
7:221-264.
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Regression Shrinkage and Selection via the Lasso, Tibishirani
(1995), JRSSB, 58: 267-288.
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Asymptotics for Lasso Type Estimators, Knight and Fu,
(2000) Annals, 28: 1356-1378.
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=Least Angle Regression, Efron et al.,
(2004) Annals, 32:407-499.
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=Variable Selection via Nonconcave Penalized Likelihood and its oracle
Properties, Fan and Li, (2001), JASA, 96:1348-1360.
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=The Adapative Lasso and its Oracle Properties, Zou (2006), JASA,
101, 1418-1429
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=Adaptive Lasso for Sparse High Dimensional Regression , Huang et al.,
(2006) Tech. Rep., Online.
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=Lasso-Type Recovery of Sparse Representations for High Dimensional Data
, Neinshausen and Yu, (2006) Tech. Rep., Online.
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=Efficient Empirical Bayes Variable Selection and Estimation in Linear
Model, Yuan and Lin, (2005) Tech. Rep., Online.
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Rodeo: Sparse Nonparametric Regression in High Dimenions,
Lafferty and Wasserman, (2006) Tech. Rep., Online.
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The Dantzig Selector: Statistical Estimation When p is much larger
than n, Candes and Tao, (2005) Tech. Rep., Online.
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Sliced Inverse Regession for Dimension Reduction, Li, 1991, JASA Vol. 86
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Sufficient Dimension Reduction will be added later on
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Nonliear dimensionality reduction by locally linear embedding. Roweis and Saul,
2000, Science, 290.
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A global geometric framework for nonlinear dimensionality reduction,
Tenenbaum, Silva, Langford, 2000, Science, 290
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Laplacian eigenmaps for dimensionality reduction and data representation,
Belkin and Niyogi, 2003, Neural Computation, 15.
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Hessian eigenmaps: locally linear embedding techniques for high-dimensional data,Donoho and Grimes, 2003, PNAS, 100.
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The fastest mixing Markov process on a graph and a connection to a
maximum variance unfolding problem, Sun, Boyd, Xiao and Diconis, 2004.
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Analysis and extension of spectral methods for nonlinear dimensionality reduction, Sha and Saul, 2005.