tuning: Calculating Tuning Parameters
In IrisTeng/CVEK: Cross-Validated Kernel Ensemble

Description Usage Arguments Details Value Author(s) References Examples

Calculate tuning parameters based on given criteria.

1	tuning(Y, K_mat, mode, lambda)

`Y`	(vector of length n) Reponses of the dataframe.
`K_mat`	(matrix, n*n) Estimated ensemble kernel matrix.
`mode`	(character) A character string indicating which tuning parameter criteria is to be used.
`lambda`	(numeric) A numeric string specifying the range of noise to be chosen. The lower limit of lambda must be above 0.

There are four tuning parameter selections here:

leave-one-out Cross Validation

λ_{n-CV}=\underset{λ \in Λ}{argmin}\;\Big\{log\;y^{\star T}[I-diag(A_λ)-\frac{1}{n}I]^{-1}(I-A_λ)^2[I-diag(A_λ)-\frac{1}{n}I]^{-1}y^\star \Big\}

Akaike Information Criteria

λ_{AICc}=\underset{λ \in Λ}{argmin}\Big\{log\; y^{\star T}(I-A_λ)^2y^\star+\frac{2[tr(A_λ)+2]}{n-tr(A_λ)-3}\Big\}

Generalized Cross Validation

λ_{GCVc}=\underset{λ \in Λ}{argmin}\Big\{log\; y^{\star T}(I-A_λ)^2y^\star-2log[1-\frac{tr(A_λ)}{n}-\frac{2}{n}]_+\Big\}

Generalized Maximum Profile Marginal Likelihood

λ_{GMPML}=\underset{λ \in Λ}{argmin}\Big\{log\; y^{\star T}(I-A_λ)y^\star-\frac{1}{n-1}log \mid I-A_λ \mid \Big\}

lambda0

(numeric) The estimated tuning parameter.

Wenying Deng

Philip S. Boonstra, Bhramar Mukherjee, and Jeremy M. G. Taylor. A Small-Sample Choice of the Tuning Parameter in Ridge Regression. July 2015.

Trevor Hastie, Robert Tibshirani, and Jerome Friedman. The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition. Springer Series in Statistics. Springer- Verlag, New York, 2 edition, 2009.

Hirotogu Akaike. Information Theory and an Extension of the Maximum Likelihood Princi- ple. In Selected Papers of Hirotugu Akaike, Springer Series in Statistics, pages 199–213. Springer, New York, NY, 1998.

Clifford M. Hurvich and Chih-Ling Tsai. Regression and time series model selection in small samples. June 1989.

Hurvich Clifford M., Simonoff Jeffrey S., and Tsai Chih-Ling. Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. January 2002.