ensemble_exp: Estimating Ensemble Kernel Matrices Using EXP
In CVEK: Cross-Validated Kernel Ensemble

Description Usage Arguments Details Value Author(s) References See Also

Give the ensemble projection matrix and weights of the kernels in the library using exponential weighting.

1	ensemble_exp(beta_exp, error_mat, A_hat)

`beta_exp`	(numeric/character) A numeric value specifying the parameter when strategy = "exp". See Details.
`error_mat`	(matrix, nK) A n\K matrix indicating errors.
`A_hat`	(list of length K) A list of projection matrices to kernel space for each kernel in the kernel library.

Exponential Weighting

Additionally, another scholar gives a new strategy to calculate weights based on the estimated errors \{\hat{ε}_d\}_{d=1}^D.

u_d(β)=\frac{exp(-\parallel \hat{ε}_d \parallel_2^2/β)}{∑_{d=1}^Dexp(-\parallel \hat{ε}_d \parallel_2^2/β)}

beta_exp

The value of beta_exp can be "min"=min\{RSS\}_{d=1}^D/10, "med"=median\{RSS\}_{d=1}^D, "max"=max\{RSS\}_{d=1}^D*2 and any other positive numeric number, where \{RSS\} _{d=1}^D are the set of residual sum of squares of D base kernels.

`A_est`	(matrix, n*n) The ensemble projection matrix.
`u_hat`	(vector of length K) A vector of weights of the kernels in the library.

Wenying Deng

Jeremiah Zhe Liu and Brent Coull. Robust Hypothesis Test for Nonlinear Effect with Gaussian Processes. October 2017.

Xiang Zhan, Anna Plantinga, Ni Zhao, and Michael C. Wu. A fast small-sample kernel inde- pendence test for microbiome community-level association analysis. December 2017.

Arnak S. Dalalyan and Alexandre B. Tsybakov. Aggregation by Exponential Weighting and Sharp Oracle Inequalities. In Learning Theory, Lecture Notes in Computer Science, pages 97– 111. Springer, Berlin, Heidelberg, June 2007.

mode: tuning

CVEK documentation built on Jan. 8, 2021, 5:42 p.m.