Give the ensemble projection matrix and weights of the kernels in the library using simple averaging.
ensemble_avg(beta_exp, error_mat, A_hat)(numeric/character) A numeric value specifying the parameter
when strategy = "exp" ensemble_exp.
(matrix, n*K) A n\*K matrix indicating errors.
(list of length K) A list of projection matrices to kernel space for each kernel in the kernel library.
(matrix, n*n) The ensemble projection matrix.
(vector of length K) A vector of weights of the kernels in the library.
Simple Averaging
Motivated by existing literature in omnibus kernel, we propose another way to obtain the ensemble matrix by simply choosing unsupervised weights \(u_d=1/D\) for \(d=1,2,...D\).
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<U+2013> 111. Springer, Berlin, Heidelberg, June 2007.
mode: tuning