ridgeLR: generates a closure for the computation of the likelihood...
In kernelPSI: Post-Selection Inference for Nonlinear Variable Selection

Description Usage Arguments Details Value References See Also Examples

The main inspiration for the kernel ridge prototype is the prototype concept developed in Reid (2018, see references). A prototype is a synthetic scalar variable that aggregates the effect of a set of variables in the outcome. Here, we extend this concept to kernels, where the prototype is the prediction of ridge regression with the selected kernels. In this function, we implement a likelihood ratio (LR) statistic to test for the effect of the the prototype on the outcome Y.

1	ridgeLR(K, mu = 0, sigma = 1, lambda = 1, tol = 1e-06, n_iter = 10000)

`K`	a single or a list of selected kernel similarity matrices.
`mu`	mean of the response Y
`sigma`	standard deviation of the response
`lambda`	regularization parameter for the ridge prototype
`tol`	convergence tolerance used a stopping criterion for the Newton- Raphson algorithm
`n_iter`	maximum number of iterations for the Newton-Raphson algorithm

To maximize the likelihood objective function, we implement in the output closure a Newton-Raphson algorithm that determines the maximum for each input vector Y.

For our post-selection inference framework, The output closure is used to compute the test statistics for both the replicates and the original outcome in order to derive empirical p-values.

a closure for the calculation of the LR statistic for the ridge prototype

Reid, S., Taylor, J., & Tibshirani, R. (2018). A General Framework for Estimation and Inference From Clusters of Features. Journal of the American Statistical Association, 113(521), 280–293.

pcaLR

Other prototype: pcaLR()

n <- 30
p <- 20
K <- replicate(5, matrix(rnorm(n*p), nrow = n, ncol = p), simplify = FALSE)
K <-  sapply(K, function(X) return(X %*% t(X) / dim(X)[2]), simplify = FALSE)
print(typeof(ridgeLR(K, mu = 0, sigma = 1, lambda = .1)) == "closure")