kernelPSI (version 1.1.1)

ridgeLR: generates a closure for the computation of the likelihood ratio statistic for the ridge prototype.

Description

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.

Usage

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

Arguments

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

Value

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

Details

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.

References

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<U+2013>293.

See Also

pcaLR

Other prototype: pcaLR()

Examples

# NOT RUN {
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")

# }