In pknight24/KPR: Kernel-penalized regression

The purpose of this experiment is to study the relative change in KPR coefficients after making permutations to the Q, H, and Z matrices.

The file "helpers.R" loads the yatsunenko data set, and includes helper functions for comparing models.

knitr::opts_chunk$set(dev = 'pdf')

source("helpers.R")

Q

Eigenvalue Permutations

Q <- generateSimilarityKernel(patristic)
Q.1 <- permuteEigenvalue(Q, 1)
Q.2 <- permuteEigenvalue(Q, 75)
Q.3 <- permuteEigenvalue(Q, 149)

fit <- KPR(designMatrix = Z, Y = Y, Q = Q)
fit.1 <- KPR(designMatrix = Z, Y = Y, Q = Q.1)
fit.2 <- KPR(designMatrix = Z, Y = Y, Q = Q.2)
fit.3 <- KPR(designMatrix = Z, Y = Y, Q = Q.3)

compareModels(fit, fit.1, main = "Eigenvalue 1")
compareModels(fit, fit.2, main = "Eigenvalue 75")
compareModels(fit, fit.3, main = "Eigenvalue 149")

H

Eigenvalue Permutations

# H <- generateSimilarityKernel(unifrac)
H <- solve(ec %*% t(ec))
H.1 <- permuteEigenvalue(H, 1)
H.2 <- permuteEigenvalue(H, 50)
H.3 <- permuteEigenvalue(H, 100)

fit <- KPR(designMatrix = Z, Y = Y, H = H)
fit.1 <- KPR(designMatrix = Z, Y = Y, H = H.1)
fit.2 <- KPR(designMatrix = Z, Y = Y, H = H.2)
fit.3 <- KPR(designMatrix = Z, Y = Y, H = H.3)

compareModels(fit, fit.1, main = "Eigenvalue 1")
compareModels(fit, fit.2, main = "Eigenvalue 50")
compareModels(fit, fit.3, main = "Eigenvalue 100")

Note: when I generate $H$ from the EC data, perturbing later eigenvalues actually improves performance. Then when I plugged in $H^{-1}$, I saw the same behavior as with the UniFrac $H$ kernel. This seems to lend more confusion to the $H$ vs $H^{-1}$ debate.

Z

Gaussian Noise

Z.1 <- Z + rnorm(n = length(Z))
fit <- KPR(designMatrix = Z, Y = Y)
fit.1 <- KPR(designMatrix = Z.1, Y = Y)

compareModels(fit, fit.1, main = "Gaussian noise")