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use_robregcc.R
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use_robregcc.R
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## Title: Robust regression with compositional covariates
## Author: Aditya Mishra
## Date: July 27, 2019
## Description: We demonstrate the usage of functions available for robust model fitting and outlier detection.
## -----------------------------------------------------------------------------
## Load package
rm(list = ls())
library(robregcc)
library(magrittr)
#--------------------------------------------------------------
## Define parameters to simulate example
##
p <- 80 # number of predictors
n <- 300 # number of sample
O <- 0.15*n # number of outlier, e.g. 15% of observation
L <- 1 # indicator variable for outlier type, L = {0,1} => leveraged {no, yes}
# generate outlier by shifting "O"observation by amount equals to shFac times true error variance sigma.
# shFac = {6,8} corresponds to {moderate, high} outlier
shFac <- 6
ngrp <- 4 # number of sub-composition
snr <- 3 # Signal to noise ratio
example_seed <- 2*p+1 # example seed
set.seed(example_seed)
#--------------------------------------------------------------
## Simulate true model variables, i.e., y, X, C, beta
## Follow examples from [Pixu Shi 2016]
# Simulate subcomposition matrix
C1 <- matrix(0,ngrp,23)
tind <- c(0,10,16,20,23)
for(ii in 1:ngrp)
C1[ii,(tind[ii]+1):tind[ii+1]] <- 1
C <- matrix(0,ngrp,p)
C[,1:ncol(C1)] <- C1
# model parameter beta
beta <- c(1, - 0.8, 0.4, 0, 0, - 0.6, 0, 0, 0, 0, -1.5,
0, 1.2, 0, 0, 0.3)
beta <- c(beta,rep(0,p-length(beta)))
# Simulate response and predictor, i.e., X, y
Sigma <- 1:p %>% outer(.,.,'-') %>% abs(); Sigma <- 0.5^Sigma
data.case <- vector("list",1)
data.case <- robregcc_sim(n,beta,O = O,Sigma,levg = L, snr,shft = shFac,0,
C,out=data.case)
#--------------------------------------------------------------
## Data preprocessing:
X <- data.case$X # predictor matrix
y <- data.case$y # model response
#
# Predictor transformation due to compositional constraint:
# Equivalent to performing centered log-ratio transform
Xt <- svd(t(C))$u %>% tcrossprod() %>% subtract(diag(p),.) %>%
crossprod(t(X),.)
Xm <- colMeans(Xt)
Xt <- scale(Xt,Xm,FALSE) # centering of predictors
#
mean.y <- mean(y)
y <- y - mean.y # centering of response
#
# Account for intercept in the model
Xt <- cbind(1,Xt) # accounting for intercept in predictor
C <- cbind(0,C) # accounting for intercept in constraint
bw <- c(0,rep(1,p)) # weight matrix to not penalize intercept
#--------------------------------------------------------------
## Initialization
# Breakdown point for tukey Bisquare loss function
b1 = 0.5 # 50% breakdown point
cc1 = 1.567 # corresponding model parameter
# b1 = 0.25; cc1 = 2.937 # initalization for scale parameter
set.seed(example_seed) # unique seed
# control parameter for intialization method
control <- robregcc_option(maxiter=1000,tol = 1e-4,lminfac = 1e-7)
# intialization
fit.init <- cpsc_sp(Xt, y,alp=0.4, cfac=2, b1=b1,cc1=cc1,C,bw,1,control)
#--------------------------------------------------------------
## Model fitting
# control parameters
control <- robregcc_option()
beta.wt <- fit.init$betaR # Set weight for model parameter beta
beta.wt[1] <- 0
control$gamma = 2 # gamma for constructing weighted penalty
control$spb = 40/p # fraction of maximum non-zero model parameter beta
control$outMiter = 1000 # Outer loop iteration
control$inMiter = 3000 # Inner loop iteration
control$nlam = 50 # Number of tuning parameter lambda to be explored
control$lmaxfac = 1 # Parameter for constructing sequence of lambda
control$lminfac = 1e-8 # Parameter for constructing sequence of lambda
control$tol = 1e-20; # tolrence parameter for converging [inner loop]
control$out.tol = 1e-20 # tolerence parameter for convergence [outer loop]
control$kfold = 5 # number of fold of crossvalidation
# Robust regression using adaptive lasso penalty
fit.ada <- robregcc_sp(Xt,y,C, beta.init=fit.init$betaR,
gamma.init = fit.init$residualR,
beta.wt=abs(beta.wt),
gamma.wt = abs(fit.init$residualR),
control = control,
penalty.index = 1, alpha = 0.95)
# Robust regression using lasso penalty [Huber equivalent]
fit.soft <- robregcc_sp(Xt,y,C, beta.init=NULL, gamma.init = NULL,
beta.wt=bw, gamma.wt = NULL,
control = control, penalty.index = 2,
alpha = 0.95)
# Robust regression using hard thresholding penalty
control$lmaxfac = 1e2 # Parameter for constructing sequence of lambda
control$lminfac = 1e-3 # Parameter for constructing sequence of lambda
fit.hard <- robregcc_sp(Xt,y,C, beta.init=fit.init$betaR,
gamma.init = fit.init$residualR,
beta.wt=bw, gamma.wt = NULL,
control = control, penalty.index = 3,
alpha = 0.95)
#--------------------------------------------------------------
## Extract fitted model parameters
# coefficient estimate: [adaptive]
coef_cc(fit.ada, type = 0, s = 1)
# coefficient estimate: [lasso/Huber]
coef_cc(fit.soft, type = 0, s = 1)
# coefficient estimate: [Hard]
coef_cc(fit.hard, type = 0, s = 1)
# residual estimate: [adaptive]
residuals(fit.ada)
# residual estimate: [lasso/Huber]
residuals(fit.soft)
# residual estimate: [Hard]
residuals(fit.hard)
#--------------------------------------------------------------
## Plot model output: solution path, cross validation error, estimated residual
# [adaptive]
par(mfrow=c(1,3))
plot_path(fit.ada)
plot_cv(fit.ada)
plot_resid.robregcc(fit.ada,type = 0, s = 1)
# [soft]
par(mfrow=c(1,3))
plot_path(fit.soft)
plot_cv(fit.soft)
plot_resid.robregcc(fit.soft,type = 0, s = 1)
#title(sub ='[Soft]: Solution path, Cross-validation error, residual')
# [Hard]
par(mfrow=c(1,3))
plot_path(fit.hard)
plot_cv(fit.hard)
plot_resid.robregcc(fit.hard,type = 0, s = 1)
#title(sub ='[Hard]: Solution path, Cross-validation error, residual')
par(mfrow=c(1,1))
#--------------------------------------------------------------
## True/Estimated parameter comparison
library(reshape2)
library(ggplot2)
# [Adaptive]
tmp <- data.frame(c(0,beta),fit.ada$beta0[,1])
names(tmp) <- c('Simulated parameter','Estimated parameter')
tmp$Index <- 1:(p+1)
df <- melt(tmp,3)
names(df)[2] <- "Comparison"
ggplot(data=df, aes(x=Index, y=value, fill=Comparison)) +
geom_bar(stat="identity", position=position_dodge()) +
theme_bw() + theme(legend.position="bottom") + ggtitle('Adaptive lasso') +
theme(plot.title = element_text(hjust = 0.5))
# [Lasso/Huber]
tmp <- data.frame(c(0,beta),fit.soft$beta0[,1])
names(tmp) <- c('Simulated parameter','Estimated parameter')
tmp$Index <- 1:(p+1)
df <- melt(tmp,3)
names(df)[2] <- "Comparison"
ggplot(data=df, aes(x=Index, y=value, fill=Comparison)) +
geom_bar(stat="identity", position=position_dodge()) +
theme_bw() + theme(legend.position="bottom") + ggtitle('Lasso') +
theme(plot.title = element_text(hjust = 0.5))
# [Hard]
tmp <- data.frame(c(0,beta),fit.hard$beta0[,1])
names(tmp) <- c('Simulated','Estimated')
tmp$Index <- 1:(p+1)
df <- melt(tmp,3)
names(df)[2] <- "Comparison"
ggplot(data=df, aes(x=Index, y=value, fill=Comparison)) +
geom_bar(stat="identity", position=position_dodge()) +
theme_bw() + theme(legend.position="bottom") + ggtitle('Hard penalty') +
theme(plot.title = element_text(hjust = 0.5))