regularization
Matthew Stephens
2022-04-05
Last updated: 2022-04-05
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Knit directory: stat34800/analysis/
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Introduction
I took this code illustrating regularization from https://www.r-bloggers.com/2017/07/machine-learning-explained-regularization/
My intention here is to run the code and show the figures it produced (since the plots are not shown in the html above). I had to move the require(ggplot2) command to the top of the code get it to run. I also added a plot of the L1 coefficients because that was missing from the code. I downloaded the data from https://www.kaggle.com/datasets/harlfoxem/housesalesprediction?resource=download
Unfortunately the graphical results do not seem to match the description in the text in the html. For example, there does not seem to be any need for regularization: the lowest error in the CV occurs at or near the least squares solution. I do not know the reason for this.
require(data.table)Loading required package: data.tableWarning: package 'data.table' was built under R version 4.1.1require(glmnet)Loading required package: glmnetWarning: package 'glmnet' was built under R version 4.1.1Loading required package: MatrixLoaded glmnet 4.1-3require(ggplot2)Loading required package: ggplot2Warning: package 'ggplot2' was built under R version 4.1.1set.seed(123)
###reading data
housingData=fread('../data/kc_house_data.csv')
##Removing non numeric var
housingData[,floors:=as.numeric(floors)][,c('zipcode','lat','long','id','date','sqft_basement'):=NULL]
###Splitting data
indexTrain=sample.int(nrow(housingData),nrow(housingData)*0.005)
##no Reg
lmNoReg=lm(price~.,housingData[indexTrain])
summary(lmNoReg)
Call:
lm(formula = price ~ ., data = housingData[indexTrain])
Residuals:
Min 1Q Median 3Q Max
-329868 -109393 -19223 78141 891663
Coefficients: (1 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.617e+06 1.997e+06 2.312 0.02296 *
bedrooms -3.024e+04 3.179e+04 -0.951 0.34389
bathrooms 7.125e+04 6.078e+04 1.172 0.24405
sqft_living 4.155e+01 6.850e+01 0.607 0.54564
sqft_lot -1.188e+00 1.016e+00 -1.170 0.24493
floors 4.427e+04 5.359e+04 0.826 0.41080
waterfront NA NA NA NA
view 9.330e+04 3.734e+04 2.499 0.01421 *
condition 3.881e+04 3.003e+04 1.292 0.19944
grade 9.142e+04 3.126e+04 2.925 0.00432 **
sqft_above 4.036e+01 5.998e+01 0.673 0.50267
yr_built -2.710e+03 1.016e+03 -2.668 0.00899 **
yr_renovated 1.234e+02 4.521e+01 2.730 0.00755 **
sqft_living15 7.727e+01 5.408e+01 1.429 0.15634
sqft_lot15 -7.130e-01 1.981e+00 -0.360 0.71968
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 189400 on 94 degrees of freedom
Multiple R-squared: 0.6416, Adjusted R-squared: 0.592
F-statistic: 12.94 on 13 and 94 DF, p-value: 8.307e-16pred_no_reg=predict(lmNoReg,housingData[-indexTrain])Warning in predict.lm(lmNoReg, housingData[-indexTrain]): prediction from a
rank-deficient fit may be misleadingsqrt(mean((pred_no_reg-housingData[-indexTrain]$price)^2))[1] 239795.3plotCoeffEvolution=function(penalizedGlm,type='L1')
{
lambda=penalizedGlm$lambda
coeff=as.matrix(penalizedGlm$beta)
rowName=rownames(coeff)
coeff=data.table(coeff)
coeff[,name:=rowName]
coeff=melt(coeff,id.vars = 'name')
coeff[,variable:=rep(lambda,each=length(unique(name)))]
ggplot(coeff,aes(x=variable,y=value,color=name))+geom_line()+xlab(paste0(type,' regularisation'))+ylab('Value of coefficient')+scale_x_log10()
}
##Different L1 regularisation
fit = glmnet(as.matrix(housingData[indexTrain,-c('price'),with=F]),as.matrix(housingData[indexTrain]$price) , family="gaussian",alpha=1)
pred_L1_reg=data.table(predict(fit,as.matrix(housingData[-indexTrain,-c('price'),with=F])))
RMSE_L1=sqrt(apply(pred_L1_reg[,(.SD-housingData[-indexTrain]$price)^2,.SD=1:ncol(pred_L1_reg)],2,mean))
DF_plot=data.frame(lambda=fit$lambda,rmse=RMSE_L1)
plotCoeffEvolution(fit,'L1') # I added this line
ggplot(DF_plot,aes(x=lambda,y=rmse))+geom_line()+ggtitle("Evolution of test error vs lambda value")+scale_x_log10()
require(plotly)Loading required package: plotlyWarning: package 'plotly' was built under R version 4.1.1
Attaching package: 'plotly'The following object is masked from 'package:ggplot2':
last_plotThe following object is masked from 'package:stats':
filterThe following object is masked from 'package:graphics':
layout## L2 regularisation
fit = glmnet(as.matrix(housingData[indexTrain,-c('price'),with=F]),as.matrix(housingData[indexTrain]$price) , family="gaussian",alpha=0)
pred_L2_reg=data.table(predict(fit,as.matrix(housingData[-indexTrain,-c('price'),with=F])))
RMSE_L2=sqrt(apply(pred_L2_reg[,(.SD-housingData[-indexTrain]$price)^2,.SD=1:ncol(pred_L2_reg)],2,mean))
DF_plot=data.frame(lambda=fit$lambda,rmse=RMSE_L2)
plotCoeffEvolution(fit,'L2')
require(ggplot2)
ggplot(DF_plot,aes(x=lambda,y=rmse))+geom_line()+ggtitle("Evolution of test error vs lambda value")+scale_x_log10()
##Different L1L2 regularisation
fit = glmnet(as.matrix(housingData[indexTrain,-c('price'),with=F]),as.matrix(housingData[indexTrain]$price) , family="gaussian",alpha=0.03)
pred_L1L2_reg=data.table(predict(fit,as.matrix(housingData[-indexTrain,-c('price'),with=F])))
RMSE_L1L2=sqrt(apply(pred_L1L2_reg[,(.SD-housingData[-indexTrain]$price)^2,.SD=1:ncol(pred_L1L2_reg)],2,mean))
DF_plot=data.frame(lambda=fit$lambda,rmse=RMSE_L1L2)
plotCoeffEvolution(fit,'Elastic')
require(ggplot2)
ggplot(DF_plot,aes(x=lambda,y=rmse))+geom_line()+ggtitle("Evolution of test error vs lambda value")+scale_x_log10()
sessionInfo()R version 4.1.0 Patched (2021-07-20 r80657)
Platform: aarch64-apple-darwin20 (64-bit)
Running under: macOS Monterey 12.2
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/4.1-arm64/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.1-arm64/Resources/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] plotly_4.10.0 ggplot2_3.3.5 glmnet_4.1-3 Matrix_1.3-4
[5] data.table_1.14.2
loaded via a namespace (and not attached):
[1] shape_1.4.6 tidyselect_1.1.1 xfun_0.28 purrr_0.3.4
[5] splines_4.1.0 lattice_0.20-45 colorspace_2.0-2 vctrs_0.3.8
[9] generics_0.1.1 viridisLite_0.4.0 htmltools_0.5.2 yaml_2.2.1
[13] utf8_1.2.2 survival_3.2-13 rlang_0.4.12 jquerylib_0.1.4
[17] later_1.3.0 pillar_1.6.4 glue_1.5.0 withr_2.4.2
[21] DBI_1.1.1 bit64_4.0.5 foreach_1.5.1 lifecycle_1.0.1
[25] stringr_1.4.0 munsell_0.5.0 gtable_0.3.0 workflowr_1.7.0
[29] htmlwidgets_1.5.4 codetools_0.2-18 evaluate_0.14 labeling_0.4.2
[33] knitr_1.36 fastmap_1.1.0 httpuv_1.6.3 fansi_0.5.0
[37] highr_0.9 Rcpp_1.0.7 promises_1.2.0.1 scales_1.1.1
[41] jsonlite_1.7.2 farver_2.1.0 bit_4.0.4 fs_1.5.0
[45] digest_0.6.28 stringi_1.7.5 dplyr_1.0.7 grid_4.1.0
[49] rprojroot_2.0.2 tools_4.1.0 magrittr_2.0.2 lazyeval_0.2.2
[53] tibble_3.1.6 tidyr_1.1.4 crayon_1.4.2 whisker_0.4
[57] pkgconfig_2.0.3 ellipsis_0.3.2 httr_1.4.2 assertthat_0.2.1
[61] rmarkdown_2.11 iterators_1.0.13 R6_2.5.1 git2r_0.29.0
[65] compiler_4.1.0