overfitting
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 overfitting from https://www.r-bloggers.com/2017/06/machine-learning-explained-overfitting/
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 commented out some output to make it less verbose.
###Overfitting
require(data.table)Loading required package: data.tableWarning: package 'data.table' was built under R version 4.1.1library(rpart)
require(ggplot2)Loading required package: ggplot2Warning: package 'ggplot2' was built under R version 4.1.1set.seed(456)
##Reading data
overfitting_data=data.table(airquality)
ggplot(overfitting_data,aes(Wind,Ozone))+geom_point()+ggtitle("Ozone vs wind speed")Warning: Removed 37 rows containing missing values (geom_point).
data_test=na.omit(overfitting_data[,.(Wind,Ozone)])
train_sample=sample(1:nrow(data_test),size = 0.7*nrow(data_test))
###creation of polynomial models
degree_of_poly=1:20
degree_to_plot=c(1,3,5,10,20)
polynomial_model=list()
df_result=NULL
for (degree in degree_of_poly)
{
fm=as.formula(paste0("Ozone~poly(Wind,",degree,",raw=T)"))
polynomial_model=c(polynomial_model,list(lm(fm,data_test[train_sample])))
Polynomial_degree=paste0(degree)
data_fitted=tail(polynomial_model,1)[[1]]$fitted.values
new_df=data.table(Wind=data_test[train_sample,Wind],Ozone_real=data_test[train_sample,Ozone],Ozone_fitted=tail(polynomial_model,1)[[1]]$fitted.values,degree=as.factor(degree))
if (is.null(df_result))
df_result=new_df
else
df_result=rbind(df_result,new_df)
}
gg=ggplot(df_result[degree%in%degree_to_plot],aes(x=Wind))+geom_point(aes(y=Ozone_real))+geom_line(aes(color=degree,y=Ozone_fitted))
gg+ggtitle('Ozone vs wind for several polynomial regressions')+ylab('Ozone')
###Computing SE
SE_train_list=c()
SE_test_list=c()
for (poly_mod in polynomial_model)
{
#print(summary(poly_mod))
SE_train_list=c(SE_train_list,sqrt(mean(poly_mod$residuals^2)))
SE_test=sqrt(mean((data_test[-train_sample]-predict(poly_mod,data_test[-train_sample,]))^2))
SE_test_list=c(SE_test_list,SE_test)
}Warning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NAWarning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NA
Warning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NA
Warning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NA
Warning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NA
Warning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NA
Warning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NA
Warning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NA
Warning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NA
Warning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NA
Warning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NAWarning in predict.lm(poly_mod, data_test[-train_sample, ]): prediction from a
rank-deficient fit may be misleadingWarning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NAWarning in predict.lm(poly_mod, data_test[-train_sample, ]): prediction from a
rank-deficient fit may be misleadingWarning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NAWarning in predict.lm(poly_mod, data_test[-train_sample, ]): prediction from a
rank-deficient fit may be misleadingWarning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NAWarning in predict.lm(poly_mod, data_test[-train_sample, ]): prediction from a
rank-deficient fit may be misleadingWarning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NAWarning in predict.lm(poly_mod, data_test[-train_sample, ]): prediction from a
rank-deficient fit may be misleadingWarning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NAWarning in predict.lm(poly_mod, data_test[-train_sample, ]): prediction from a
rank-deficient fit may be misleadingWarning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NAWarning in predict.lm(poly_mod, data_test[-train_sample, ]): prediction from a
rank-deficient fit may be misleadingWarning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NAWarning in predict.lm(poly_mod, data_test[-train_sample, ]): prediction from a
rank-deficient fit may be misleadingWarning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NAWarning in predict.lm(poly_mod, data_test[-train_sample, ]): prediction from a
rank-deficient fit may be misleadingWarning in mean.default((data_test[-train_sample] - predict(poly_mod,
data_test[-train_sample, : argument is not numeric or logical: returning NAdata_plot=data.table(SE_test_list,SE_train_list,degree_of_poly)
ggplot(data_plot[degree_of_poly<=8])+geom_line(aes(x=degree_of_poly,y=SE_test_list),color='red')+geom_line(aes(x=degree_of_poly,y=SE_train_list))+ylab('MSE')+xlab('Degrees of polynomial')Warning: Removed 8 row(s) containing missing values (geom_path).
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] ggplot2_3.3.5 rpart_4.1-15 data.table_1.14.2 workflowr_1.7.0
loaded via a namespace (and not attached):
[1] tidyselect_1.1.1 xfun_0.28 purrr_0.3.4 colorspace_2.0-2
[5] vctrs_0.3.8 generics_0.1.1 htmltools_0.5.2 yaml_2.2.1
[9] utf8_1.2.2 rlang_0.4.12 jquerylib_0.1.4 later_1.3.0
[13] pillar_1.6.4 glue_1.5.0 withr_2.4.2 DBI_1.1.1
[17] lifecycle_1.0.1 stringr_1.4.0 munsell_0.5.0 gtable_0.3.0
[21] evaluate_0.14 labeling_0.4.2 knitr_1.36 callr_3.7.0
[25] fastmap_1.1.0 httpuv_1.6.3 ps_1.6.0 fansi_0.5.0
[29] highr_0.9 Rcpp_1.0.7 promises_1.2.0.1 scales_1.1.1
[33] farver_2.1.0 fs_1.5.0 digest_0.6.28 stringi_1.7.5
[37] processx_3.5.2 dplyr_1.0.7 getPass_0.2-2 rprojroot_2.0.2
[41] grid_4.1.0 tools_4.1.0 magrittr_2.0.2 tibble_3.1.6
[45] crayon_1.4.2 whisker_0.4 pkgconfig_2.0.3 ellipsis_0.3.2
[49] assertthat_0.2.1 rmarkdown_2.11 httr_1.4.2 rstudioapi_0.13
[53] R6_2.5.1 git2r_0.29.0 compiler_4.1.0