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Homework 1

Amin Yakubu 2/23/2019

library(tidyverse)
library(glmnet)
library(caret)
library(corrplot)
library(plotmo)
library(pls)

Data

train = read_csv('./data/solubility_train.csv')
test = read_csv('./data/solubility_test.csv')

The data has been divided into training and testing. The testing data has 951 observations and the test data has 356 observations. There are 229 predictors. 208 are binary variables that indicate the presence or absence of a particular chemical substructure, 16 are count descriptors, such as the number of bonds or the number of bromine atoms, and 4 are continuous descriptors, such as molecular weight or surface area. The response is in the column Solubility which is a continuous variable

# Checking for missing values
missing_train <- sapply(train, function(x) sum(is.na(x)))
missing_train[missing_train > 0]
## named integer(0)

missing_test <- sapply(test, function(x) sum(is.na(x)))
missing_test[missing_test > 0]
## named integer(0)

No missing data

plot(train$Solubility)

Data processing

#Training set
X.train = model.matrix(Solubility ~ ., train)[,-1]
y.train = train$Solubility

#Testing set
X.test = model.matrix(Solubility ~ ., test)[,-1]
y.test = test$Solubility

ctrl1 <- trainControl(method = "repeatedcv", number = 10, repeats = 5)

Question 1 -- Linear Model

set.seed(2)
lm.fit <- train(X.train, y.train,
                method = "lm",
                trControl = ctrl1)

pred.lm <- predict(lm.fit$finalModel, newdata = data.frame(X.test))

mean((pred.lm - y.test)^2)
## [1] 0.5558898

Question 2 -- Ridge Regression

set.seed(2)
ridge.fit <- train(X.train, y.train,
                     method = "glmnet",
                     tuneGrid = expand.grid(alpha = 0, 
                                            lambda = exp(seq(-10, 10, length = 200))),
                     trControl = ctrl1)

plot(ridge.fit)

plot(ridge.fit, xTrans = function(x) log(x)) # here were are plotting log lambda so it looks like the previous plots

ridge.fit$bestTune
##    alpha    lambda
## 80     0 0.1274155

bestlam.ridge = ridge.fit$bestTune$lambda
bestlam.ridge
## [1] 0.1274155

ridge.pred = predict(ridge.fit$finalModel, s = bestlam.ridge, newx = X.test)
mean((ridge.pred - y.test)^2)
## [1] 0.5134603

The mean test error is 0.51346

Question 3 -- The Lasso

set.seed(2)
lasso.fit <- train(X.train, y.train,
                     method = "glmnet",
                     tuneGrid = expand.grid(alpha = 1, 
                                            lambda = exp(seq(-10,10, length = 200))),
                     trControl = ctrl1)

plot(lasso.fit)

plot(lasso.fit, xTrans = function(x) log(x)) # here were are plotting log lambda so it looks like the previous plots

bestlam.lasso = lasso.fit$bestTune$lambda
bestlam.lasso
## [1] 0.005110889

lasso.pred = predict(lasso.fit$finalModel, s = bestlam.lasso, newx = X.test)
mean((lasso.pred - y.test)^2)
## [1] 0.4963234

The mean error is 0.4987.

lasso.coef = predict(lasso.fit$finalModel, type = "coefficients", s = bestlam.lasso)[1:ncol(train),]
length(lasso.coef)
## [1] 229

length(lasso.coef[lasso.coef != 0])
## [1] 144

There are 144 non-zero coefficient

Question 4 -- PCR

set.seed(2)
pcr.fit <- train(X.train, y.train,
                  method = "pcr",
                  tuneLength = 228,
                  trControl = ctrl1,
                  scale = TRUE)

pred.pcr <- predict(pcr.fit$finalModel, newdata = X.test, 
                       ncomp = pcr.fit$bestTune$ncomp)

mean((pred.pcr - y.test)^2)
## [1] 0.540555

ggplot(pcr.fit, highlight = TRUE) + theme_bw()

Question 5 -- Discussion

resamp <- resamples(list(lasso = lasso.fit, 
                         ridge = ridge.fit, 
                         pcr = pcr.fit,
                         lm = lm.fit))
summary(resamp)
## 
## Call:
## summary.resamples(object = resamp)
## 
## Models: lasso, ridge, pcr, lm 
## Number of resamples: 50 
## 
## MAE 
##            Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
## lasso 0.4358345 0.4852452 0.5201107 0.5186882 0.5409710 0.6036287    0
## ridge 0.4496804 0.4940707 0.5233784 0.5242992 0.5580663 0.6004447    0
## pcr   0.4696066 0.5185551 0.5448078 0.5441795 0.5711752 0.6393132    0
## lm    0.4470475 0.5007241 0.5381286 0.5310430 0.5615846 0.6043591    0
## 
## RMSE 
##            Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
## lasso 0.5783339 0.6301845 0.6811869 0.6787085 0.7099573 0.8181034    0
## ridge 0.5875062 0.6432311 0.6869788 0.6869960 0.7265436 0.8082616    0
## pcr   0.6100096 0.6726117 0.7060811 0.7095926 0.7438545 0.8470371    0
## lm    0.6092505 0.6699831 0.7106012 0.7117147 0.7531688 0.8772079    0
## 
## Rsquared 
##            Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
## lasso 0.8527973 0.8776698 0.8897130 0.8906161 0.9050896 0.9256949    0
## ridge 0.8533529 0.8764841 0.8873173 0.8881426 0.9043198 0.9228772    0
## pcr   0.8458710 0.8683380 0.8806705 0.8809669 0.8926659 0.9163149    0
## lm    0.8423791 0.8657031 0.8779699 0.8812886 0.9012601 0.9208367    0

bwplot(resamp, metric = "RMSE")