Multiple Parameter Gradient Descent in R - r

Question

I am an R user and I am currently trying to use a Gradient Descent algorithm for which to compare against a multiple linear regression. I have seen some codes online but they do not work on all data sets. I use the
UCI bike sharing data set (hour) as an example
Data set can be found here:
https://archive.ics.uci.edu/ml/machine-learning-databases/00275/
Split the data into training/test sets and create matrices:
data1 <- data[, c("season", "mnth", "hr", "holiday", "weekday", "workingday", "weathersit", "temp", "atemp", "hum", "windspeed", "cnt")]
# Split the data
trainingObs<-sample(nrow(data1),0.70*nrow(data1),replace=FALSE)
# Create the training dataset
trainingDS<-data1[trainingObs,]
# Create the test dataset
testDS<-data1[-trainingObs,]
x0 <- rep(1, nrow(trainingDS)) # column of 1's
x1 <- trainingDS[, c("season", "mnth", "hr", "holiday", "weekday", "workingday", "weathersit", "temp", "atemp", "hum", "windspeed")]
# create the x- matrix of explanatory variables
x <- as.matrix(cbind(x0,x1))
# create the y-matrix of dependent variables
y <- as.matrix(trainingDS$cnt)
m <- nrow(y)
solve(t(x)%*%x)%*%t(x)%*%y
Followed by the gradient function
gradientDesc <- function(x, y, learn_rate, conv_threshold, max_iter) {
n <- nrow(x)
m <- runif(ncol(x), 0, 1) # m is a vector of dimension ncol(x), 1
yhat <- x %*% m # since x already contains a constant, no need to add another one
MSE <- sum((y - yhat) ^ 2) / n
converged = F
iterations = 0
while(converged == F) {
m <- m - learn_rate * ( 1/n * t(x) %*% (yhat - y))
yhat <- x %*% m
MSE_new <- sum((y - yhat) ^ 2) / n
if( abs(MSE - MSE_new) <= conv_threshold) {
converged = TRUE
}
iterations = iterations + 1
MSE <- MSE_new
if(iterations >= max_iter) break
}
return(list(converged = converged,
num_iterations = iterations,
MSE = MSE_new,
coefs = m) )
}
ols <- solve(t(x)%*%x)%*%t(x)%*%y
out <- gradientDesc(x,y, 0.005, 1e-7, 200000)
data.frame(ols, out$coefs)
It works fine and produces the following comparison between multiple regression and the gradient solution:
ols out.coefs
x0 30.8003341 33.4473667
season 19.7839676 19.8020073
mnth -0.1249776 -0.1290033
hr 7.4554424 7.4619508
holiday -15.6022846 -15.8630012
weekday 1.8238997 1.7930636
workingday 5.0487553 5.0088699
weathersit -2.2088254 -2.3389047
temp 85.6214524 141.1351024
atemp 235.5992391 173.1234342
hum -226.7253991 -226.1559532
windspeed 33.5144866 30.1245570
It also works for the iris data set following the exact same commands as before:
iris
head(iris)
data2 <-iris[,c("Sepal.Width", "Petal.Length","Petal.Width","Sepal.Length")]
# Split the data
trainingObs1<-sample(nrow(data2),0.70*nrow(data2),replace=FALSE)
# Create the training dataset
trainingDS1<-data2[trainingObs1,]
# Create the test dataset
testDS2<-data2[-trainingObs1,]
x0a <- rep(1, nrow(trainingDS1)) # column of 1's
x1a<-trainingDS1[, c("Sepal.Width", "Petal.Length","Petal.Width")]
z <- as.matrix(cbind(x0a,x1a))
y<-as.matrix(trainingDS1$Sepal.Length)
m<-nrow(y)
solve(t(z)%*%z)%*%t(z)%*%y
ols <- solve(t(z)%*%z)%*%t(z)%*%y
out <- gradientDesc(z,y, 0.005, 1e-7, 200000)
data.frame(ols, out$coefs)
Producing the following output:
ols out.coefs
x0a 1.7082712 1.3933410
Sepal.Width 0.6764848 0.7578847
Petal.Length 0.7225420 0.7571403
Petal.Width -0.5436298 -0.6001406
However when using it with the mtcars data set:
mtcars<-mtcars
head(mtcars)
data3<-mtcars[,c("hp","wt","gear","cyl","mpg")]
trainingObs2<-sample(nrow(data3),0.70*nrow(data3),replace=FALSE)
trainingDS2<-data3[trainingObs2,]
testDS3<-data3[-trainingObs2,]
x0b <- rep(1, nrow(trainingDS2)) # column of 1's
x1b<-trainingDS2[, c("hp", "wt","gear","cyl")]
w <- as.matrix(cbind(x0b,x1b))
y<-as.matrix(trainingDS2$mpg)
m<-nrow(y)
solve(t(w)%*%w)%*%t(w)%*%y
ols <- solve(t(w)%*%w)%*%t(w)%*%y
out <- gradientDesc(w,y, 0.005, 1e-7, 200000)
data.frame(ols, out$coefs)
It fails to produce a comparison, creating the following error:
> ols <- solve(t(w)%*%w)%*%t(w)%*%y
> out <- gradientDesc(w,y, 0.005, 1e-7, 200000)
Error in if (abs(MSE - MSE_new) <= conv_threshold) { :
missing value where TRUE/FALSE needed
> data.frame(ols, out$coefs)
Error in data.frame(ols, out$coefs) :
arguments imply differing number of rows: 5, 4
I'd appreciate any help and pointers. Thank you very much for your time.