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Regression using Gradient Descent.R
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Regression using Gradient Descent.R
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##
## title: "Algorithms from scratch using Gradient Descent to predict average GPU Run Time & classify it's run type"
## author: "Sarthak Mohapatra"
## date: "1/29/2020"
##
options(scipen = 999)
##
## Loading the required packages.
##
pacman::p_load(data.table, forecast, leaps, tidyverse, caret, corrplot, glmnet, mlbench, ggplot2, gplots, pivottabler,MASS,
e1071, fpp2, gains, pROC, knitr, gplots, FNN, RColorBrewer, viridis, cowplot, ggpubr, gridExtra, rlist, d3heatmap)
##
## Importing the dataset from the working directory
##
setwd('D:/Second Semester - MSBA - UTD/Applied Machine Learning/Assignment 1/sgemm_product_dataset')
gpu.df <- read.csv("sgemm_product.csv")
head(gpu.df)
##
## Renaming the last 4 column names
##
names(gpu.df)[15] = "Run1"
names(gpu.df)[16] = "Run2"
names(gpu.df)[17] = "Run3"
names(gpu.df)[18] = "Run4"
head(gpu.df)
##
## Creating a new feature Average. It will contain the average of Run1 through Run4
##
gpu.df$Average <- (gpu.df$Run1 + gpu.df$Run2 + gpu.df$Run3 + gpu.df$Run4) / 4
head(gpu.df)
##
## Data Partioning
##
set.seed(16)
##
## randomly order the dataset
##
rows <- sample(nrow(gpu.df))
gpu <- gpu.df[rows, -15:-18]
##
## find rows to split on
##
split <- round(nrow(gpu) * 0.7)
gpu.train.df <- gpu[1:split, ]
gpu.test.df <- gpu[(split+1):nrow(gpu), ]
##
## confirm the size of the split
##
round(nrow(gpu.train.df)/nrow(gpu), digits = 3)
head(gpu.train.df)
head(gpu.test.df)
##
## Normalizing the dataset.
##
gpu_train_norm <- gpu.train.df
gpu_test_norm <- gpu.test.df
gpu_norm_df <- gpu
norm.values <- preProcess(gpu.train.df[, 1:15], method=c("center", "scale"))
gpu_train_norm[, 1:15] <- predict(norm.values, gpu.train.df[, 1:15])
gpu_test_norm[, 1:15] <- predict(norm.values, gpu.test.df[, 1:15])
gpu_norm_df[, 1:15] <- predict(norm.values, gpu[, 1:15])
new.gpu.norm.df <- predict(norm.values, gpu)
##
## Creating the feature and target datasets ( X & Y)
##
x_gpu_train <- as.matrix(gpu_train_norm[c(1:14)])
y_gpu_train <- as.matrix(gpu_train_norm[c('Average')])
x_gpu_test <- as.matrix(gpu_test_norm[c(1:14)])
y_gpu_test <- as.matrix(gpu_test_norm[c('Average')])
x_gpu_train <- cbind(Intercept=1,x_gpu_train)
head(x_gpu_train)
head(y_gpu_train)
x_gpu_test <- cbind(Intercept=1, x_gpu_test)
head(x_gpu_test)
length(y_gpu_train)
length(y_gpu_test)
##
## The Below code chunks is the implementation of the Gradient Descent method. Based on the experimentation performed, the best alpha selected for demonstration here
## is alpha = 0.0001 and the threshold as thold = 0.000001.
##
##
## Here, we are defining the Gradient Descent algorithm. First, we are declaring the variables to store cost, beta co-efficients, predicted target variable value and error.
##
gradient_descent <- function(x, y, alpha, m, beta, thold)
{
cost_iter <<- list()
beta_iter <<- matrix(0,nrow=m,ncol=15)
yhat_iter <<- list()
error_iter <<- list()
##
## We are iterating over the matrices with the goal of minimizing the cost function value.
##
for (i in 1:30000){
yhat <- as.matrix(x) %*% beta_value ## Predictions of target variable.
yhat_iter[i] <- yhat ## Storing the predicted value.
error <- yhat - y ## Calculating the error value.
error_iter[i] <- error ## Storing the error value.
cost <- (1/(2*m)) * (t(error) %*% error) ## Calculating the cost function value.
cost_iter[i] <- cost ## storing the cost function value.
beta_value <- beta_value - (alpha * (1/m) * (t(x) %*% (yhat - y))) ## Calculating the new beta coefficinets values.
beta_iter[i,1:15] <- t(beta_value) ## storing the beta coefficients value.
if ((i > 1) && ((cost_iter[[i-1]] - cost_iter[[i]]) < thold)) {
print('Threshold reached')
break
}
}
final_val <- list(cost_iter, beta_iter, yhat_iter, error_iter) ## Storing the variables in a single variable so that it can be returned.
return (final_val) ## Returning the values.
}
##
## Prediction function for the validation dataset.
##
linear_test_predict <- function(beta_conv_iter, x_gpu_test, y_gpu_test)
{
yhat_test <- as.matrix(x_gpu_test) %*% beta_conv_iter
error_test <- yhat_test - y_gpu_test
cost_test <- (1/(2*length(y_gpu_test))) * sum(t(error_test) %*% error_test)
test_val <- list(yhat_test, error_test, cost_test)
return(test_val)
}
##
## Let's define the main function for initializing the initial values of beta-i (slope) and beta-0 (y intercept)
##
main_function <- function(alpha, m, beta_value, thold){
cost_return_train <- list()
beta_return_train <- list()
yhat_return_train <- list()
final_return_train <- list()
cost_return_test <- list()
yhat_return_test <- list()
error_return_test <- list()
final <- list()
final_test <- list()
final <- gradient_descent(x_gpu_train, y_gpu_train, alpha, m, beta, thold)
cost_return_train <- final[[1]]
beta_return_train <- final[[2]]
yhat_return_train <- final[[3]]
error_return_train <- final[[4]]
conv_iter <- length(cost_return_train)
conv_iter
beta_conv_iter <- beta_return_train[conv_iter,1:15]
beta_conv_iter
cost_return_train[conv_iter]
final_test <- linear_test_predict(beta_conv_iter, x_gpu_test, y_gpu_test)
cost_return_test <- final_test[[3]]
yhat_return_test <- final_test[[1]]
error_return_test <- final_test[[2]]
cost_return_test
cost_result <- list(cost_return_train, cost_return_test, conv_iter, beta_conv_iter)
return(cost_result)
}
##
## Invoking the main function to apply the Gradient Descent algorithm.
##
thold <- 0.00000001
alpha <- 0.0001
m <- nrow(gpu.train.df)
beta_value <<- rep(0,15)
cost_return <- main_function(alpha, m, beta_value, thold)
cost_return_train <- cost_return[[1]]
cost_return_test <- cost_return[[2]]
conv_iter <- cost_return[[3]]
beta_val <- cost_return[[4]]
cost_train_0.0001_a <- cost_return_train
cost_train_min_0.0001_a <- cost_return_train[conv_iter]
cost_test_0.0001_a <- cost_return_test
cost_train_all_a <- matrix(c(cost_train_min_0.0001_a))
cost_test_all_a <- matrix(c(cost_test_0.0001_a))
##
## Plotting various performance validation curves
##
plot(1:length(cost_train_0.0001_a), cost_train_0.0001_a, main = 'Cost function convergence at alpha 0.0001.', xlab = 'No. of Iterations', ylab = 'Cost Function value', col='red', type='l', xlim=c(0,30000), ylim=c(0.28,0.5),sub='Convergence Threshold value - 0.000001')
legend("topright",c("alpha=0.0001"),cex=0.7, bty='n', fill=c("red"))
linear_model <- lm(Average ~ ., data=gpu_train_norm)
summary(linear_model)
conv_iter
beta_val