Linear regression gradient descent.

gistfile1.txt

# Load data and initialize values
data <- read.csv("http://www.statalgo.com/wp-content/uploads/2011/10/housing.csv")

alpha <- 0.01
m <- nrow(data)
x <- matrix(c(rep(1,m), data$area), ncol=2)
y <- matrix(data$price, ncol=1) / 1000

# Z-Score the feature
x.scaled <- x
x.scaled[,2] <- (x[,2] - mean(x[,2]))/sd(x[,2])

# Gradient descent function
grad <- function(x, y, theta) {
  gradient <- (t(x) %*% ((x %*% t(theta)) - y))
  return(t(gradient))
}

gradient.path <- function(x) {
    # Initialize the parameters
    theta <- matrix(c(0, 0), nrow=1)

    # Look at the values over each iteration
    theta.path <- matrix(ncol=2)
    for (i in 1:500) {
      theta <- theta - alpha * 1/m * grad(x, y, theta)
	if(all(is.na(theta))) break
      theta.path <- rbind(theta.path, theta)
    }
    theta.path
}

unscaled.theta <- gradient.path(x)
scaled.theta <- gradient.path(x.scaled)

summary(lm(y ~ x[, 2]))
summary(lm(y ~ x.scaled[, 2]))