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Created Jul 27, 2012
 ## ## Linear regression by gradient descent ## ## A learning exercise to help build intuition about gradient descent. ## J. Christopher Bare, 2012 ## # generate random data in which y is a noisy function of x x <- runif(1000, -5, 5) y <- x + rnorm(1000) + 3 # fit a linear model res <- lm( y ~ x ) # plot the data and the model plot(x,y, col=rgb(0.2,0.4,0.6,0.4), main='Linear regression') abline(res, col='blue') # squared error cost function cost <- function(X, y, theta) { sum( (X %*% theta - y)^2 ) / (2*length(y)) } # learning rate and iteration limit alpha <- 0.01 num_iters <- 1000 # keep history cost_history <- double(num_iters) theta_history <- list(num_iters) # initialize coefficients theta <- matrix(c(0,0), nrow=2) # add a column of 1's for the intercept coefficient X <- cbind(1, matrix(x)) # gradient descent for (i in 1:num_iters) { error <- (X %*% theta - y) delta <- t(X) %*% error / length(y) theta <- theta - alpha * delta cost_history[i] <- cost(X, y, theta) theta_history[[i]] <- theta } # plot data and converging fit plot(x,y, col=rgb(0.2,0.4,0.6,0.4), main='Linear regression by gradient descent') for (i in c(1,3,6,10,14,seq(20,num_iters,by=10))) { abline(coef=theta_history[[i]], col=rgb(0.8,0,0,0.3)) } abline(coef=theta, col="blue") # check out the trajectory of the cost function cost_history[seq(1,num_iters, by=100)] plot(cost_history, type='l', col='blue', lwd=2, main='Cost function', ylab='cost', xlab='Iterations')

### beyhangl commented May 18, 2016

 perfect

### smsatyam commented Jun 4, 2018

i have doubt in this ,

# squared error cost function

cost <- function(X, y, theta) {
sum( (X %% theta - y)^2 ) / (2length(y))
}
what is the meaning of %*% in this and how it will work ,

# plot data and converging fit

plot(x,y, col=rgb(0.2,0.4,0.6,0.4), main='Linear regression by gradient descent')
for (i in c(1,3,6,10,14,seq(20,num_iters,by=10))) {
abline(coef=theta_history[[i]], col=rgb(0.8,0,0,0.3))
}
abline(coef=theta, col="blue")