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# scaled features.
# x = square feet
# y = sale price
x <- c(1, 2, 4)
y <- c(2, 2.5, 3)
# function to calculate the predicted value
h <- function(x, t0, t1)
{
result = t0 + t1 * x
result
}
# given a theta_0 and theta_1, this function calculates
# their cost. We don't need this function, strictly speaking...
# but it is nice to print out the costs as gradient descent iterates.
# We should see the cost go down every time the values of theta get updated.
cost <- function (theta_0, theta_1, x, y)
{
distance <- 0
for (i in 1:length(x)) # arrays in R are indexed starting at 1
{
square_feet <- x[i]
predicted_value <- theta_0 + theta_1 * square_feet
actual_value <- y[i]
# how far off was the predicted value (make sure you get the absolute value)?
distance <- distance + abs(actual_value - predicted_value)
}
# get how far off we were on average
distance <- distance / length(x)
distance
}
alpha <- 0.1
iters <- 1500
m <- length(x)
# initial values
theta_0 <- 0
theta_1 <- 0
for (i in 1:iters)
{
# we store this calculation in temporary variables,
# because theta_0 and theta_1 must be updated *together*.
# i.e. we can't update theta_0 and use the new theta_0 value
# while updating theta_1.
cost_0 <- 0
for (j in 1:m)
{
cost_0 <- cost_0 + (h(x[j], theta_0, theta_1) - y[j])
}
temp_0 <- theta_0 - alpha * 1/m * cost_0
cost_1 <- 0
for (j in 1:m)
{
cost_1 = cost_1 + ((h(x[j], theta_0, theta_1) - y[j]) * x[j])
}
temp_1 <- theta_1 - alpha * 1/m * cost_1
theta_0 <- temp_0
theta_1 <- temp_1
# print out the new values of theta for each iteration,
# as well as the new, lower cost
print(theta_0, theta_1, cost(theta_0, theta_1, x, y))
}
# scale the values of theta, they
# were too small because we did feature scaling
theta_0 <- theta_0 * 100000
theta_1 <- theta_1 * 100
# un-scale the features. So now we should be
# back to [1000, 2000, 4000] for square feet,
# from [1, 2, 4].
x <- x * 1000
y <- y * 100000
plot(x, y, col='red')
lines(1000:4000, h(1000:4000, theta_0, theta_1), col='green')
print(h(3000, theta_0, theta_1))
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