CODEWITHSUNDEEP
r
marie
marie

Reputation: 21

Trying to write a gradient descent algorithm in R

Implement the gradient descent algorithm in this question. Let {X1,…,Xn} be a dataset and g(x)=n−1∑ni=1(x−Xi)2. It is known that the mean of the dataset is the solution to the following minimization problem minx∈ℝg(x).

To minimize g(x), you are going to use a while loop to implement the gradient descent algorithm, as follows.

Step 0. Initialize x1=0 Step 1. In the kth step, where k=1,2,…, set xk+1=xk−0.99k×g′(xk).

Step 2. Repeat Step 1 until |g′(xk)| is smaller than a small tolerance level tol (e.g., set it to 1e-5) or if k exceeds the maximum number of iterations Kmax (e.g., set it to 1000).

You are going to implement the gradient descent algorithm to find the mean. Use the dataset cars$speed for {X1,…,Xn}.You don’t have to write the algorithm into a function in this question; you are going to do this in the next.

Could someone help me with this?

Here is what I have so far

data(cars)
x1 <- 0
k <- 1
toleranceLevel <-0.00005
X <- cars$speed
kmax <- 10000

while(x1 > toleranceLevel){
  gxprime <- 2 * mean(x1 - X)
  gxprime
  x1 <-(((x1)-(.99^k))*gxprime)
  if(x1 < toleranceLevel){ 
    k <- k + 1
  } else {
  }
  if(k == kmax){
    break
  }
  print(k)
}

Upvotes: 1

Views: 352

Answers (1)

Onyambu
Onyambu

Reputation: 79298

data(cars)
x_old <- 0
k <- 1
toleranceLevel <-0.00005
X <- cars$speed
kmax <- 10000
err <- 1
while(err > toleranceLevel & k < kmax){
  x_new <- x_old -.99^k * 2 * mean(x_old - X)
  err <- abs(x_new - x_old)
  x_old <- x_new
  k <- k + 1
}
x_new

Upvotes: 1

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