Gradient Descent Matlab implementation

Question

I have gone through many codes in stack overflow and made my own on same line. there is some problem with this code I am unable to understand. I am storing the value theta1 and theta 2 and also the cost function for analysis purpose. The data for x and Y can be downloaded from this Openclassroom page. It has x and Y data in form of .dat files that you can open in notepad. ``` %Single Variate Gradient Descent Algorithm%% clc clear all close all; % Step 1 Load x series/ Input data and Output data* y series x=load('D:\Office Docs_Jay\software\ex2x.dat'); y=load('D:\Office Docs_Jay\software\ex2y.dat'); %Plot the input vectors plot(x,y,'o'); ylabel('Height in meters'); xlabel('Age in years'); % Step 2 Add an extra column of ones in input vector [m n]=size(x); X=[ones(m,1) x];%Concatenate the ones column with x; % Step 3 Create Theta vector theta=zeros(n+1,1);%theta 0,1 % Create temporary values for storing summation temp1=0; temp2=0; % Define Learning Rate alpha and Max Iterations alpha=0.…

Accepted Answer

I have been trying to implement the iterative step with matrices and vectors (i.e not update each parameter of theta). Here is what I came up with (only the gradient step is here):

```
h = X * theta;  # hypothesis
err = h - y;    # error
gradient = alpha * (1 / m) * (X' * err); # update the gradient
theta = theta - gradient;
```

The hard part to grasp is that the "sum" in the gradient step of the previous examples is actually performed by the matrix multiplication `X'*err`. You can also write it as `(err'*X)'`

Gradient Descent Matlab implementation

Solution

Problem