Cost Function

We can measure the accuracy of our hypothesis function by using a cost function.

This takes an average difference (actually a fancier version of an average) of all the results of the hypothesis with inputs from x’s and the actual output y’s.

To break it apart, it is (1/2)xˉ where xˉ is the mean of the squares of hθ​(xi​−yi​ )or the difference between the predicted value and the actual value.

This function is otherwise called the “Squared error function”, or “Mean squared error”. The mean is halved (1/2) as a convenience for the computation of the gradient descent, as the derivative term of the square function will cancel out the (1/2)​ term.

For higher accuracy of the hypothesis, we need to get minimum cost function. Now the questions arise how could we minimize the cost function? So how to choose θ to minimize the cost function?

The following image summarizes what the cost function does:

Read Next: Cost Function Intuition 1

Disclaimer — This series is based on the notes that I created for myself based on various books and videos I’ve read or seen , so some of the text could be an exact quote from some book/videos out there.