Derivative of MSE function

Course Discussions Machine Learning
#1

Hello!

In the explanation related to the Machine Learning models, there is a formula for computing Mean Squared Error (MSE). I have replicated it below as snapshots.

The following properties of derivatives are found relevant for solving this:

  1. Power rule: For h(x) = x^n; h’(x) = nx^(n-1)
  2. Chain rule: For h(x) = f(g(x)); h’(x) = f’g(x) * g’(x)

However, I am struggling to figure out the solution, especially the last x(i)j in the second equation. Any help with step-by-step solution to this problem is appreciated.

MSE:image
Derivative of MSE: image

Moreover, I would also like to understand what the x(i)j represents; as θj represents the value of θ for each of the feature (i.e. θ1, θ2,…θn) and x(i) defines the feature vector for the ith instance.

Thanks!

Tag:@sandeepgiri

#2

Hi Dhyey,

The derivative here is the Partial Derivative of the equation. Partial derivative means differentiating the equation with respect to just one variable, in our case, theta j, and keeping the other variables constant, and the two rules of multi-variate calculus i.e. power rule and the chain rule is used.

I hope it helps.
Regards.

#5

Thank you for the help, @Ankur_Sinha.

Would you mind giving step-wise solution for calculating the partial derivative of the MSE function given below, please?
image

#6

Hi Dhyey,

Here is the way I understood it. I hope it helps.

IMG-6069
IMG-60693024×4032 2.69 MB

Regards.

1 Like
#7

Hi! Ankur,

It was indeed helpful to me.

Many thanks for your time and effort.

#8

Hi Dhyey,

No Problem at all.

Happy Learning !!
Regards.