week 2

Question 1

Define performance measure

Answer 1

When we have a model f, we are interested in its performance in the prediction. This performance can be quantified by a cost function C(w) : R^d → R.

Question 2

define residual

Answer 2

r = y- w^t . x

Question 3

what is MSE

Answer 3

Mean Square Error

Question 4

How do you build a linear approximation of an unknown nonlinear function

Answer 4

at point x. approximation f(x’): f(x) + (x’-x) df(x)

Question 5

What is derivative of matrix a^T X

Answer 5

a

Question 6

what is derivative of (X^T) AX

Answer 6

A.X + (A^T) X

Question 7

Give formal definition of global minima

Answer 7

if all C(W) >= C(W*)

Question 8

Give formal definition of local minima

Answer 8

If there exists some region Z > 0 such that: C(W) >= C(W*) for all W within distance Z of W but C(W) ! >= C(W) for all W

Question 9

difference between linear regression and polynomial regression

Answer 9

Polynomial regression uses a basis function. It makes the function linear with respect to the features