02 Vector and Matrix Representation*

Question 1

linear model assumptions

Answer 1

1. there exits a relationship between x and y
2. this relationship is linear
3. this relationship will continue into the future

Question 2

variables

Answer 2

attribute: x
targets: y or t

Question 3

linear model

Answer 3

t = w0 + w1(x)
where w0 is the bias
w1 is the gradient

Question 4

loss in linear

Answer 4

mean square error
1. after drawing a straight line, calculate error from line to X
2. square the error
3. sum all errors and get mean

Question 5

limitations

Answer 5

1. relationship is not perfectly linear
2. relationship might not be linear forever

Question 6

polynomial models **

Answer 6

t = w0 + w1x1 + w2x2 ….
can be represented in matrix
[w0, w1, w3] @ [1, x, xsquare, xcube]…
loss = 1/N . (t-xw)T (t-xw)
w = (xT. x)-1 . xTt

to predict new t, use updated x with old w
then update w with the new t