Slide 8
Slide 8 text
Special Case: Ordinary Least Squares
Nature provides inputs ! with labels " provided by
supervisor, drawn randomly from distribution # $, & :
Training data = ()
, &)
, (*
, &*
, … , ((-
, &-
)
Given a set of possible functions, ℋ, choose the
hypothesis function ℎ∗ ∈ ℋ that minimizes Empirical Risk:
3456 ℎ =
1
9
:
;<)
-
=(&;, ℎ (; )
ℎ∗ = argmin
D∈ℋ
3456
(ℎ)
7
Squared Loss:
= &, E = E − & *
Set of functions:
ℋ = G( + I G ∈ ℝ-, I ∈ ℝ}