Slide 3
Slide 3 text
What Gaussian Process Regression is.
Dataset =
,
| = 1 ⋯
=
=
=1
(
)
Estimated by using MSE
Φ,
=
(
) : design matrix
= ΦΦ −1Φ
Linear Regression ( basis function (⋅) have to be given)
Gaussian Process Regression ( Kernel function have to be given)
We introduce prior distribution ~N , λ2
= follows gaussian distribution
~ , λ2 ≡ ,
(∗|∗, )~ ∗
T−1, ∗∗
− ∗
T−1∗
∗ ~N ,
∗
∗
T k∗∗
∗
= ∗, 1
, ⋯ , (∗,
)
k∗∗
= ∗, ∗
,′
= λ
′ = 1
exp −
1
2
− ′ 2
Example: RBF Kernel