the gaussian prior p(w)
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σ
1.00
peak density =
0.40
likelihood p(D|w)
drag data points
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noise
σₙ
0.50
reset
MLE ŵ =
·
posterior = prior × likelihood
— prior
— likelihood
— posterior
MAP
·
MLE
·
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prior
σ
1.00
noise
σₙ
0.50
the same optimization, two views
regularization view: ∑(yᵢ − wxᵢ)² + λw²
bayesian view: −log p(w|D)
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λ
1.00
σ
=
0.71
λ = σₙ²/σ²
min at ŵ =
·
playground: MLE vs MAP polynomial fit
drag points to refit
— MLE
— MAP (ridge)
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degree
6
λ
0.50
reset
randomize