PMI:MI ≈ PHSIC:HSIC

PHSIC ྨࣅͰεϜʔδϯάͨ͠ PMI ʹݟ͑Δ

PMI ͰଌΔ (x, y) ͷؔ࿈ͷྑ͞

• x = xi

∧ y = yi

ͳΔ (xi

, yi

) ͕ଘࡏ → PMI ্͕ঢ

• x = xi

⊻ y = yi

ͳΔ (xi

, yi

) ͕ଘࡏ → PMI ͕Լ

PHSIC ͰଌΔ (x, y) ͷؔ࿈ͷྑ͞

• ˜

k(x, xi

)˜

ℓ(y, yi

) > 0 ͳΔ (xi

, yi

) ͕ଘࡏ → PHSIC ্͕ঢ

ɹ “x ≈ xi

∧ y ≈ yi” ͷͱ্͖ঢ

• ˜

k(x, xi

)˜

ℓ(y, yi

) < 0 ͳΔ (xi

, yi

) ͕ଘࡏ → PHSIC ͕Լ

PMI:MI ≈ PHSIC:HSIC

MI(X,Y; Z) =

1

N

∑

i

PMI(xi

, yi; Z)

HSIC(X,Y; Z) =

1

N

∑

i

PHSIC(xi

, yi; Z)

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