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minh
X
(v;w)=e
d2(hv; hw)
π βπ£, βπ€ π
ππ£, ππ€ β Prob β2
W2(Β½v; Β½w) := infΒΌ2Β¦(Β½v;Β½w)
Β΅ZZ
R2jxΒ‘ yj2 dΒΌ(x; y)
ΒΆ1=2
Ξ (ππ£, ππ€) β2 Γ β2 ππ£
ππ€
ππ ππ
πΊ = (π, πΈ) π0 β π
π£ β π0
π£ β π0
π: π β Prob(π·)
ED[Β½] :=X
(v;w)2E
W22 (Β½v; Β½w)
Prob(β)ππ£, ππ€ β Prob(β)
πΉπ£, πΉπ€. π2 ππ£, ππ€ = πΉπ£β1 β πΉπ€
β1
2
π£ β π0 πΉπ£ ππ£ π β [0,1]ππ : π β β
π₯ππ = 0 βπ£ β π\π0 ππ π£ = πΉπ£β1 π βπ£ β π0 π£
π β¦ ππ (π£) ππ£
π£ β¦ ππ£
http://realgl.blogspot.com/2013/01/pdf-cdf-inv-cdf.html
[CDF] CDF-1
Linear solve
Prob(β)
β’
β’
v0 v1v1=2
Β½0 Β½1
v1=4 v3=4
Prob(β)
Fixed
Fixed
Propagated
v0
v1PDF Was. PDF Was.PDF Was.PDF Was.Was.PDF
Prob(π1)
Ground truth (mean)PDF (mean) Wasserstein (mean)
Ground truth (std. dev.)PDF (std. dev.) Wasserstein (std. dev.)
π π: π β π ππ: π β
Prob(π) πΏπ π£
0
1
2 10 1
π1