1 , 2 , , 1 , 2 , , ( 1 , 2 , - - PowerPoint PPT Presentation

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1 , 2 , , 1 , 2 , , ( 1 , 2 , - - PowerPoint PPT Presentation

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1 , 2 , , 1 , 2 , , ( 1 , 2 , , ) 1 , 2 , , 1 , 2 , , 1 11 1 11 1 21

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SLIDE 1
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SLIDE 2
  • ▪

𝑨1, 𝑨2, ⋯ , 𝑨𝑂 𝑧1, 𝑧2, ⋯ , 𝑧𝑁 (≈ 𝑡1, 𝑡2, ⋯ , 𝑡𝑁) 𝑡1, 𝑡2, ⋯ , 𝑡𝑁 𝑨1, 𝑨2, ⋯ , 𝑨𝑂 𝑩 𝑩 𝑏11 𝑏21 𝑏12 𝑏22 𝑡2 𝑡1 𝑧2 𝑧1 𝑥11 𝑥21 𝑥12 𝑥22 𝑨2 𝑨1

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SLIDE 3
  • ▪

▪ ▪

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SLIDE 4
  • ▪

𝑡(𝑢) 𝑁 ▪ 𝑛 𝜐𝑛 𝒜 𝑢 = 𝑨1(𝑢) 𝑨2(𝑢) ⋮ 𝑨𝑁 𝑢 = 𝑡(𝑢 − 𝜐1) 𝑡(𝑢 − 𝜐2) ⋮ 𝑡(𝑢 − 𝜐𝑁) 𝒜 𝜕 = 𝑎1(𝜕) 𝑎2(𝜕) ⋮ 𝑎𝑁 𝜕 𝑎𝑛 𝜕 ≡

−∞ ∞

𝑨𝑛 𝑢 𝑓−𝑘𝜕𝑢𝑒𝑢 =

−∞ ∞

𝑡 𝑢 − 𝜐𝑛 𝑓−𝑘𝜕𝑢𝑒𝑢 = 𝑓−𝑘𝜕𝜐𝑛𝑇(𝜕) 𝑇 𝜕 ≡

−∞ ∞

𝑡 𝑢 𝑓−𝑘𝜕𝑢𝑒𝑢 𝒃(𝜕) = 𝑏1 ⋮ 𝑏𝑁 ≡ 𝑓−𝑘𝜕𝜐1 ⋮ 𝑓−𝑘𝜕𝜐𝑁 𝒜 𝜕 = 𝒃(𝜕)𝑇(𝜕)

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SLIDE 5
  • 𝑏𝑛(𝜕) = exp 𝑘

𝑛 − 1 − 𝑁 − 1 2 2𝜌𝑒𝑦 𝜇 sin 𝜄𝑡 𝜐𝑛 = − 𝑛 − 1 − 𝑁 − 1 2 𝑒𝑦 𝑑 sin 𝜄𝑡 𝒒𝒏 = 𝑛 − 1 − 𝑁 − 1 2 𝑒𝑦, 0, 0

𝑈

𝒃(𝜕) = 𝑓−𝑘 𝑁−1 𝜔

2

1, 𝑓𝑘𝜔, 𝑓𝑘2𝜔, ⋯ , 𝑓𝑘 𝑁−1 𝜔

𝑈

𝜔 = 2𝜌𝑒𝑦 𝜇 sin 𝜄𝑡

𝑒𝑦 𝜄𝑡 𝑦 𝑧 𝑇(𝜕) 𝒜 𝜕 = [𝑎1 𝜕 , 𝑎2 𝜕 , ⋯ , 𝑎6(𝜕)] 𝒜 𝜕 = 𝒃(𝜕)𝑇(𝜕)

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SLIDE 6
  • ▪
  • ▪

▪

𝜕 −𝜌 𝜌 𝜕

𝑏𝑛(𝜕) = exp(−𝑘𝒍𝑈𝒒) = exp 𝑘 2𝜌 𝜇 𝒗𝑈𝒒𝑛

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SLIDE 7
  • y = 𝑔(𝑦)

𝑦

▪ 𝑧 ▪

𝑎1 𝜕 𝑎2 𝜕 𝑇 𝜕

𝒜 𝜕 = 𝒃(𝜕)𝑇(𝜕) 𝑎1(𝜕) 𝑎2(𝜕) = 𝑏1(𝜕) 𝑏2(𝜕) 𝑇(𝜕) 𝑇 𝜕 ∼ 𝑂𝑑(0,1) 𝒜 𝜕 ∼ 𝑂𝑑(0, 𝒃 𝜕 𝒃𝐼(𝜕))

𝒃(𝜕) = 𝑏1 ⋮ 𝑏𝑁 ≡ 𝑓−𝑘𝜕𝜐1 ⋮ 𝑓−𝑘𝜕𝜐𝑁

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SLIDE 8
  • 𝑂

𝑁

𝒜 𝜕 = 𝑎1(𝜕) 𝑎2(𝜕) ⋮ 𝑎𝑂(𝜕) 𝒕 𝜕 = 𝑇1(𝜕) 𝑇2(𝜕) ⋮ 𝑇𝑁(𝜕)

𝑇1(𝜕) 𝑇2(𝜕) 𝑎1(𝜕) 𝑎2(𝜕) 𝑎3(𝜕)

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SLIDE 9
  • 𝑂

▪ ▪ 𝑩 𝜕 = [𝒃1(𝜕), ⋯ , 𝒃𝑂(𝜕)]

𝒜𝑡(𝜕) =

𝑗=1 𝑂

𝒃𝑗 𝜕 𝑇𝑗 𝜕 = 𝑩(𝜕)𝒕(𝜕)

𝒕(𝜕) = 𝑇1(𝜕) 𝑇2(𝜕) ⋮ 𝑇𝑂(𝜕)

𝑁 × 𝑂 𝒃𝑜(𝜕) 𝑜

𝒜𝑡 𝜕 = 𝒃(𝜕)𝑇(𝜕)

𝒜𝑡 𝜕 = 𝑎𝑡1(𝜕) 𝑎𝑡2(𝜕) ⋮ 𝑎𝑡𝑁(𝜕)

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SLIDE 10
  • 𝒜 = 𝑩𝒕 + 𝒘

▪ ▪

𝑞 𝒘 = 𝑂(𝒘|𝟏, 𝑳) 𝒜 = 𝑩𝒕 + 𝒘 𝑞 𝒘 = 𝑂(𝒘|𝟏, 𝑳) 𝑞 𝒜; 𝚰 = 𝑂 𝒜 𝟏, 𝑩𝚫𝑩𝐼 + 𝑳 𝒜 = 𝑩𝒕 + 𝒘 𝑞 𝒕 = 𝑂(𝒕|𝟏, 𝚫)

𝚰 = {𝑩, 𝒕, 𝑳} 𝑞(𝒜; 𝚰)

𝚫 = 𝐹 𝒕𝒕𝐼 (= diag 𝛿1, ⋯ , 𝛿𝑂 )

𝚰 = {𝑩, 𝚫, 𝑳} 𝑞(𝒜; 𝚰)

𝑞 𝒜; 𝚰 = 𝑂 𝒜 𝑩𝒕, 𝑳

𝑩 𝑂 {𝜄1, ⋯ , 𝜄𝑂} 𝚫 𝑂 {𝛿1, ⋯ , 𝛿𝑂}

𝑞(𝚰) 𝑞 𝚰|𝒜 = 𝑞 𝒜 𝚰 𝑞 𝚰 𝑞 𝑨

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SLIDE 11
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SLIDE 12
  • ▪

▪ 𝒜 ▪

ℎ(𝑢) 𝜀(𝑢) ℎ(𝑢) ℎ 𝑢 = ℎ 𝑢 ∗ 𝜀 𝑢

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SLIDE 13
  • ▪

𝑡(𝑢) 𝑨(𝑢) ℎ(𝑢) 𝑨 𝑢 = ℎ 𝑢 ∗ 𝑡 𝑢 + 𝑤(𝑢) 𝑤(𝑢)

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SLIDE 14
  • 𝑡(𝑢)

𝑇(𝜕) ℎ(𝑢) 𝐼(𝜕) 𝑨(𝑢) 𝑎(𝜕)

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SLIDE 15
  • ▪

▪ 𝜀 𝑢 TSP 𝑢 iTSP 𝑢

= ∗

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SLIDE 16
  • ▪

ℎ 𝑢 ∗ TSP(𝑢) ℎ 𝑢 ∗ TSP 𝑢

∗

iTSP 𝑢 ℎ 𝑢 ∗ TSP 𝑢 ∗ iTSP 𝑢 = ℎ(𝑢)

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SLIDE 17
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SLIDE 18
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SLIDE 19
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SLIDE 20
  • ▪ 𝑂

𝑁 𝒜 = 𝑩𝒕 =

𝑗=1 𝑂

𝒃𝑗𝑡𝑗 𝒛 = 𝑿𝒜 𝑏11 𝑏21 𝑏12 𝑏22 𝑡2 𝑡1 𝑧2 𝑧1 𝑥11 𝑥21 𝑥12 𝑥22 𝑨2 𝑨1 𝒜 = 𝑩𝒕 𝒛 = 𝑿𝒜 = 𝑿𝑩𝒕 𝑿 = 𝑩−1 𝒛 ≈ 𝒕

𝑁 = 𝑂

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SLIDE 21
  • ▪
  • ▪

𝒛 = 𝑿PCA𝒜 𝒛 = 𝑿ICA𝒜 𝒜

𝑧1 𝑧2 = 𝑥11 𝑥12 𝑥21 𝑥22 𝑨1 𝑨2 = 𝒙1𝑨1 + 𝒙2𝑨2

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SLIDE 22
  • ▪
  • ▪

𝒂(𝜕) 𝒂(𝜕′)

𝒁 𝜕 = 𝑿(𝜕)𝒂(𝜕) 𝒁 𝜕′ = 𝑿(𝜕′)𝒂(𝜕′)

𝒁(𝜕) 𝒁(𝜕′)

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SLIDE 23
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SLIDE 24
  • ▪

𝑔 𝑢 𝑔 𝑢

𝒚𝑢𝑔 = [𝑦𝑢𝑔1, 𝑦𝑢𝑔2, ⋯ , 𝑦𝑢𝑔𝑁]

𝑛 = 1 𝑛 = 2

𝑜 = 1

𝑛 = 1 𝑛 = 2

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SLIDE 25

𝑔 𝑢 𝑔 𝑢 𝑛 = 1 𝑛 = 2

𝑛 = 1 𝑛 = 2

𝑜 = 2

  • ▪

𝒚𝑢𝑔 = [𝑦𝑢𝑔1, 𝑦𝑢𝑔2, ⋯ , 𝑦𝑢𝑔𝑁]

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SLIDE 26
  • ▪

𝑔 𝑢 𝑔 𝑢

𝒚𝑢𝑔 = [𝑦𝑢𝑔1, 𝑦𝑢𝑔2, ⋯ , 𝑦𝑢𝑔𝑁]

𝑛 = 1 𝑛 = 2

𝑜 = 1

𝑛 = 1 𝑛 = 2

𝑜 = 2

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SLIDE 27
  • ▪

𝑢 𝑔 𝑙 𝑨𝑢𝑔 = 𝑙 ▪ 𝑰𝑔𝑒 𝑔 𝑒 𝒚𝑢𝑔 ∼ 𝑂𝑑 𝒚𝑢𝑔 𝟏, 𝜇𝑢𝑔𝑰𝑔𝑒𝑨𝑢𝑔

−1

𝑒1 𝑒2 𝑒3 𝑒𝑗

𝑢 𝑔

𝑰𝑔𝑒 ∼ 𝑋

𝑑

𝒃𝑔𝑒𝒃𝑔𝑒

𝐼 + 𝜗𝑱 −1, 𝜉0

𝑔 𝑒

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SLIDE 28
  • ▪

𝑛 = 1 𝑛 = 2

𝒚𝑢𝑔 ∼ 𝑂𝑑 𝒚𝑢𝑔 𝟏, 𝜇𝑢𝑔𝑰𝑔𝑒𝑨𝑢𝑔

−1

𝑢 𝑔

𝝆𝑢𝑔 ∼ HDP(𝛽, 𝛿, 𝜸)

(𝑙 → ∞)

𝑙

𝜌𝑢𝑔𝑙

𝑨𝑢𝑔 ∼ Categorical(𝝆𝑢𝑔)

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SLIDE 29
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SLIDE 30
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SLIDE 31
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SLIDE 32
  • ×

× ⋯ ⋯ ⋯

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SLIDE 33
  • ▪

▪

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SLIDE 34
  • ▪

𝑙 𝑢 𝑔 𝜇𝑢𝑔

𝑙

𝜇𝑢𝑔

𝑙 = 𝑚=1 𝑀

𝑥

𝑔 𝑙,𝑚 ℎ𝑢 𝑙,𝑚

× × ⋯ ⋯

ℎ𝑢

𝑙,𝑚

𝑥

𝑔 𝑙,𝑚

𝜇𝑢𝑔

𝑙

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SLIDE 35
  • ▪

𝑙 𝑢 𝑔 𝜇𝑢𝑔

𝑙

𝜇𝑢𝑔

𝑙 = 𝑥 𝑔 (𝑙,𝑚′)ℎ𝑢 (𝑙,𝑚′)

𝑚′

× × ⋯ ⋯

ℎ𝑢

𝑙,𝑚

𝑥

𝑔 𝑙,𝑚

𝜇𝑢𝑔

𝑙

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SLIDE 36
  • ▪

𝑢 𝑔 𝒚𝑢𝑔 ∼ 𝑂𝑑 𝟏,

𝑙

𝜇𝑢𝑔

(𝑙)𝑯𝑔 (𝑙)

𝒚𝑢𝑔

(1) ~ 𝑂𝑑 𝟏, 𝜇𝑢𝑔 1 𝑯𝑔 1

𝒚𝑢𝑔

(2) ~ 𝑂𝑑 𝟏, 𝜇𝑢𝑔 2 𝑯𝑔 2

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SLIDE 37
  • ▪

𝑢 𝑔 𝒚𝑢𝑔

(1) ~ 𝑂𝑑 𝟏, 𝜇𝑢𝑔 1 𝑯𝑔 1

𝒚𝑢𝑔

(2) ~ 𝑂𝑑 𝟏, 𝜇𝑢𝑔 2 𝑯𝑔 2

𝒚𝑢𝑔 ∼

𝑙

𝜌𝑢𝑔

𝑙 𝑂𝑑 𝟏, 𝜇𝑢𝑔 𝑙 𝑯𝑔 𝑙

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SLIDE 38
  • ▪

▪

𝑂𝑑 𝟏,

𝑙 𝑚

𝑥

𝑔 𝑙,𝑚 ℎ𝑢 𝑙,𝑚 𝑯𝑔 𝑙 𝑙

𝜌𝑢𝑔

𝑙 𝑂𝑑

𝟏,

𝑚

𝑥

𝑔 𝑙,𝑚 ℎ𝑢 𝑙,𝑚 𝑯𝑔 𝑙

𝑂𝑑 𝟏,

𝑙 𝑚

𝜔𝑢𝑔

𝑙,𝑚 𝑥𝑔 𝑙,𝑚 ℎ𝑢 𝑙,𝑚 𝑯𝑔 𝑙 𝑙 𝑚

𝜌𝑢𝑔

𝑙 𝜔𝑢𝑔 𝑙,𝑚 𝑂𝑑 0, 𝑥 𝑔 𝑙,𝑚 ℎ𝑢 𝑙,𝑚 𝑯𝑔 𝑙

∑

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SLIDE 39
  • ▪

▪ ▪ ▪