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4. Gaussian Model

J
Jungkyu Lee

Machine Learning: a Probabilistic Perspective chapter 4

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4. Gaussian Model 4.1 Introduction 4.2 Gaussian discriminant analysis 4.2.1 Quadratic discriminant analysis (QDA) 4.2.2 Linear discriminant analysis (LDA) 4.2.3 Two-class LDA 4.2.4 MLE for discriminant analysis 4.1 Introduction る 蠏 覿
4. Gaussian Model
4.2 Gaussian discriminant analysis Class螳 譯殊伎 , feature vector Gaussian 覿朱 螳 譯殊伎 (Gaussian) discriminant analysis: posterior (2.13) //p(x|y) 蠏覿 襯 れ 2-class 覓語 蟆曙 覲 亮c,裡c MLE 豢朱 蟲(轟 4.2.4), 讀 螳 企る 蠏, 螻給 襯 れ 2-class 蟆曙, 一危一 likelihood
朱 豢豺 Decision Rule: class 覿襯 蟯 覿覈 讌郁 log襯 豬伎 螳 posterior襯 螳 class襦 覿襯 覈 class螳 蠏狩 prior 覿襯 螳譟る, 豌覯讌 prior 伎螻 覯讌 蠏 覿 4.2.1 Quadratic discriminant analysis (QDA) (2.13) likelihood prior 螳螳 multinomial 覿螻 蠏 覿 覃 (4.33) class襯 蟆一 x 襦 覲碁る(p(y=1|x) - p(y=0|x) > 0 企 y=1螻 螳) 伎姶(quadratic) 願 覿襯 覃(p(y=1|x) =p(y=0|x) 讌) れ螻 螳 螻′ り
4.2.2 Linear discriminant analysis (LDA) 覈 class 伎 螻給一 螻旧る( 螳る) 讀 企朱 (4.33) れ螻 螳 . 伎姶 xT 裡-1 x 覈 class 伎 狩覩襦 覿襯 レ 殊讌 蠍 覓語 殊螻, decision boundary linear 讌. 手 覃 (4.35) れ螻 螳 螻 (4.38) 企 覈 soft max豌 蠍 覓語 S softmax 手 覿襴磯. 襯 れ澗侶 = (3,0,1)企朱 れ螻 螳 豕螳 3 伎 0.8 襯 豪
4.2.3 Two-class LDA 2-class 覓語襯 螳螻 (4.38) log襯 豬伎 れ螻 螳 linear 覃伎 . 硫c'- 硫c 覿襯 覃伎 覯 覯″郁 螻粒c'- 粒c 覿襯 覃伎 bias螳 . 4.2.4 MLE for discriminant analysis (4.35) mu sigma れ螻 螳 MLE襦 豢 螻 蟆郁骸 れ螻 螳 讀, 螳 class 伎 feature vectorれ 蠏螻 覿一企.
讀, 螳 class 伎 feature vectorれ 蠏螻 覿一企.

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4. Gaussian Model

  • 1. 4. Gaussian Model 4.1 Introduction 4.2 Gaussian discriminant analysis 4.2.1 Quadratic discriminant analysis (QDA) 4.2.2 Linear discriminant analysis (LDA) 4.2.3 Two-class LDA 4.2.4 MLE for discriminant analysis 4.1 Introduction る 蠏 覿
  • 3. 4.2 Gaussian discriminant analysis Class螳 譯殊伎 , feature vector Gaussian 覿朱 螳 譯殊伎 (Gaussian) discriminant analysis: posterior (2.13) //p(x|y) 蠏覿 襯 れ 2-class 覓語 蟆曙 覲 亮c,裡c MLE 豢朱 蟲(轟 4.2.4), 讀 螳 企る 蠏, 螻給 襯 れ 2-class 蟆曙, 一危一 likelihood
  • 4. 朱 豢豺 Decision Rule: class 覿襯 蟯 覿覈 讌郁 log襯 豬伎 螳 posterior襯 螳 class襦 覿襯 覈 class螳 蠏狩 prior 覿襯 螳譟る, 豌覯讌 prior 伎螻 覯讌 蠏 覿 4.2.1 Quadratic discriminant analysis (QDA) (2.13) likelihood prior 螳螳 multinomial 覿螻 蠏 覿 覃 (4.33) class襯 蟆一 x 襦 覲碁る(p(y=1|x) - p(y=0|x) > 0 企 y=1螻 螳) 伎姶(quadratic) 願 覿襯 覃(p(y=1|x) =p(y=0|x) 讌) れ螻 螳 螻′ り
  • 5. 4.2.2 Linear discriminant analysis (LDA) 覈 class 伎 螻給一 螻旧る( 螳る) 讀 企朱 (4.33) れ螻 螳 . 伎姶 xT 裡-1 x 覈 class 伎 狩覩襦 覿襯 レ 殊讌 蠍 覓語 殊螻, decision boundary linear 讌. 手 覃 (4.35) れ螻 螳 螻 (4.38) 企 覈 soft max豌 蠍 覓語 S softmax 手 覿襴磯. 襯 れ澗侶 = (3,0,1)企朱 れ螻 螳 豕螳 3 伎 0.8 襯 豪
  • 6. 4.2.3 Two-class LDA 2-class 覓語襯 螳螻 (4.38) log襯 豬伎 れ螻 螳 linear 覃伎 . 硫c'- 硫c 覿襯 覃伎 覯 覯″郁 螻粒c'- 粒c 覿襯 覃伎 bias螳 . 4.2.4 MLE for discriminant analysis (4.35) mu sigma れ螻 螳 MLE襦 豢 螻 蟆郁骸 れ螻 螳 讀, 螳 class 伎 feature vectorれ 蠏螻 覿一企.
  • 7. 讀, 螳 class 伎 feature vectorれ 蠏螻 覿一企.