SlideShare a Scribd company logo

Prml1.2.5~1.2.6

•
•
T
Tomoyuki Hioki

パターン認識と機械学習 (ベイズ理論による統計的予測) 1.2.5~1.2.6 Pattern Recognition and Machine Learning (PRML)

Data & Analytics
1 of 8
Download to read offline
パターン認識と機械学習 (ベイズ理論による統計的予測) 1.2.5~1.2.6 Pattern Recognition and Machine Learning (PRML)
第1章 序論 1.1 多項式フィッティング 1.2 確率論 1.2.1 確率密度 1.2.2 期待値と分散 1.2.3 ベイズ確率 1.2.4 ガウス分布 1.2.5 曲線フィッティング再訪 1.2.6 ベイズ曲線フィッティング 1.3 モデル選択 1.4 次元の呪い 1.5 決定理論 1.5.1 識別率の最⼩化 1.5.2 期待値損失と最⼩化 1.5.3 棄却オプション 1.5.4 推論と決定 1.5.5 回帰のための損失関数 1.6 情報理論 1.6.1 相対エントロピーと相互情報量 ⽬次
尤度関数 wが与えられた状態の曲線を平均,分散を精度パラメータβとして ⽬標値⽅向に広がる正規分布 𝒙 = (𝑥%, … . . , 𝑥))+ …訓練データ群 𝒕 = (𝑡%, … . . , 𝑡))+ …⽬標データ群 1.2.5 曲線フィッティング再訪
尤度の最⼤化 ⇨⼆乗誤差の最⼩化 ・尤度関数ln(t|x,w,β) を解いて求められるwは最⼩⼆乗誤差の最⼩化に等価 ・βは(左辺の微分)=0 の解には影響しない ・𝛽−1に関する微分を解いてβの最尤解も計算 1.2.5 曲線フィッティング再訪
予測分布 ⇨ 曲線の不確実さを表すパラメータを最尤パラメータに置き換えたもの 新規データに対して点で結果を出すのではなく,確率分布として算出 1.2.5 曲線フィッティング再訪
事前分布の導⼊とMAP推定 ⇨ 事前分布として平均0,分散𝛼−1のガウス分布を導⼊ αのような分布を制御するパラメータを超パラメータ（hyper parameter）という MAP推定の結果は正則化と⼀致 1.2.5 曲線フィッティング再訪
事前分布の導⼊とMAP推定 ⇨前で⽰した予測分布は与えられたwによるもの wの点推定を⾏なっているだけではベイズ的な扱いとは⾔えない 完全なベイズアプローチでは確率の加法・乗法定理を⽭盾なく適応する ⇨ ベイズ的な取り扱いでは全てのwの値に関して積分する必要がある …単純化のためαとβは省略した …パラメータの事後分布 1.2.6 ベイズ曲線フィッティング
予測分布,平均,分散 予測分布… 平均… 分散… 事後分布は解析的に溶け,ガウス分布に従う 平均,分散はxに依存 分散の第⼆項はベイズ的な取り扱い 1.2.6 ベイズ曲線フィッティング

Recommended

PRML1.2
PRML1.2PRML1.2
PRML1.2Tomoyuki Hioki
 
Prml1.2.3
Prml1.2.3Prml1.2.3
Prml1.2.3Tomoyuki Hioki
 
PRML1.1
PRML1.1PRML1.1
PRML1.1Tomoyuki Hioki
 
PRML1.1
PRML1.1PRML1.1
PRML1.1Tomoyuki Hioki
 
Prml1.2.1~1.2.2
Prml1.2.1~1.2.2Prml1.2.1~1.2.2
Prml1.2.1~1.2.2Tomoyuki Hioki
 
[PRML] パターン認識と機械学習（第1章：序論）
[PRML] パターン認識と機械学習（第1章：序論）[PRML] パターン認識と機械学習（第1章：序論）
[PRML] パターン認識と機械学習（第1章：序論）Ryosuke Sasaki
 
Analysis of cancer by structural equation
Analysis of cancer by structural equationAnalysis of cancer by structural equation
Analysis of cancer by structural equationTomoyuki Hioki
 
Analysis of cancer and health in each prefecture
Analysis of cancer and health in each prefecture Analysis of cancer and health in each prefecture
Analysis of cancer and health in each prefectureTomoyuki Hioki
 

Recommended

PRML1.2
PRML1.2PRML1.2
PRML1.2Tomoyuki Hioki
 
Prml1.2.3
Prml1.2.3Prml1.2.3
Prml1.2.3Tomoyuki Hioki
 
PRML1.1
PRML1.1PRML1.1
PRML1.1Tomoyuki Hioki
 
PRML1.1
PRML1.1PRML1.1
PRML1.1Tomoyuki Hioki
 
Prml1.2.1~1.2.2
Prml1.2.1~1.2.2Prml1.2.1~1.2.2
Prml1.2.1~1.2.2Tomoyuki Hioki
 
[PRML] パターン認識と機械学習（第1章：序論）
[PRML] パターン認識と機械学習（第1章：序論）[PRML] パターン認識と機械学習（第1章：序論）
[PRML] パターン認識と機械学習（第1章：序論）Ryosuke Sasaki
 
Analysis of cancer by structural equation
Analysis of cancer by structural equationAnalysis of cancer by structural equation
Analysis of cancer by structural equationTomoyuki Hioki
 
Analysis of cancer and health in each prefecture
Analysis of cancer and health in each prefecture Analysis of cancer and health in each prefecture
Analysis of cancer and health in each prefectureTomoyuki Hioki
 
Marketing Strategy by American Express
Marketing Strategy by American ExpressMarketing Strategy by American Express
Marketing Strategy by American ExpressTomoyuki Hioki
 
製品改良と満足度との関係：多属性モデルに基づくシミュレーション
製品改良と満足度との関係：多属性モデルに基づくシミュレーション製品改良と満足度との関係：多属性モデルに基づくシミュレーション
製品改良と満足度との関係：多属性モデルに基づくシミュレーションTomoyuki Hioki
 
Power energy system optimization research by reinforcement learning extended ...
Power energy system optimization research by reinforcement learning extended ...Power energy system optimization research by reinforcement learning extended ...
Power energy system optimization research by reinforcement learning extended ...Tomoyuki Hioki
 
Power energy system optimization research by reinforcement learning extended ...
Power energy system optimization research by reinforcement learning extended ...Power energy system optimization research by reinforcement learning extended ...
Power energy system optimization research by reinforcement learning extended ...Tomoyuki Hioki
 
【論文紹介】Understanding Back-Translation at Scale
【論文紹介】Understanding Back-Translation at Scale【論文紹介】Understanding Back-Translation at Scale
【論文紹介】Understanding Back-Translation at ScaleTomoyuki Hioki
 
Smart Grid Optimization by Deep Reinforcement Learning over Discrete and Cont...
Smart Grid Optimization by Deep Reinforcement Learning over Discrete and Cont...Smart Grid Optimization by Deep Reinforcement Learning over Discrete and Cont...
Smart Grid Optimization by Deep Reinforcement Learning over Discrete and Cont...Tomoyuki Hioki
 
【論文紹介】Deep Mimic: Example-Guided Deep Reinforcement Learning of Physics-Based...
【論文紹介】Deep Mimic: Example-Guided Deep Reinforcement Learning of Physics-Based...【論文紹介】Deep Mimic: Example-Guided Deep Reinforcement Learning of Physics-Based...
【論文紹介】Deep Mimic: Example-Guided Deep Reinforcement Learning of Physics-Based...Tomoyuki Hioki
 
【論文紹介】Seq2Seq (NIPS 2014)
【論文紹介】Seq2Seq (NIPS 2014)【論文紹介】Seq2Seq (NIPS 2014)
【論文紹介】Seq2Seq (NIPS 2014)Tomoyuki Hioki
 
[論文紹介] LSTM (LONG SHORT-TERM MEMORY)
[論文紹介] LSTM (LONG SHORT-TERM MEMORY)[論文紹介] LSTM (LONG SHORT-TERM MEMORY)
[論文紹介] LSTM (LONG SHORT-TERM MEMORY)Tomoyuki Hioki
 
【論文紹介】Deep Reinforcement Learning for Solving the Vehicle Routing Problem

【論文紹介】Deep Reinforcement Learning for Solving the Vehicle Routing Problem
【論文紹介】Deep Reinforcement Learning for Solving the Vehicle Routing Problem

【論文紹介】Deep Reinforcement Learning for Solving the Vehicle Routing Problem
Tomoyuki Hioki
 
Prml1.2.4
Prml1.2.4Prml1.2.4
Prml1.2.4Tomoyuki Hioki
 

More Related Content

More from Tomoyuki Hioki

Marketing Strategy by American Express
Marketing Strategy by American ExpressMarketing Strategy by American Express
Marketing Strategy by American ExpressTomoyuki Hioki
 
製品改良と満足度との関係：多属性モデルに基づくシミュレーション
製品改良と満足度との関係：多属性モデルに基づくシミュレーション製品改良と満足度との関係：多属性モデルに基づくシミュレーション
製品改良と満足度との関係：多属性モデルに基づくシミュレーションTomoyuki Hioki
 
Power energy system optimization research by reinforcement learning extended ...
Power energy system optimization research by reinforcement learning extended ...Power energy system optimization research by reinforcement learning extended ...
Power energy system optimization research by reinforcement learning extended ...Tomoyuki Hioki
 
Power energy system optimization research by reinforcement learning extended ...
Power energy system optimization research by reinforcement learning extended ...Power energy system optimization research by reinforcement learning extended ...
Power energy system optimization research by reinforcement learning extended ...Tomoyuki Hioki
 
【論文紹介】Understanding Back-Translation at Scale
【論文紹介】Understanding Back-Translation at Scale【論文紹介】Understanding Back-Translation at Scale
【論文紹介】Understanding Back-Translation at ScaleTomoyuki Hioki
 
Smart Grid Optimization by Deep Reinforcement Learning over Discrete and Cont...
Smart Grid Optimization by Deep Reinforcement Learning over Discrete and Cont...Smart Grid Optimization by Deep Reinforcement Learning over Discrete and Cont...
Smart Grid Optimization by Deep Reinforcement Learning over Discrete and Cont...Tomoyuki Hioki
 
【論文紹介】Deep Mimic: Example-Guided Deep Reinforcement Learning of Physics-Based...
【論文紹介】Deep Mimic: Example-Guided Deep Reinforcement Learning of Physics-Based...【論文紹介】Deep Mimic: Example-Guided Deep Reinforcement Learning of Physics-Based...
【論文紹介】Deep Mimic: Example-Guided Deep Reinforcement Learning of Physics-Based...Tomoyuki Hioki
 
【論文紹介】Seq2Seq (NIPS 2014)
【論文紹介】Seq2Seq (NIPS 2014)【論文紹介】Seq2Seq (NIPS 2014)
【論文紹介】Seq2Seq (NIPS 2014)Tomoyuki Hioki
 
[論文紹介] LSTM (LONG SHORT-TERM MEMORY)
[論文紹介] LSTM (LONG SHORT-TERM MEMORY)[論文紹介] LSTM (LONG SHORT-TERM MEMORY)
[論文紹介] LSTM (LONG SHORT-TERM MEMORY)Tomoyuki Hioki
 
【論文紹介】Deep Reinforcement Learning for Solving the Vehicle Routing Problem

【論文紹介】Deep Reinforcement Learning for Solving the Vehicle Routing Problem
【論文紹介】Deep Reinforcement Learning for Solving the Vehicle Routing Problem

【論文紹介】Deep Reinforcement Learning for Solving the Vehicle Routing Problem
Tomoyuki Hioki
 

More from Tomoyuki Hioki (11)

Marketing Strategy by American Express
Marketing Strategy by American ExpressMarketing Strategy by American Express
Marketing Strategy by American Express
 
製品改良と満足度との関係：多属性モデルに基づくシミュレーション
製品改良と満足度との関係：多属性モデルに基づくシミュレーション製品改良と満足度との関係：多属性モデルに基づくシミュレーション
製品改良と満足度との関係：多属性モデルに基づくシミュレーション
 
Power energy system optimization research by reinforcement learning extended ...
Power energy system optimization research by reinforcement learning extended ...Power energy system optimization research by reinforcement learning extended ...
Power energy system optimization research by reinforcement learning extended ...
 
Power energy system optimization research by reinforcement learning extended ...
Power energy system optimization research by reinforcement learning extended ...Power energy system optimization research by reinforcement learning extended ...
Power energy system optimization research by reinforcement learning extended ...
 
【論文紹介】Understanding Back-Translation at Scale
【論文紹介】Understanding Back-Translation at Scale【論文紹介】Understanding Back-Translation at Scale
【論文紹介】Understanding Back-Translation at Scale
 
Smart Grid Optimization by Deep Reinforcement Learning over Discrete and Cont...
Smart Grid Optimization by Deep Reinforcement Learning over Discrete and Cont...Smart Grid Optimization by Deep Reinforcement Learning over Discrete and Cont...
Smart Grid Optimization by Deep Reinforcement Learning over Discrete and Cont...
 
【論文紹介】Deep Mimic: Example-Guided Deep Reinforcement Learning of Physics-Based...
【論文紹介】Deep Mimic: Example-Guided Deep Reinforcement Learning of Physics-Based...【論文紹介】Deep Mimic: Example-Guided Deep Reinforcement Learning of Physics-Based...
【論文紹介】Deep Mimic: Example-Guided Deep Reinforcement Learning of Physics-Based...
 
【論文紹介】Seq2Seq (NIPS 2014)
【論文紹介】Seq2Seq (NIPS 2014)【論文紹介】Seq2Seq (NIPS 2014)
【論文紹介】Seq2Seq (NIPS 2014)
 
[論文紹介] LSTM (LONG SHORT-TERM MEMORY)
[論文紹介] LSTM (LONG SHORT-TERM MEMORY)[論文紹介] LSTM (LONG SHORT-TERM MEMORY)
[論文紹介] LSTM (LONG SHORT-TERM MEMORY)
 
【論文紹介】Deep Reinforcement Learning for Solving the Vehicle Routing Problem

【論文紹介】Deep Reinforcement Learning for Solving the Vehicle Routing Problem
【論文紹介】Deep Reinforcement Learning for Solving the Vehicle Routing Problem

【論文紹介】Deep Reinforcement Learning for Solving the Vehicle Routing Problem

 
Prml1.2.4
Prml1.2.4Prml1.2.4
Prml1.2.4
 

Prml1.2.5~1.2.6