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Energy based models and boltzmann machines - v2.0

Soowan Lee
Soowan Lee

This is version 2.0 of my previous slides. (http://www.slideshare.net/blaswan/energy-based-models-and-boltzmann-machines) Removed very simple recommendation example and Added feature extractor example referenced from Hinton's lecture.

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Energy-Based Models and Boltzmann Machines Learning Deep Architectures for AI - Ch 5
覈谿 Energy-Based Models Boltzmann Machines Restricted Boltzmann Machines Contrastive Divergence Examples
Energy-Based Models Definition 螳 (x) 讌襯 螻, 覈 れ 讌螳 豕 螳 襦 讌 朱誤磯れ 牛 覈 讌 蠍磯 襯 覈語 讌 襯 伎 襯 覿襯 れ螻 螳 郁(覓朱Μ) 覲殊襷 覿 覯豺 蟆暑 蟆 蟯 覲碁る 企一 覲殊襷 覿 企 覿手 覲 螻 一 state 覿 讌 手 伎
Energy-Based Models Introducing Hidden Variables 覈語 (expressive power) 讀螳り鍵 蟯豸°讌 (non-observed) 覲れ 豢螳覃 襯 覿襯 螳
Energy-Based Models Free Energy 襯 覿襯 螳 襦 襷り鍵 讌(Free Energy) 螳 . 讀, hidden 覲れ 襯 覈語 螳 る蠍 朱 危危覃 . 覿覿 る 伎 朱 讌襯 る 蠏 企 覓朱Μ 襷 蟾れ 讌 企 螳語り . 讌襯 螻壱覃 れ螻 螳 螳 .
Energy-Based Models Log-likelihood gradient EBM 一危一 log-likelihood襯 伎伎 gradient descent 覦覯朱 螳ロ. Log-likelihood襯 螻壱覃 れ螻 螳. (螻 ) 豌覯讌 input vector(x)螳 譯殊伎 所 蟲 讌襷 覯讌 覈 螳ロ input 螻壱伎 覩襦 蟆 螻壱 蟆 螳 襷れ る 蟇碁Π.
Energy-Based Models Average log-likelihood gradient 蟲 Log-likelihood Average襯 蟲覃 れ螻 螳. ( 朱語 ) ^P traing set 蟆渚朱 蟆一 覿(empirical distribution)襯 覩 . P 覈 豌伎 覿襯 覩誤. 讌 蟯 覲碁る 覈語 讌 覿手 伎 . 襷 朱瑚骸 襴殊 覲願鍵 所 れ螻 螳 .
Energy-Based Models The idea of stochastic estimator of the log-likelihood gradient EBM 旧 伎 覯讌 觜襯願 螻壱伎 . 襷 覈語 覿 P襦覿 襷 伎 讌襯 觜襯願 (tractably) 螻壱 る Monte-Carlo 覦覯 伎 gradient 螳 豢 .
Energy-Based Models Approach overview 覈語 襷 讌 讌 讌 襦覿 襯 覿 螳 Log-likelihood gradient 螳 MCMC method襯 伎 覈語 蠍磯螳 螻壱螻 蟆郁骸朱 gradient 豢
Boltzmann Machines Definition Boltzmann Machine hidden unit 豢螳 EBM 殊企. MRF (Markov Random Field, Markov Network) 殊願鍵 . Unitり 郁屋 曙 覈 郁屋 覈語企.
Boltzmann Machines Energy Function 讌 螳. 讌 企至 蟆手? BM 讌 Hopfield Network Ising Model襦覿 (螻 ..). BM & RBM 訖襷 RBM 覲, るジ EBM 覿覿 (覓朱Μ, 伎 ) 覈碁 蟆朱覿 詞伎.
Boltzmann Machines Problems 覈語 豺願 Binary Unit企朱 螳 EBM 襯 蠏碁襦 伎企螳 . 讀, 讌襦覿 襯 蟲螻 Log-likelihood gradient襯 螻壱 れ MCMC Sampling 牛 stochastic 蟆 gradient襯 豢 . れ RBM 誤 る０ 蟆企. 讌襷 Stochastic蟆 gradient襯 豢り 企 覓 襷 (曙 ) 郁屋覓語 朱朱 螻一 觜瑚 る 蟇碁Π. 讌 覲語 讌 螳 覈語 伎, 郁屋 螳 蠍一 讌朱 讀螳.
Restricted Boltzmann Machines Definition 蠍一ヾ BM り 郁屋 豪 蟇語 螳 蟆 譴 れ 螳ロ襦 覲 蟆暑 visible layer 1螳, hidden layer 1螳襦 蟲焔 企 蠏碁 覈碁 visible-visible, hidden-hidden り 郁屋 BM U V螳 0覯″
Restricted Boltzmann Machines Energy, Free Energy RBM 讌螳 れ螻 螳 . RBM EBM 殊願鍵 覓語 FreeEnergy Distribution 蠏碁襦 磯 螳. Partition function Z intractable.
Restricted Boltzmann Machines Conditional Distribution RBM 蟲譟一 input 譯殊伎覃 hidden unit 螳 conditionally independent覃 蠏 狩蟆 焔 煙 螻 螳 蟆 譴譯朱 伎螳
Restricted Boltzmann Machines RBMs with Binary units Binary unit企手 螳覃 P(h|x) 螳螻 conditionally independent る 煙 伎 P(h_i = 1|x) 詞 . 蠏 襷谿螳讌. (螻 ) れ Sampling update rule . 螳 unit 0螻 1 伎 れ螳 蟆曙磯 ロ 蟆 Gaussian-Bernoulli RBM (GBRBM) 企.
Restricted Boltzmann Machines Negative Log-likelihood gradient 旧 Negative Log-likelihood gradient襯 螻壱覃 れ螻 螳. 豌覯讌 positive phase, 覯讌 negative phase手 . 襷谿螳讌襦 negative phase 螻壱蠍 企給. RBM Sampling 牛 螳 豢.
Restricted Boltzmann Machines Update Equations with Binary Units RBM 讌 襦覿 螳 朱誤一 ｸ覩碁 螻壱覃 れ螻 螳. 讌 螳 願鍵 覓語 覩碁螳 襷れ 螳伎. RBM 豕譬 Update Equation れ螻 螳 詞 .
Restricted Boltzmann Machines Gibbs Sampling in RBMs 襯 覲 譟郁唄覿 襯 覿螳 譯殊伎朱襦 Gibbs Sampling 牛 覈 豌伎 覿 覲語 讌 . 一危一 豢覦伎 讌 覃 豐蠍一 豌 螳 譟危讌襷 豢覿 螳 讌 豐蠍 蟯螻 覈 豌伎 蠍磯 覲語 讌 . 讌 蟯 る覃 Gibbs Sampling 豢覿 襷 覃 RBM 讌 蟆 .
Contrastive Divergence Definition negative phase襯 覈 螳ロ 一危一 蠍磯螳朱 螻壱讌 螻 覈語 讌 螳 襦襷 蠏殊. 覈語 讌 る 蠏 螳 蠏 螳蟾 螳レ煙 蠍 覓語 Reasonable . Gibbs Sampling 伎 視. Update rule れ螻 螳 れ .
Contrastive Divergence CD-k with Alternative Gibbs Sampling [Hinton 02] Gibbs Sampling 螳 training data襦 . Gibbs Sampling 覓危覯 讌 螻 k覯襷 . れ朱 1覯襷 企 豢覿 譬 詞 . Training 襦 覈語 螳讌 覿 training set 覿襯 磯手. 讀, training data螳 企 覈語 覿襯 企 螻 る 蟆企. 磯殊 training data襦覿 襷 覃 企 企 企 讌覿 襷 蟆企手 覲 伎 1覯襷 譬 詞 . 1覯 襷伎 詞伎 visible data襯 reconstrunction企手 螻 碁企 襦 螻 る reconstruction error螳 螳. 讀, 伎 RBM input data襯 讌企ｌ朱 狩 reconstruction visible data襯 詞 .
Contrastive Divergence persistent CD [Tieleman 08] Gibbs Sampling 蠍一ヾ CD-k 襷る 螳螳 training data 襷讌襷 persistent CD 伎 Gibbs Sampling 螻磯 data (reconstruction data)襯 れ 覯 Sampling 朱 . 讀, 豌 覯讌 training data螳 persistent chain 螻 覯 Gibbs Sampling 蟆郁骸襯 れ 覯 training 朱 Chain 伎企螳. 企蟆 Chain 伎 螳覃 覓危覯 Sampling 蟆螻 觜訣伎 螻朱ゼ 螳蟆 . 覓朱 襷 Gibbs Sampling襷 朱誤郁 Update 伎 覈語 覲蠍 讌襷 襷れ 螳願鍵 覓語 蠏殊朱 焔渚.
Examples [Hintons lecture] 2襯 牛 16 x 16 蠍一 企語 (256 螳 visible 企) 50螳 binary hidden 企 蟆曙 Hidden unit = Feature detector = Feature Extractor CD-1朱 螳 企一 Weight り朱 豐蠍壱
Examples [Hintons lecture] 50螳 Hidden Unit Weight襯 企語襦 蠏碁Π 蟆
Examples [Hintons lecture]
Examples [Hintons lecture]
Examples [Hintons lecture]
Examples [Hintons lecture]
Examples [Hintons lecture]
Examples [Hintons lecture]
Examples [Hintons lecture]
Examples [Hintons lecture] 螳 企一 2 襦 るジ Feature襯 ′企 蟆 覲
Examples [Hintons lecture] ろ 企語襦 Reconstruction 企慨覃.. ろ語 企語 Reconstruction ろ語 企語 Reconstruction ろ語 2 伎襷 蠍 覓語 覈 企語襯 2襦 危危り .
Examples [Larochelle 09] MNIST
Examples [Larochelle 09] MNIST 螳 Hidden unit Edge(ろ碁)襯 觸企 蟆 覲 .
Extensions Unsupervised Learning Feature Extractor るジ Supervised Learning pre-training Deep Belief Network [Hinton Neural Computation 06] Deep Auto-Encoder [Hinton Science 06] Collaborative Filtering (Netflix Prize 2007 winner) [Salakhutdinov 07] Conditional RBM (with Gaussian Unit) Conditional Factored RBM Generator (Human motion modeling) [Taylor 06] Conditional RBM
Extensions Supervised Learning Classifier [Larochelle 08] Classification RBM Discriminitive RBM Hybrid Discriminitive RBM
References [Bengio 09] Learning Deep Architectures for AI [Deeplearning.net] Deep learning tutorial - RBM [Hinton 02] Training Products of Experts by Minimizing Contrastive Divergence [Tieleman 08] Training Restricted Boltzmann Machines using Approximations to the Likelihood Gradient [Larochelle 09] Exploring Strategies for Training Deep Neural Networks [Hinton Neural Computation 06] A Fast Learning Algorithm for Deep Belief Network [Hinton Science 06] Reducing the Dimensionality of Data with Neural Networks [Salakhutdinov 07] Restricted Boltzmann machines for collaborative filtering [Taylor 06] Modeling Human Motion Using Binary Latent Variables [Larochelle 08] Classification using Discriminative Restricted Boltzmann Machines
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Energy based models and boltzmann machines - v2.0

  • 1. Energy-Based Models and Boltzmann Machines Learning Deep Architectures for AI - Ch 5
  • 2. 覈谿 Energy-Based Models Boltzmann Machines Restricted Boltzmann Machines Contrastive Divergence Examples
  • 3. Energy-Based Models Definition 螳 (x) 讌襯 螻, 覈 れ 讌螳 豕 螳 襦 讌 朱誤磯れ 牛 覈 讌 蠍磯 襯 覈語 讌 襯 伎 襯 覿襯 れ螻 螳 郁(覓朱Μ) 覲殊襷 覿 覯豺 蟆暑 蟆 蟯 覲碁る 企一 覲殊襷 覿 企 覿手 覲 螻 一 state 覿 讌 手 伎
  • 4. Energy-Based Models Introducing Hidden Variables 覈語 (expressive power) 讀螳り鍵 蟯豸°讌 (non-observed) 覲れ 豢螳覃 襯 覿襯 螳
  • 5. Energy-Based Models Free Energy 襯 覿襯 螳 襦 襷り鍵 讌(Free Energy) 螳 . 讀, hidden 覲れ 襯 覈語 螳 る蠍 朱 危危覃 . 覿覿 る 伎 朱 讌襯 る 蠏 企 覓朱Μ 襷 蟾れ 讌 企 螳語り . 讌襯 螻壱覃 れ螻 螳 螳 .
  • 6. Energy-Based Models Log-likelihood gradient EBM 一危一 log-likelihood襯 伎伎 gradient descent 覦覯朱 螳ロ. Log-likelihood襯 螻壱覃 れ螻 螳. (螻 ) 豌覯讌 input vector(x)螳 譯殊伎 所 蟲 讌襷 覯讌 覈 螳ロ input 螻壱伎 覩襦 蟆 螻壱 蟆 螳 襷れ る 蟇碁Π.
  • 7. Energy-Based Models Average log-likelihood gradient 蟲 Log-likelihood Average襯 蟲覃 れ螻 螳. ( 朱語 ) ^P traing set 蟆渚朱 蟆一 覿(empirical distribution)襯 覩 . P 覈 豌伎 覿襯 覩誤. 讌 蟯 覲碁る 覈語 讌 覿手 伎 . 襷 朱瑚骸 襴殊 覲願鍵 所 れ螻 螳 .
  • 8. Energy-Based Models The idea of stochastic estimator of the log-likelihood gradient EBM 旧 伎 覯讌 觜襯願 螻壱伎 . 襷 覈語 覿 P襦覿 襷 伎 讌襯 觜襯願 (tractably) 螻壱 る Monte-Carlo 覦覯 伎 gradient 螳 豢 .
  • 9. Energy-Based Models Approach overview 覈語 襷 讌 讌 讌 襦覿 襯 覿 螳 Log-likelihood gradient 螳 MCMC method襯 伎 覈語 蠍磯螳 螻壱螻 蟆郁骸朱 gradient 豢
  • 10. Boltzmann Machines Definition Boltzmann Machine hidden unit 豢螳 EBM 殊企. MRF (Markov Random Field, Markov Network) 殊願鍵 . Unitり 郁屋 曙 覈 郁屋 覈語企.
  • 11. Boltzmann Machines Energy Function 讌 螳. 讌 企至 蟆手? BM 讌 Hopfield Network Ising Model襦覿 (螻 ..). BM & RBM 訖襷 RBM 覲, るジ EBM 覿覿 (覓朱Μ, 伎 ) 覈碁 蟆朱覿 詞伎.
  • 12. Boltzmann Machines Problems 覈語 豺願 Binary Unit企朱 螳 EBM 襯 蠏碁襦 伎企螳 . 讀, 讌襦覿 襯 蟲螻 Log-likelihood gradient襯 螻壱 れ MCMC Sampling 牛 stochastic 蟆 gradient襯 豢 . れ RBM 誤 る０ 蟆企. 讌襷 Stochastic蟆 gradient襯 豢り 企 覓 襷 (曙 ) 郁屋覓語 朱朱 螻一 觜瑚 る 蟇碁Π. 讌 覲語 讌 螳 覈語 伎, 郁屋 螳 蠍一 讌朱 讀螳.
  • 13. Restricted Boltzmann Machines Definition 蠍一ヾ BM り 郁屋 豪 蟇語 螳 蟆 譴 れ 螳ロ襦 覲 蟆暑 visible layer 1螳, hidden layer 1螳襦 蟲焔 企 蠏碁 覈碁 visible-visible, hidden-hidden り 郁屋 BM U V螳 0覯″
  • 14. Restricted Boltzmann Machines Energy, Free Energy RBM 讌螳 れ螻 螳 . RBM EBM 殊願鍵 覓語 FreeEnergy Distribution 蠏碁襦 磯 螳. Partition function Z intractable.
  • 15. Restricted Boltzmann Machines Conditional Distribution RBM 蟲譟一 input 譯殊伎覃 hidden unit 螳 conditionally independent覃 蠏 狩蟆 焔 煙 螻 螳 蟆 譴譯朱 伎螳
  • 16. Restricted Boltzmann Machines RBMs with Binary units Binary unit企手 螳覃 P(h|x) 螳螻 conditionally independent る 煙 伎 P(h_i = 1|x) 詞 . 蠏 襷谿螳讌. (螻 ) れ Sampling update rule . 螳 unit 0螻 1 伎 れ螳 蟆曙磯 ロ 蟆 Gaussian-Bernoulli RBM (GBRBM) 企.
  • 17. Restricted Boltzmann Machines Negative Log-likelihood gradient 旧 Negative Log-likelihood gradient襯 螻壱覃 れ螻 螳. 豌覯讌 positive phase, 覯讌 negative phase手 . 襷谿螳讌襦 negative phase 螻壱蠍 企給. RBM Sampling 牛 螳 豢.
  • 18. Restricted Boltzmann Machines Update Equations with Binary Units RBM 讌 襦覿 螳 朱誤一 ｸ覩碁 螻壱覃 れ螻 螳. 讌 螳 願鍵 覓語 覩碁螳 襷れ 螳伎. RBM 豕譬 Update Equation れ螻 螳 詞 .
  • 19. Restricted Boltzmann Machines Gibbs Sampling in RBMs 襯 覲 譟郁唄覿 襯 覿螳 譯殊伎朱襦 Gibbs Sampling 牛 覈 豌伎 覿 覲語 讌 . 一危一 豢覦伎 讌 覃 豐蠍一 豌 螳 譟危讌襷 豢覿 螳 讌 豐蠍 蟯螻 覈 豌伎 蠍磯 覲語 讌 . 讌 蟯 る覃 Gibbs Sampling 豢覿 襷 覃 RBM 讌 蟆 .
  • 20. Contrastive Divergence Definition negative phase襯 覈 螳ロ 一危一 蠍磯螳朱 螻壱讌 螻 覈語 讌 螳 襦襷 蠏殊. 覈語 讌 る 蠏 螳 蠏 螳蟾 螳レ煙 蠍 覓語 Reasonable . Gibbs Sampling 伎 視. Update rule れ螻 螳 れ .
  • 21. Contrastive Divergence CD-k with Alternative Gibbs Sampling [Hinton 02] Gibbs Sampling 螳 training data襦 . Gibbs Sampling 覓危覯 讌 螻 k覯襷 . れ朱 1覯襷 企 豢覿 譬 詞 . Training 襦 覈語 螳讌 覿 training set 覿襯 磯手. 讀, training data螳 企 覈語 覿襯 企 螻 る 蟆企. 磯殊 training data襦覿 襷 覃 企 企 企 讌覿 襷 蟆企手 覲 伎 1覯襷 譬 詞 . 1覯 襷伎 詞伎 visible data襯 reconstrunction企手 螻 碁企 襦 螻 る reconstruction error螳 螳. 讀, 伎 RBM input data襯 讌企ｌ朱 狩 reconstruction visible data襯 詞 .
  • 22. Contrastive Divergence persistent CD [Tieleman 08] Gibbs Sampling 蠍一ヾ CD-k 襷る 螳螳 training data 襷讌襷 persistent CD 伎 Gibbs Sampling 螻磯 data (reconstruction data)襯 れ 覯 Sampling 朱 . 讀, 豌 覯讌 training data螳 persistent chain 螻 覯 Gibbs Sampling 蟆郁骸襯 れ 覯 training 朱 Chain 伎企螳. 企蟆 Chain 伎 螳覃 覓危覯 Sampling 蟆螻 觜訣伎 螻朱ゼ 螳蟆 . 覓朱 襷 Gibbs Sampling襷 朱誤郁 Update 伎 覈語 覲蠍 讌襷 襷れ 螳願鍵 覓語 蠏殊朱 焔渚.
  • 23. Examples [Hintons lecture] 2襯 牛 16 x 16 蠍一 企語 (256 螳 visible 企) 50螳 binary hidden 企 蟆曙 Hidden unit = Feature detector = Feature Extractor CD-1朱 螳 企一 Weight り朱 豐蠍壱
  • 24. Examples [Hintons lecture] 50螳 Hidden Unit Weight襯 企語襦 蠏碁Π 蟆
  • 32. Examples [Hintons lecture] 螳 企一 2 襦 るジ Feature襯 ′企 蟆 覲
  • 33. Examples [Hintons lecture] ろ 企語襦 Reconstruction 企慨覃.. ろ語 企語 Reconstruction ろ語 企語 Reconstruction ろ語 2 伎襷 蠍 覓語 覈 企語襯 2襦 危危り .
  • 35. Examples [Larochelle 09] MNIST 螳 Hidden unit Edge(ろ碁)襯 觸企 蟆 覲 .
  • 36. Extensions Unsupervised Learning Feature Extractor るジ Supervised Learning pre-training Deep Belief Network [Hinton Neural Computation 06] Deep Auto-Encoder [Hinton Science 06] Collaborative Filtering (Netflix Prize 2007 winner) [Salakhutdinov 07] Conditional RBM (with Gaussian Unit) Conditional Factored RBM Generator (Human motion modeling) [Taylor 06] Conditional RBM
  • 37. Extensions Supervised Learning Classifier [Larochelle 08] Classification RBM Discriminitive RBM Hybrid Discriminitive RBM
  • 38. References [Bengio 09] Learning Deep Architectures for AI [Deeplearning.net] Deep learning tutorial - RBM [Hinton 02] Training Products of Experts by Minimizing Contrastive Divergence [Tieleman 08] Training Restricted Boltzmann Machines using Approximations to the Likelihood Gradient [Larochelle 09] Exploring Strategies for Training Deep Neural Networks [Hinton Neural Computation 06] A Fast Learning Algorithm for Deep Belief Network [Hinton Science 06] Reducing the Dimensionality of Data with Neural Networks [Salakhutdinov 07] Restricted Boltzmann machines for collaborative filtering [Taylor 06] Modeling Human Motion Using Binary Latent Variables [Larochelle 08] Classification using Discriminative Restricted Boltzmann Machines
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