Deep Unsupervised Learning Russ Salakhutdinov Machine Learning Department Carnegie Mellon University Canadian Institute of Advanced Research 1
Mining for Structure Massive increase in both computational power and the amount of data available from web, video cameras, laboratory measurements. Images & Video Text & Language Speech & Audio Gene Expression Relational Data/ Product fMRI Tumor region Social Network Recommendation Mostly Unlabeled • Develop statistical models that can discover underlying structure, cause, or statistical correlation from data in unsupervised or semi-supervised way. • Multiple application domains. 2
Mining for Structure Massive increase in both computational power and the amount of data available from web, video cameras, laboratory measurements. Images & Video Text & Language Speech & Audio Gene Expression Deep Learning Models that Relational Data/ Product fMRI Tumor region Social Network support inferences and discover Recommendation structure at multiple levels. Mostly Unlabeled • Develop statistical models that can discover underlying structure, cause, or statistical correlation from data in unsupervised or semi-supervised way. • Multiple application domains. 3
Impact of Deep Learning • Speech Recognition • Computer Vision • Recommender Systems • Language Understanding • Drug Discovery & Medical Image Analysis 4
Building Artificial Intelligence Develop computer algorithms that can: - See and recognize objects around us - Perceive human speech - Understand natural language - Navigate around autonomously - Display human like Intelligence Personal assistants, self-driving cars, etc. 5
Speech Recognition 6
Deep Autoencoder Model Reuters dataset: 804,414 Learned latent code newswire stories: unsupervised European Community Interbank Markets Monetary/Economic Energy Markets Disasters and Accidents Leading Legal/Judicial Economic Indicators Bag of words Government Accounts/ Borrowings Earnings 7 (Hinton & Salakhutdinov, Science 2006)
Unsupervised Learning Non-probabilistic Models Probabilistic (Generative) Models Ø Sparse Coding Ø Autoencoders Ø Others (e.g. k-means) Non-Tractable Models Tractable Models Ø Generative Adversarial Ø Boltzmann Machines Ø Fully observed Networks Ø Variational Belief Nets Ø Moment Matching Autoencoders Ø NADE Networks Ø Helmholtz Machines Ø PixelRNN Ø Many others… Explicit Density p(x) Implicit Density 8
Talk Roadmap • Basic Building Blocks: Sparse Coding Ø Autoencoders Ø • Deep Generative Models Restricted Boltzmann Machines Ø Deep Boltzmann Machines Ø Helmholtz Machines / Variational Autoencoders Ø • Generative Adversarial Networks • Open Research Questions 9
Sparse Coding • Sparse coding (Olshausen & Field, 1996). Originally developed to explain early visual processing in the brain (edge detection). • Objective: Given a set of input data vectors learn a dictionary of bases such that: Sparse: mostly zeros • Each data vector is represented as a sparse linear combination of bases. 10
Sparse Coding Natural Images Learned bases: “Edges” New example = 0.8 * + 0.3 * + 0.5 * x = 0.8 * + 0.3 * + 0.5 * [0, 0, … 0.8 , …, 0.3 , …, 0.5 , …] = coefficients (feature representation) 11 Slide Credit: Honglak Lee
Sparse Coding: Training • Input image patches: • Learn dictionary of bases: Reconstruction error Sparsity penalty • Alternating Optimization: 1. Fix dictionary of bases and solve for activations a (a standard Lasso problem). 2. Fix activations a , optimize the dictionary of bases (convex QP problem). 12
Sparse Coding: Testing Time • Input: a new image patch x* , and K learned bases • Output: sparse representation a of an image patch x*. = 0.8 * + 0.3 * + 0.5 * x* = 0.8 * + 0.3 * + 0.5 * [0, 0, … 0.8 , …, 0.3 , …, 0.5 , …] = coefficients (feature representation) 13
Image Classification Evaluated on Caltech101 object category dataset. Classification Algorithm (SVM) 9K images, 101 classes Learned Features (coefficients) Input Image bases Algorithm Accuracy Baseline (Fei-Fei et al., 2004) 16% PCA 37% Sparse Coding 47% 14 Lee, Battle, Raina, Ng, 2006 Slide Credit: Honglak Lee
Interpreting Sparse Coding a Sparse features a Implicit Explicit g (a) f (x) nonlinear Linear encoding Decoding x’ x • Sparse, over-complete representation a. • Encoding a = f( x ) is implicit and nonlinear function of x . • Reconstruction (or decoding) x’ = g( a ) is linear and explicit. 15
Autoencoder Feature Representation Feed-back, Feed-forward, generative, Decoder Encoder bottom-up top-down path Input Image • Details of what goes insider the encoder and decoder matter! • Need constraints to avoid learning an identity. 16
Autoencoder Binary Features z Decoder Encoder filters D filters W. z= σ (Wx) Dz Linear Sigmoid function function path Input Image x 17
Autoencoder Binary Features z • An autoencoder with D inputs, D outputs, and K hidden units, with K<D. z= σ (Wx) Dz • Given an input x, its reconstruction is given by: Input Image x Decoder Encoder 18
Autoencoder Binary Features z • An autoencoder with D inputs, D outputs, and K hidden units, with K<D. z= σ (Wx) Dz Input Image x • We can determine the network parameters W and D by minimizing the reconstruction error: 19
Autoencoder Linear Features z • If the hidden and output layers are linear, it will learn hidden units that are a linear function of the data and minimize the squared error. z=Wx Wz • The K hidden units will span the same space as the first k principal components. The weight vectors Input Image x may not be orthogonal. • With nonlinear hidden units, we have a nonlinear generalization of PCA. 20
Another Autoencoder Model Binary Features z Encoder filters W. σ ( W T z) z= σ (Wx) Sigmoid Decoder function filters D path Binary Input x • Need additional constraints to avoid learning an identity. • Relates to Restricted Boltzmann Machines (later). 21
Predictive Sparse Decomposition Binary Features z Encoder L 1 Sparsity filters W. D z z= σ (Wx) Sigmoid Decoder function filters D path Real-valued Input x At training time path Encoder Decoder 22 Kavukcuoglu, Ranzato, Fergus, LeCun, 2009
Stacked Autoencoders Class Labels Decoder Encoder Features Decoder Encoder Sparsity Features Decoder Encoder Sparsity Input x 23
Stacked Autoencoders Class Labels • Remove decoders and Encoder use feed-forward part. • Standard, or Features convolutional neural network architecture. Encoder • Parameters can be Features fine-tuned using backpropagation. Encoder Input x 24
Deep Autoencoders Decoder 30 W 4 Top 500 RBM T T W W + � 1 1 8 2000 2000 T T 500 W W + � 2 2 7 1000 1000 W 3 T T 1000 W W + � RBM 3 3 6 500 500 T T W W + � 4 4 5 30 Code layer 30 1000 W W + � 4 4 4 W 2 500 500 2000 RBM W W + � 3 3 3 1000 1000 W W + � 2 2 2 2000 2000 2000 W W W + � 1 1 1 1 RBM Encoder Pretraining Unrolling Fine � tuning 25
Deep Autoencoders • 25x25 – 2000 – 1000 – 500 – 30 autoencoder to extract 30-D real- valued codes for Olivetti face patches. • Top : Random samples from the test dataset. • Middle : Reconstructions by the 30-dimensional deep autoencoder. • Bottom : Reconstructions by the 30-dimentinoal PCA. 26
Information Retrieval 2-D LSA space European Community Interbank Markets Monetary/Economic Energy Markets Disasters and Accidents Leading Legal/Judicial Economic Indicators Government Accounts/ Borrowings Earnings • The Reuters Corpus Volume II contains 804,414 newswire stories (randomly split into 402,207 training and 402,207 test). • “Bag-of-words” representation: each article is represented as a vector containing the counts of the most frequently used 2000 words in the training set. 27 (Hinton and Salakhutdinov, Science 2006)
Semantic Hashing European Community Monetary/Economic Address Space Disasters and Accidents Semantically Similar Documents Semantic Hashing Government Function Borrowing Energy Markets Document Accounts/Earnings • Learn to map documents into semantic 20-D binary codes. • Retrieve similar documents stored at the nearby addresses with no search at all. 28 (Salakhutdinov and Hinton, SIGIR 2007)
Searching Large Image Database using Binary Codes • Map images into binary codes for fast retrieval. • Small Codes, Torralba, Fergus, Weiss, CVPR 2008 • Spectral Hashing, Y. Weiss, A. Torralba, R. Fergus, NIPS 2008 • Kulis and Darrell, NIPS 2009, Gong and Lazebnik, CVPR 20111 • Norouzi and Fleet, ICML 2011, 29
Talk Roadmap • Basic Building Blocks: Sparse Coding Ø Autoencoders Ø • Deep Generative Models Restricted Boltzmann Machines Ø Deep Boltzmann Machines Ø Helmholtz Machines / Variational Autoencoders Ø • Generative Adversarial Networks 30
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