Lecture3 xing fei-fei

Machine Learning

Neural Networks

Eric XingLecture 3, August 12, 2010

Reading: Chap. 5 CB

Learning highly non-linear functions

f: X Y f might be non-linear function X (vector of) continuous and/or discrete vars Y (vector of) continuous and/or discrete vars

The XOR gate Speech recognition

From biological neuron to artificial neuron (perceptron)

Activation function

Artificial neuron networks supervised learning gradient descent

Perceptron and Neural Nets

Soma Soma

Synapse

Dendrites

Synapse

DendritesAxon

Threshold

Inputs

OutputY∑

HardLimiter

LinearCombiner

iiiwxX

ω<−ω≥+

Y if , if ,

Input Layer Output Layer

Middle Layer

Connectionist Models Consider humans:

Neuron switching time ~ 0.001 second

Number of neurons ~ 1010

Connections per neuron ~ 104-5

Scene recognition time ~ 0.1 second

100 inference steps doesn't seem like enough much parallel computation

Properties of artificial neural nets (ANN) Many neuron-like threshold switching units Many weighted interconnections among units Highly parallel, distributed processes

Synapses

Dendrites

Synapses+++--

(weights)

Male Age Temp WBC PainIntensity

PainDuration

37 10 11 20 1adjustableweights

0 1 0 0000

AppendicitisDiverticulitis

PerforatedNon-specific

CholecystitisSmall Bowel

PancreatitisObstructionPainDuodenal Ulcer

Abdominal Pain Perceptron

0.8Myocardial Infarction “Probability” of MI

112 150

MaleAgeSmokerECG: STPainIntensity

PainDuration Elevation

Myocardial Infarction Network

The "Driver" Network

weights

Output units

No disease Pneumonia Flu Meningitis

Input units

Cough Headache

what we gotwhat we wanted-error

∆ rulechange weights todecrease the error

Perceptrons

Input units

Input to unit j: aj = Σwijai

Input to unit i: ai

measured value of variable i

Output of unit j:

oj = 1/ (1 + e- (aj+θj) )Output

Perceptrons

Jargon Pseudo-Correspondence Independent variable = input variable Dependent variable = output variable Coefficients = “weights” Estimates = “targets”

Logistic Regression Model (the sigmoid unit)Inputs Output

Age 34

1Gender

Stage 4

“Probability of beingAlive”

Coefficients

a, b, c

Independent variables

x1, x2, x3Dependent variable

p Prediction

The perceptron learning algorithm

Recall the nice property of sigmoid function

Consider regression problem f:XY , for scalar Y:

Let’s maximize the conditional data likelihood

Gradient Descent

xd = input

td = target output

od =observed unit

output

wi =weight i

The perceptron learning rules

xd = input

td = target output

od =observed unit

output

wi =weight i

Batch mode:Do until converge:

1. compute gradient ∇ED[w]

Incremental mode:Do until converge:

For each training example d in D

1. compute gradient ∇Ed[w]

MLE vs MAP Maximum conditional likelihood estimate

Maximum a posteriori estimate

What decision surface does a perceptron define?

x y Z (color)

0 0 10 1 11 0 11 1 0

some possible values for w1 and w2

0.200.200.250.40

0.350.400.300.20

f(x1w1 + x2w2) = y f(0w1 + 0w2) = 1 f(0w1 + 1w2) = 1 f(1w1 + 0w2) = 1 f(1w1 + 1w2) = 0

θ = 0.5

f(a) = 1, for a > θ0, for a ≤ θ

x y Z (color)

0 0 00 1 11 0 11 1 0

some possible values for w1 and w2

f(x1w1 + x2w2) = y f(0w1 + 0w2) = 0 f(0w1 + 1w2) = 1 f(1w1 + 0w2) = 1 f(1w1 + 1w2) = 0

θ = 0.5

f(a) = 1, for a > θ0, for a ≤ θ

x y Z (color)

0 0 00 1 11 0 11 1 0

f(a) = 1, for a > θ0, for a ≤ θ

θw1 w4w3

θ = 0.5 for all units

a possible set of values for (w1, w2, w3, w4, w5 , w6):(0.6,-0.6,-0.7,0.8,1,1)

Cough No cough

CoughNo coughNo headache No headache

Headache Headache

No disease

Meningitis Flu

Pneumonia

No treatmentTreatment

000 100

111011

Non Linear Separation

Inputs

Weights

Output

Dependent variable

Prediction

Age 34

2Gender

Stage 4

WeightsHiddenLayer

Neural Network Model

Inputs

Weights

Output

Dependent variable

Prediction

Age 34

2Gender

Stage 4

WeightsHiddenLayer

“Combined logistic models”

Inputs

Weights

Output

Dependent variable

Prediction

Age 34

2Gender

Stage 4

WeightsHiddenLayer

Inputs

Weights

Output

Dependent variable

Prediction

Age 34

1Gender

Stage 4

WeightsHiddenLayer

WeightsIndependent variables

Dependent variable

Prediction

Age 34

2Gender

Stage 4

WeightsHiddenLayer

Not really, no target for hidden units...

weights

Output units

No disease Pneumonia Flu Meningitis

Input units

Cough Headache

∆ rulechange weights todecrease the error

Perceptrons

Input units

Output units

Hiddenunits

∆ rule

Hidden Units and Backpropagation

Backpropagation Algorithm Initialize all weights to small random numbers

Until convergence, Do

1. Input the training example to the network and compute the network outputs

1. For each output unit k

2. For each hidden unit h

3. Undate each network weight wi,j

xd = input

td = target output

od =observed unit

output

wi =weight i

More on Backpropatation It is doing gradient descent over entire network weight vector Easily generalized to arbitrary directed graphs Will find a local, not necessarily global error minimum

In practice, often works well (can run multiple times)

Often include weight momentum α

Minimizes error over training examples Will it generalize well to subsequent testing examples?

Training can take thousands of iterations, very slow! Using network after training is very fast

Learning Hidden Layer Representation A network:

A target function:

Can this be learned?

Learning Hidden Layer Representation A network:

Learned hidden layer representation:

Training

Expressive Capabilities of ANNs Boolean functions:

Every Boolean function can be represented by network with single hidden layer But might require exponential (in number of inputs) hidden units

Continuous functions: Every bounded continuous function can be approximated with arbitrary small

error, by network with one hidden layer [Cybenko 1989; Hornik et al 1989] Any function can be approximated to arbitrary accuracy by a network with two

hidden layers [Cybenko 1988].

Application: ANN for Face Reco. The model The learned hidden unit

weights

X1 X2 X3

“X1” “X1X3” “X1X2X3”

“X2”

X1 X2 X3 X1X2 X1X3 X2X3

(23-1) possible combinations

X1X2X3

Y = a(X1) + b(X2) + c(X3) + d(X1X2) + ...

Regression vs. Neural Networks

winitial wtrained

initial error

final error

Error surface

positive change

negative derivative

local minimum

Minimizing the Error

Overfitting in Neural NetsC

Overfitted model “Real” model

cycles

Overfitted model

holdout

training

Alternative Error Functions Penalize large weights:

Training on target slopes as well as values

Tie together weights E.g., in phoneme recognition

Artificial neural networks – what you should know Highly expressive non-linear functions Highly parallel network of logistic function units Minimizing sum of squared training errors

Gives MLE estimates of network weights if we assume zero mean Gaussian noise on output values

Minimizing sum of sq errors plus weight squared (regularization) MAP estimates assuming weight priors are zero mean Gaussian

Gradient descent as training procedure How to derive your own gradient descent procedure

Discover useful representations at hidden units Local minima is greatest problem Overfitting, regularization, early stopping

Neural Network Approaches for Visual Recognition

L. Fei-Fei

Computer Science Dept.

Stanford University

Machine learning in computer vision

• Aug 12, Lecture 3: Neural Network– Convolutional Nets for object recognition

– Unsupervised feature learning via Deep Belief Net

7 August 2010 40L. Fei-Fei, Dragon Star 2010, Stanford

(slides courtesy to Yann LeCun (NYU))

[[Reference paper: Yann LeCun et al. Proc. IEEE, 1998]]

Mammalian visual pathway is hierarchical

• The ventral (recognition) pathway in the visual cortex– Retina → LGN → V1 → V2 → V4 → PIT → AIT (80-100ms)

• Efficient Learning Algorithms for multi-stage “Deep Architectures”– Multi-stage learning is difficult

• Learning good internal representations of the world (features)– Hierarchy of features that capture the relevant information and

eliminates irrelevant variabilities• Learning with unlabeled samples (unsupervised learning)

– Animals can learn vision by just looking at the world– No supervision is required

• Deep learning algorithms that can be applied to other modalities– If we can learn feature hierarchies for vision, we can learn feature

hierarchies for audition, natural language, ....

Some challenges for machine learning in vision

• The raw input is pre-processed through a hand-crafted feature extractor

• The features are not learned• The trainable classifier is often generic (task independent), and

“simple” (linear classifier, kernel machine, nearest neighbor,.....)• The most common Machine Learning architecture: the Kernel

Machine

“Simple” Trainable Classifier

Pre-processing / Feature Extraction

this part is mostly hand-craftedInternal Representation

The traditional “shallow” architecture for recognition

• In Language: hierarchy in syntax and semantics–Words->Parts of Speech->Sentences->Text–Objects,Actions,Attributes...-> Phrases -> Statements ->

Stories• In Vision: part-whole hierarchy–Pixels->Edges->Textons->Parts->Objects->Scenes

TrainableFeature

Extractor

TrainableFeature

Extractor

TrainableClassifier

Good representations are hierarchical

• Deep Learning: learning a hierarchy of internal representations• From low-level features to mid-level invariant representations, to

object identities• Representations are increasingly invariant as we go up the layers• using multiple stages gets around the specificity/invariance

dilemma

TrainableFeature

Extractor

TrainableFeature

Extractor

TrainableClassifier

Learned Internal Representation

“Deep” learning: learning hierarchical representations

• We can approximate any function as close as we want with shallow architecture. Why would we need deep ones?

–kernel machines and 2-layer neural net are “universal”.

• Deep learning machines• Deep machines are more efficient for representing

certain classes of functions, particularly those involved in visual recognition

– they can represent more complex functions with less “hardware”

• We need an efficient parameterization of the class of functions that are useful for “AI” tasks.

Do we really need deep architecture?

FilterBank

SpatialPooling

Non-Linearity

• Multiple Stages• Each Stage is composed of

– A bank of local filters (convolutions)– A non-linear layer (may include harsh non-linearities, such as

rectification, contrast normalization, etc...).– A feature pooling layer

• Multiple stages can be stacked to produce high-level representations– Each stage makes the representation more global, and more

invariant• The systems can be trained with a combination of unsupervised and

supervised methods

ClassifierFilterBank

SpatialPooling

Non-Linearity

Hierarchical/deep architectures for vision

• [Hubel & Wiesel 1962]: – simple cells detect local features

– complex cells “pool” the outputs of simple cells within a retinotopicneighborhood.

pooling subsampling

“Simple cells”“Complex cells”

Multiple convolutions

Retinotopic Feature Maps

Filtering+NonLinearity+Pooling = 1 stage of a Convolutional Net

• Biologically-inspired models of low-level feature extraction– Inspired by [Hubel and Wiesel 1962]

• Only 3 types of operations needed for traditional ConvNets:– Convolution/Filtering– Pointwise Non-Linearity– Pooling/Subsampling

FilterBank

SpatialPooling

Non-Linearity

Feature extraction by filtering and pooling

Convolutional Network: Multi-Stage Trainable Architecture

Hierarchical ArchitectureRepresentations are more global, more invariant, and more abstract as we go up the layers

Alternated Layers of Filtering and Spatial PoolingFiltering detects conjunctions of featuresPooling computes local disjunctions of features

Fully TrainableAll the layers are trainable

Convolutions,Filtering

PoolingSubsampling

Convolutions,Filtering Pooling

Subsampling

Convolutions,Filtering

Convolutions,Classification

Convolutional network architecture

• Building a complete artificial vision system:– Stack multiple stages of simple cells / complex cells layers– Higher stages compute more global, more invariant features– Stick a classification layer on top– [Fukushima 1971-1982]

• neocognitron– [LeCun 1988-2007]

• convolutional net– [Poggio 2002-2006]

• HMAX– [Ullman 2002-2006]

• fragment hierarchy– [Lowe 2006]

• HMAX QUESTION: How do we find (or learn) the filters?

Convolutional Nets and other Multistage Hubel-Wiesel Architectures

Convolutional Net Training: Gradient Back-Propagation

Convolutional Net Architecture for Hand-writing recognition

input1@32x32

Layer 16@28x28

Layer 26@14x14

Layer 312@10x10 Layer 4

12@5x5

Layer 5100@1x1

5x5convolution

5x5convolution2x2

pooling/subsampling

2x2pooling/subsampling

Layer 6: 10

Convolutional net for handwriting recognition (400,000 synapses)Convolutional layers (simple cells): all units in a feature plane share the same weightsPooling/subsampling layers (complex cells): for invariance to small distortions.Supervised gradient-descent learning using back-propagationThe entire network is trained end-to-end. All the layers are trained simultaneously.[LeCun et al. Proc IEEE, 1998]

MNIST Handwritten Digit Dataset

Handwritten Digit Dataset MNIST: 60,000 training samples, 10,000 test samples

CLASSIFIER DEFORMATION PREPROCESSING ERROR (%) Referencelinear classifier (1-layer NN) none 12.00 LeCun et al. 1998linear classifier (1-layer NN) deskewing 8.40 LeCun et al. 1998pairwise linear classifier deskewing 7.60 LeCun et al. 1998K-nearest-neighbors, (L2) none 3.09 Kenneth Wilder, U. ChicagoK-nearest-neighbors, (L2) deskewing 2.40 LeCun et al. 1998K-nearest-neighbors, (L2) deskew, clean, blur 1.80 Kenneth Wilder, U. ChicagoK-NN L3, 2 pixel jit ter deskew, clean, blur 1.22 Kenneth Wilder, U. ChicagoK-NN, shape context m atching shape context feature 0.63 Belongie et al. IEEE PAMI 200240 PCA + quadrat ic classifier none 3.30 LeCun et al. 19981000 RBF + linear classifier none 3.60 LeCun et al. 1998K-NN, Tangent Distance subsam p 16x16 pixels 1.10 LeCun et al. 1998SVM, Gaussian Kernel none 1.40SVM deg 4 polynom ial deskewing 1.10 LeCun et al. 1998Reduced Set SVM deg 5 poly deskewing 1.00 LeCun et al. 1998Virtual SVM deg-9 poly Affine none 0.80 LeCun et al. 1998V-SVM, 2-pixel jit tered none 0.68 DeCoste and Scholkopf, MLJ 2002V-SVM, 2-pixel jit tered deskewing 0.56 DeCoste and Scholkopf, MLJ 20022-layer NN, 300 HU, MSE none 4.70 LeCun et al. 19982-layer NN, 300 HU, MSE, Affine none 3.60 LeCun et al. 19982-layer NN, 300 HU deskewing 1.60 LeCun et al. 19983-layer NN, 500+ 150 HU none 2.95 LeCun et al. 19983-layer NN, 500+ 150 HU Affine none 2.45 LeCun et al. 19983-layer NN, 500+ 300 HU, CE, reg none 1.53 Hinton, unpublished, 20052-layer NN, 800 HU, CE none 1.60 Sim ard et al., ICDAR 20032-layer NN, 800 HU, CE Affine none 1.10 Sim ard et al., ICDAR 20032-layer NN, 800 HU, MSE Elast ic none 0.90 Sim ard et al., ICDAR 20032-layer NN, 800 HU, CE Elast ic none 0.70 Sim ard et al., ICDAR 2003Convolut ional net LeNet-1 subsam p 16x16 pixels 1.70 LeCun et al. 1998Convolut ional net LeNet-4 none 1.10 LeCun et al. 1998Convolut ional net LeNet-5, none 0.95 LeCun et al. 1998Conv. net LeNet-5, Affine none 0.80 LeCun et al. 1998Boosted LeNet-4 Affine none 0.70 LeCun et al. 1998Conv. net , CE Affine none 0.60 Sim ard et al., ICDAR 2003Com v net , CE Elast ic none 0.40 Sim ard et al., ICDAR 2003

Results on MNIST handwritten Digits

Invariance and Robustness to Noise

Face Detection and Pose Estimation with Convolutional Nets

• Training: 52,850, 32x32 grey-level images of faces, 52,850 non-faces.

• Each sample: used 5 times with random variation in scale, in-plane rotation, brightness and contrast.

• 2nd phase: half of the initial negative set was replaced by false positives of the initial version of the detector .

Face Detection: Results

x93%86%Schneiderman & Kanade

x96%89%Rowley et al

x83%70%xJones & Viola (profile)

xx95%90%Jones & Viola (tilted)

88%83%83%67%97%90%Our Detector

1.280.53.360.4726.94.42

MIT+CMUPROFILETILTEDData Set->

False positives per image->

Face Detection and Pose Estimation: Results

Face Detection with a Convolutional Net

Yann LeCun

Industrial Applications of ConvNets

• AT&T/Lucent/NCR– Check reading, OCR, handwriting recognition (deployed 1996)

• Vidient Inc– Vidient Inc's “SmartCatch” system deployed in several airports

and facilities around the US for detecting intrusions, tailgating, and abandoned objects (Vidient is a spin-off of NEC)

• NEC Labs– Cancer cell detection, automotive applications, kiosks

• Google– OCR, face and license plate removal from StreetView

• Microsoft– OCR, handwriting recognition, speech detection

• France Telecom– Face detection, HCI, cell phone-based applications

• Other projects: HRL (3D vision)....

(slides courtesy to Honglak Lee (Stanford))

Machine Learning’s Success• Data mining

– Web data mining– Biomedical data mining– Time series data mining

• Artificial Intelligence– Computer vision– Speech recognition– Autonomous car driving

However, machine learning’s success has relied on having a good feature representation of the data.

How can we develop good representations automatically?7 August 2010 70L. Fei-Fei, Dragon Star 2010,

Stanford

The Learning Pipeline

Input spaceMotorbikes“Non”-Motorbikes

LearningAlgorithm

pixel 1

pixel 2

The Learning Pipeline

Input space Feature spaceMotorbikes“Non”-Motorbikes

Low-level features

LearningAlgorithm

pixel 1

“wheel”

“han

dle”

“feature engineering”handle

Computer vision features

SIFT Spin image

HoG RIFT

Textons GLOH

Drawbacks of feature engineering1. Needs expert knowledge2. Time consuming hand-tuning

Feature learning from unlabeled data

• Main idea– Finding underlying structure (cause) or statistical

correlation from the input data.

• Sparse coding [Olshausen and Field, 1997]

– Objective: Given input data {x}, search for a set of bases {bj} such that

where aj are mostly zeros.

Sparse coding on imagesNatural Images Learned bases: “Edges”

= 0.8 * + 0.3 * + 0.5 *

x = 0.8 * b36

+ 0.3 * b42 + 0.5 * b65

[0, 0, … 0.8, …, 0.3, …, 0.5, …] = coefficients (feature representation)

New example

Lee, Ng, et al. 20077 August 2010 75L. Fei-Fei, Dragon Star 2010, Stanford

OptimizationGiven input data {x(1), …, x(m)}, we want to find good bases {b1, …, bn}:

∑∑ ∑ +−i

iab abax 1

)()(, ||||||||min β

Reconstruction error Sparsity penalty

1||||: ≤∀ jbj Normalization constraint

Solve by alternating minimization:-- Keep b fixed, find optimal a. -- Keep a fixed, find optimal b. Lee, Ng, 20067 August 2010 76L. Fei-Fei, Dragon Star 2010,

Stanford

Evaluated on Caltech101 object category dataset.

Image classification

Previous reported results:Fei-Fei et al, 2004: 16%Berg et al., 2005: 17%Holub et al., 2005: 40%Serre et al., 2005: 35%Berg et al, 2005: 48%Lazebnik et al, 2006: 64%Varma et al. 2008: 78%

ClassificationAlgorithm

Algorithm Accuracy

Baseline (Fei-Fei et al., 2004) 16%

PCA 37%

Our method 47%

36% error reduction

Input Image Features (coefficients)Learned

Learning Feature Hierarchy

Input image (pixels)

“Sparse coding”(edges)

[Related work: Hinton, Bengio, LeCun, and others.]

DBN (Hinton et al., 2006) with additional sparseness constraint.

Higher layer(Combinations

of edges)

Restricted Boltzmann Machine (RBM)

– Undirected, bipartite graphical model

– Inference is easy

– Training by approximating maximum likelihood (Contrastive Divergence [Hinton, 2002])

visible nodes (data)

hidden nodes

Weights W (bases) encodes statistical relationship between h and v.

Deep Belief Network• Deep Belief Network (DBN) [Hinton et al., 2006]

– Generative model with multiple hidden layers

– Successful applications• Recognizing handwritten digits

• Learning motion capture data

• Collaborative filtering

– Bottom-up, layer-wise training

using Restricted Boltzmann machines

visible nodes (data)

Sparse Restricted Boltzmann Machines [NIPS-2008]

• Main idea– Constrain the hidden layer nodes to have “sparse”

average activation (similar to sparse coding)

– Regularize with a sparsity penalty

Log-likelihood Sparsity penalty

Average activation Target sparsity7 August 2010 81L. Fei-Fei, Dragon Star 2010, Stanford

Sparse representation from digits [NIPS 2008]

Sparse RBM bases“pen-strokes”

Sparse RBMs often give readily interpretable featuresand good discriminative power.

Training examples

Learning object representations

• Learning objects and parts in images

• Large image patches contain interesting higher-level structures.– E.g., object parts and full objects

Applying DBN to large image

Input image

Problem: - Typically, input dimension ~ 1,000 (30x30 pixels)- Computationally intractable to learn from realistic image sizes (e.g. 200x200 pixels)

Convolutional architecturesWeight sharing by convolution (e.g., [Lecun et al., 1989])

“Max-pooling”Invariance Computational efficiencyDeterministic and feed-forward

We develop convolutional Restricted Boltzmann machine (CRBM).

We define probabilistic max-pooling that combine bottom-up and top-down information.

convolution filter

Detection layer

maximum 2x2 grid

Max-pooling layer

Detection layer

Max-pooling layer

convolution

maximum 2x2 grid

V (visible layer)

Detection layer H

Max-pooling layer P

Convolutional RBM (CRBM) [ICML 2009]

Hidden nodes (binary)

“Filter“ weights (shared)

For “filter” k,

At most one hidden nodes are active.

‘’max-pooling’’ node (binary)

Input data V

Probabilistic max pooling

Xj are stochastic binary and mutually exclusive.

X3X1 X2 X4

Collapse 2n configurations into n+1 configurations. Permits bottom up and top down inference.

Pooling node

Detection nodes

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

0 0 0 0

Probabilistic max pooling

X3X1 X2 X4

Bottom-up inference

I1 I2 I3 I4

Pooling node

Detection nodes

Probability can be written as a softmax function. Sample from multinomial distribution.

Output of convolution W*V from below

Convolutional Deep Belief Networks

• Bottom-up (greedy), layer-wise training– Train one layer (convolutional RBM) at a time.

• Inference (approximate)– Undirected connections for all layers (Markov net)

[Related work: Salakhutdinov and Hinton, 2009]

– Block Gibbs sampling or mean-field

– Hierarchical probabilistic inference

Unsupervised learning of object-parts

Faces Cars Elephants Chairs

Object category classification (Caltech 101)

• Our model is comparable to the results using state-of-the-art features (e.g., SIFT).

CDBN (first layer)

CDBN (first+second layer)

Ranzato et al. (2007)

Mutch and Lowe (2006)

Lazebnik et al. (2006)

Zhang et al. (2006)

Our method

Unsupervised learning of object-parts

Trained from multiple classes (cars, faces, motorbikes, airplanes)

Object-specific features

& shared features

“Grouping” the object parts

(highly specific)

Review of main contributions Developed efficient algorithms for unsupervised feature learning.

Showed that unsupervised feature learning is useful for many machine learning tasks. Object recognition, image segmentation, audio classification, text

classification, robotic perception, and others.

Object parts “Filling in”

Weaknesses & Criticisms

• Learning everything. Better to encode prior knowledge about structure of images.

A: Compare with machine learning vs. linguists debate in NLP.

• Results not yet competitive with best engineered systems.

A: Agreed. True for some domains.

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