Restricted Boltzmann Machines and
Deep Networks for Unsupervised Learning
Instituto Italiano di Tecnologia, Genova
June 7th, 2011
Loris Bazzani
University of Verona
Brief Intro
•
Unsupervised Learning
•
Learning features from
(
visual
) data
•
Focus here on Restricted
Boltzmann Machines
2
Outline Presentation
•
Restricted Boltzmann Machines (RBMs)
–
Binary RBMs
–
Gaussian

binary RBMs
–
RBMs for Classification
–
Deep Belief Networks (DBNs)
•
Learning Algorithms
Applications
Theor
y
•
RBMs for Modeling Natural Scenes
[Ranzato, CVPR 2010]
•
Learning Attentional Policies
[Bazzani, ICML 2011]
Outline Presentation
•
Restricted Boltzmann Machines (RBMs)
–
Binary RBMs
–
Gaussian

binary RBMs
–
RBMs for Classification
–
Deep Belief Networks (DBNs)
•
Learning Algorithms
Applications
Theor
y
•
RBMs for Modeling Natural Scenes
[Ranzato, CVPR 2010]
•
Learning Attentional Policies
[Bazzani, ICML 2011]
Restricted Boltzmann Machines
5
•
Bipartite Probabilistic Graphical Model
W
: parameters governing the interactions
between
visible
and
hidden units
•
Property:
”given the hidden units, all of the visible units
become independent and given the visible units, all of the
hidden units become independent”
Binary RBMs
•
We can sample from
•
Use the expected value of the hidden units as
features:
6
Gaussian

binary RBMs
•
Popular extension for modeling natural images
•
Make the visible units conditionally Gaussian
given the hidden units
•
Conditional distributions
7
RBMs for Classification
1)
Feed the hidden representation into a
standard classifier (e.g., multinomial logistic
regression, SVM, random forest,…)
2)
Embed the class into the visible units
and, the class vector will be sample from
8
Deep Belief Networks
•
Goal
: reach a high level of abstraction,
so that classification becomes simple
(
e.g.
, linear)
•
Multiple stacked RBMs
•
Learning consists in greedy training each
level sequentially from the bottom
•
Add fine

tuning with back

propagation
•
Or a non

linear classifier can be used
•
PB
: how many layers?
9
Outline Presentation
•
Restricted Boltzmann Machines (RBMs)
–
Binary RBMs
–
Gaussian

binary RBMs
–
RBMs for Classification
–
Deep Belief Networks (DBNs)
•
Learning Algorithms
Applications
Theor
y
•
RBMs for Modeling Natural Scenes
[Ranzato, CVPR 2010]
•
Learning Attentional Policies
[Bazzani, ICML 2011]
•
Maximum Likelihood (ML) techniques
•
No close

form solution for the maximization
•
Problem
: Partition function usually not
efficiently computable
•
Solutions
:
•
Approximate ML
•
Sacrifices convergence properties to make it
computationally feasible
•
Alternatives
:
variational methods, max

margin learning,
etc.
How to Learn the Parameters
11
ML Problem
12
Gradient:
Match the gradient of the free energy under the data
distribution with the gradient under the model distribution
Marginalizing
Contrastive Divergence (1)
•
It is just a gradient descent
•
At each step, it contrasts the data distribution
with the model distribution
•
E.g.,
binary RBM
13
Contrastive Divergence (2)
•
Algorithm for binary RBMs:
14
Outline Presentation
•
Restricted Boltzmann Machines (RBMs)
–
Binary RBMs
–
Gaussian

binary RBMs
–
RBMs for Classification
–
Deep Belief Networks (DBNs)
•
Learning Algorithms
Applications
Theor
y
•
RBMs for Modeling Natural Scenes
[Ranzato, CVPR 2010]
•
Learning Attentional Policies
[Bazzani, ICML 2011]
Modeling Natural Images
•
Motivations:
–
Learning a generative model of natural images
–
Extracting features that capture regularities
–
Opposed to using engineered features
•
RBM with two set of hidden units:
–
One represents the pixel intensity
–
Another one, the pair

wise dependencies
•
Called Mean

Covariance RBM (mc

RBM)
•
It is still a Gaussian

binary RBM
17
mc

RBM Model (1)
•
Capture pair

wire interactions with:
•
Sketch:
18
Covariance
hiddens
mc

RBM Model (2)
•
Representation of mean pixel intensities:
•
Conditional distributions:
19
mc

RBM Model (3)
•
Final Energy term:
•
Free Energy formulation is also computable
•
Learning with
–
Stochastic gradient descent
–
And, Contrastive Divergence
–
Sampling using Hybrid Monte Carlo
20
Regularization
Training Protocol for Recognition
•
Images are pre

processed by PCA whitening
•
Train the mc

RBM
•
Extract features with mc

RBM
•
Train a classifier for object recognition:
–
Multinomial Logistic Classifier
21
Object Recognition on CIFAR 10
22
Outline Presentation
•
Restricted Boltzmann Machines (RBMs)
–
Binary RBMs
–
Gaussian

binary RBMs
–
RBMs for Classification
–
Deep Belief Networks (DBNs)
•
Learning Algorithms
Applications
Theor
y
•
RBMs for Modeling Natural Scenes
[Ranzato, CVPR 2010]
•
Learning Attentional Policies
[Bazzani, ICML 2011]
Where do you look at?
Original video source:
http://gpu4vision.icg.tugraz.at/index.php?content=subsites/prost/prost.php
Goal
•
Human tracking and recognition is amazingly
efficient and effective
•
Large stream of data is filtered by attention
•
We propose a model for tracking and recognition
that takes inspiration from human visual system
•
Tracking and recognition of “something” that is
moving in the scene
•
Accumulate gaze data
•
Plan where to look at in the next future
25
Parallelism with Human Brain
26
Source image:
http://www.waece.org/cd_morelia2006/ponencias/stoodley.htm
Sketch of the Model
27
(mc

)RBM
Multi

fixation RBM
Classifier
Policy Learning
Learning
•
Offline Training
•
Extract gaze data from a training dataset
•
Train the (mc

)RBM
•
Train the multi

fixation RBM (3 random gazes)
•
Train the multinomial logistic classifier
28
•
Online Learning
•
Hedge algorithm for policy learning
Online
from moving “things” with multiple
saccades
Modularity
autoencoders, sparse coding
, etc.
SVM, random forest,
etc.
other bandit techniques or Bayesian optimization
•
10 synthetic video sequences with moving and
background digits (from MNIST dataset)
Experiments (1)
Tracking error in pixels
Classification accuracy
Code available at:
http://www.lorisbazzani.info/code

datasets/rbm

tracking/
Experiments (2)
Dataset available at:
http://seqam.rutgers.edu/softdata/facedata/facedata.html
Summary
•
Several RBMs models
•
How to train RBMs
•
Their extensions for classification
•
RBMs as block for deep architectures
•
They are useful for learning features from
images, without engineering them
•
Taking inspiration from human learning, DBNs
have been used
32
References (1)
Learning
attentional
policies
for
tracking
and
recognition
in
video
with
deep
networks
,
Loris
Bazzani,
Nando
de
Freitas,
Hugo
Larochelle,
Vittorio
Murino,
and
Jo

Anne
Ting,
International
Conference
on
Machine
Learning,
2011
Tutorial
on
Stochastic
Approximation
Algorithms
for
Training
Restricted
Boltzmann
Machines
and
Deep
Belief
Nets
,
Swersky
and
Bo
Chen,
Benjamin
Marlin,
and
Nando
de
Freitas,
Information
Theory
and
Applications
(ITA)
Workshop,
2010
Inductive
Principles
for
Restricted
Boltzmann
Machine
Learning
,
Benjamin
Marlin,
Kevin
Swersky,
Bo
Chen,
and
Nando
de
Freitas,
AISTATS,
2010
Modeling
Pixel
Means
and
Covariances
Using
Factorized
Third

Order
Boltzmann
,
Marc'Aurelio
Ranzato
and
Geoffrey
E
.
Hinton,
IEEE
Computer
Society
Conference
on
Computer
Vision
and
Pattern
Recognition,
2010
Factored
3

Way
Restricted
Boltzmann
Machines
For
Modeling
Natural
Images
,
Marc'Aurelio
Ranzato,
Alex
Krizhevsky
and
Geoffrey
E
.
Hinton,
International
Conference
on
Artificial
Intelligence
and
Statistics,
2010
On
Deep
Generative
Models
with
Applications
to
Recognition
,
Marc'Aurelio
Ranzato,
Joshua
Susskind,
Volodymyr
Mnih,
and
Geoffrey
Hinton,
IEEE
Computer
Society
Conference
on
Computer
Vision
and
Pattern
Recognition,
2011
Learning
to
combine
foveal
glimpses
with
a
third

order
Boltzmann
machine
,
Hugo
Larochelle
and
Geoffrey
E
.
Hinton,
Neural
Information
Processing
Systems,
2010
33
References (2)
Stacks
of
Convolutional
Restricted
Boltzmann
Machines
for
Shift

Invariant
Feature
Learning
,
Mohammad
Norouzi,
Mani
Ranjbar,
and
Greg
Mori,
IEEE
Computer
Society
Conference
on
Computer
Vision
and
Pattern
Recognition,
2009
Deconvolutional
Networks
,
Matthew
D
.
Zeiler,
Dilip
Krishnan,
Graham
W
.
Taylor,
and
Rob
Fergus,
IEEE
Computer
Society
Conference
on
Computer
Vision
and
Pattern
Recognition,
2010
Convolutional
deep
belief
networks
for
scalable
unsupervised
learning
of
hierarchical
representation
s,
Lee,
Honglak,
Grosse,
Roger,
Ranganath,
Rajesh
and
Ng,
Andrew,
International
Conference
on
Machine
Learning,
2009
A
deep
learning
approach
to
machine
transliteration
,
Deselaers,
Thomas,
Hasan,
Savsa,
Bender,
Oliver
and
Ney,
Hermann,
Proceedings
of
the
Fourth
Workshop
on
Statistical
Machine
Translation,
2009
Learning
Multilevel
Distributed
Representations
for
High

dimensional
Sequences
,
Sutskever,
I
.
and
Hinton,
G
.
E
.
,
Proceeding
of
the
Eleventh
International
Conference
on
Artificial
Intelligence
and
Statistics,
2007
On
Contrastive
Divergence
Learning
,
Miguel
A
.
Carreira

Perpinan
and
Geoffrey
E
.
Hinton,
International
Conference
on
Artificial
Intelligence
and
Statistics,
2005
Convolutional
learning
of
spatio

temporal
features
,
Taylor,
Graham
W
.
,
Fergus,
Rob,
LeCun,
Yann
and
Bregler,
Christoph,
Proceedings
of
the
11
th
European
conference
on
Computer
vision,
2010
A
Practical
Guide
to
Training
Restricted
Boltzmann
Machines
,
Geoffrey
E
.
Hinton,
University
of
Toronto,
2010
,
TR
2010

003
34
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