Brief introduction on GAN

Generative Adversarial
Networks
Dai-‐Hai
Nguyen
Bioinformatics
Center
Kyoto
University
28/04/2018 1

Outline
• Overview
of
generative
models
• Variational AutoEncoder (VAE)
• Generative
Adversarial
Networks
(GAN)
• GAN:
applications
• Conclusion
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Generative Models
28/04/2018 3

Supervised vs. Unsupervised Learning
• Supervised Learning
Data : (x, y)
x: data, y: label
Goal: Learn a function f to map x-> y
Tasks: Classification, Regression, Detection, etc
http://cs231n.stanford.edu/slides/2017/cs231n_2017_lecture13.pdf
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Supervised vs. Unsupervised Learning
• Unsupervised Learning
Data : only data x, no label y
Goal: Learn some underlying hidden structures of data
Tasks: clustering, dim reduction, density estimation, etc.
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Unsupervised Learning
• Taxonomy tree of unsupervised leanring
Source:
https://allenlu2007.wordpress.com/2018/01/10/variational-autoencoder-的原理/
28/04/2018 6

Generative models
• Goal:
Given training samples, generate new samples from the
same distribution
Training data ~ 𝑝"#$#(𝑥) Generated samples ~ 𝑝()"*+(𝑥)
In other words, try to learn a model 𝑝()"*+(𝑥) similar to 𝑝"#$#(𝑥)
28/04/2018 7

Generative models
• Maximum Likelihood Estimation (MLE):
Given training samples 𝑥,, 𝑥.,…, 𝑥/, how to learn 𝑝()"*+ 𝑥; 𝜃 from
which training samples are likely to be generated
𝜃∗
= 𝑎𝑟𝑔𝑚𝑎𝑥8 9 log
𝑝()"*+(𝑥>; 𝜃)
/
>?,
28/04/2018 8

Unsupervised Learning
• RECAP
Source:
28/04/2018 9

Variational Auto-Encoder (VAE)
28/04/2018 10

Variational Autoencoder
• (probabilistic) generative model to generate samples from latent
variable.
• Assumption: training data {𝑥,, 𝑥.,…, 𝑥/} is generated from latent
variable 𝑧
Sample 𝑥~𝑝8(𝑥|𝑧)
Sample z~𝑝(𝑧)
Vary
z1
Vary
z2
Example:

Samples
x
are
face
images
Latent
z
is
2d
vector:
Z1:
head
orientation
Z2
:
degree
of
smile
28/04/2018 11

• How to learn the model?
MLE again !
𝜃∗
= 𝑎𝑟𝑔𝑚𝑎𝑥8 9 log 𝑝8(𝑥>)
/
>?,
Where 𝑝8 𝑥 = ∫ 𝑝8 𝑥 𝑧 𝑝 𝑧 𝑑𝑧E
-> intractable to compute
• Solution: Variational Approximation
28/04/2018 12

• Variational approximation
log 𝑝8(𝑥) can be written as the following formulation:
Likelihood
term
to
quantifyhow
good

the
sample
is

reconstructed
from
z.
This
can

be
estimated
by
a
network.
KL
divergence
term
to
estimate
the

difference
between
two
distribution
This
has
good
form
if
both
of

distributions
are
Gaussian-‐>
easy
to

estimate
This
KL
divergence
term
is
intractable

because
p(z|x)
cannot
computed.
But
it
is
aways >=
0
28/04/2018 13

Tractable
lower
bound
(ELBO)
28/04/2018 14

Tractable
lower
bound
(ELBO) Strategy:
• Maxmizing ELBO instead of intractable logp(x)
• What to be modeled:
1. 𝑝8(𝑥|𝑧) by a network (decoder)
2. 𝑞J 𝑥 𝑥 by another network (encoder)
28/04/2018 15

Variational Autoencoder: model
q training
Make q(z|x)
close to p(z)Minimize
reconstruction
error
28/04/2018 16

Variational Autoencoder: model
q Sampling: use decoder network only and sample z from prior
Sample
z
from
N(0,
I)
28/04/2018 17

Variational Autoencoder: generated
samples
28/04/2018 18

Reminder
• Taxonomy tree of unsupervised leanring
Source:
28/04/2018 19

Generative Adversarial Network (GAN)
28/04/2018 20

Generative Adversarial Network: Idea
Key
points:
q Belongs
to
“Implicit
density”
group
and
“hot”
method
in
ML
by
Goodfellow
q Motivated
by
game
theory
q Two
players:
1. Generator
tries
to
generate
“fake”

samples
from
its
model
2. Discriminator
tries
to
distinguish

“fake”
and
“real”
samples
28/04/2018 21

GAN: Two player game
Model:
q Generator
network:
try
to
fool
the
discriminator
by
generating
“like-‐‑real”

images
qDiscriminator
network:
try
to
distinguish
real
and
fake
samples
28/04/2018 22

Objective
fucntion:
Loss
for
real
data
x Loss
for
fake
data
x
How
this
work
-‐‑ D
tries
to
maximize
the
cost
such
that
D(x)
close
to
1
(for
real
x)
and
D(G(z))

close
to
0
(fake)
-‐‑ G
tries
to
minimize
the
cost
such
that
D(G(z))
is
close
to
1
(try
to
make
generated
samples
real-‐‑looking
as
much
as
possible,
to
fool
D)
28/04/2018 23

Objective
fucntion:
Loss
for
real
data
x Loss
for
fake
data
x
How
to
train:
alternative
approach
-‐‑ Fix
G,
D
maximize
the
cost
-‐‑ Fix
D,
G
minimize
the
cost
28/04/2018 24

GAN: density ratio estimation
Density
estimation
via
density
ratio
estimation:
28/04/2018 25

Generative Adversarial Network: Result
Some
generated
samples
28/04/2018 26

GAN: Applications
28/04/2018 27

GAN: applications
Image-‐‑to-‐‑Image
translation
Goal:
learn
a
mapping
from

input
image-‐‑>output
image
Ref:

Image-‐to-‐Image
Translation
with
Conditional
Adversarial
Networks,
CVPR201628/04/2018 28

GAN: applications
translation
Generator:

• In:
noise
+
input
image;
Out:
sample
Discriminator:

§ In:
pairs
of
in/out
images;
Out:
fake/real
Optimization:
Where
Encourage
less
blurring
Similar
to
original
GAN
28/04/2018 29

GAN: applications
translation
Result:
Ref:

Image-‐to-‐Image
Translation
with
Conditional
Adversarial
Networks,
CVPR201628/04/2018 30

GAN: applications
Text-‐‑to-‐‑Image
translation
Goal:
learn
a
mapping
from

input
text>output
image
Ref:

Generative
Adversarial
Text
to
Image
Synthesis,
ICML201628/04/2018 31

GAN: applications
translation
Generator:

• In:
noise
+
text
;
Out:
image
Discriminator:

§ In:
pairs
of
text/
images;
Out:
fake/real
Model:
28/04/2018 32

GAN: applications
translation
Result:
Ref:

Generative
Adversarial
Text
to
Image
Synthesis,
ICML201628/04/2018 33

Conclusion
• Taxonomy tree of unsupervised leanring, AGAIN!
Source:
28/04/2018 34

Brief introduction on GAN

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