Machine Learning (CSE 446):Generative Adversarial Networks (GANs)

Sham M Kakade

c� 2019

University of Washingtoncse446-staff@cs.washington.edu

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Announcements

I Weds is the final.

I One page of notes.

I List of topics posted tomorrow.

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Class results with random Fourier features, HW3, Q7

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AnimalSarah

Image Generation

These are computer generated images from the “bigGAN”.

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Classification

I SPAM detection.

I x is an email.

I Suppose Q(x) is the distribution over true emails.

I Suppose G(x) is spammer’s generative distribution over emails.

I usual supervised learning: make a dataset of (x, y) pairs, say with 50% labeled

true and 50% spam.

I suppose Pr✓(Y = 1|X) = D✓(X) is our model’s probably of that Y = 1, trueemail.

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T between O and F

Building Our Classifier

I Maximum likelihood is:

min✓

E log Pr✓(Y = 1|X)

I every ✓ corresponds to some model D.

I If our data is equally split, where all the Y = 1’s come from Q and and all the

Y = 0’s come from G, then:

max✓

E log Pr✓(Y = 1|X) =

maxD

✓Ex⇠Q[

1

2logD(x)] +

1

2Ex⇠G[log(1�D(x))]

◆

I Likelihood function:

L(D,G) =

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Dad PpfYAX

datadistI

DG.gl k HQ yet

fk K Egeo

whenY Ewhen4 0

I Exno I lyDaa t zExellegapas

The Spammer’s Job

I If the spam detector D was fixed, then our spammer wants to:

minG

L(G,D)

I The spammer wants to make the discriminator D’s likelihood large.

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O3small

We have a game:

I Let’s think more abstractly: D is procedure to spot fake images, G is a procedure

to generate images.

I The game can be viewed as:

minG

maxD

L(G,D) =

minG

maxD

✓Ex⇠Q[

1

2logD(x)] +

1

2Ex⇠G[log(1�D(x))]

◆

I Is this a powerful idea?

Remember AD:

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if we can get gradientseasily the let's try to play game

the Discriminator

I just binary image classification “fake or not”

I we know how to do supervised learning

I for a given G and samples from the truth Q, we can learn D.

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r learning

easy

create a labeled datasetand do binary classification

the Generator

I what is a model for generating images?

and how do we update G the model?

I let say z ⇠ N(0, I) where I is a d⇥ d matrix.

I a network:

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G Rd X GCEimage space z Source of

randomness

randy d

GCE image

the Generator network

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2 2256O O O O Oinput we

Z O O O O O

convolutional 0 O O O O G G O Oout

Wd256 2356 256imageoutput 7 o o o o

256 toooo o

Learning

I Fix G, update D.

easy: just supervised learning.

I Now fix D. Recall:

L(G,D) =

✓Ex⇠Q[

1

2logD(x)] +

1

2Ex⇠G[log(1�D(x))]

◆

=

✓Ex⇠Q[

1

2logD(x)] +

1

2Ez⇠Normal(0,I)[log(1�D(G(z)))]

◆

I We can estimate this loss easily. Why?

I Update G: how?

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for Gfix Dfeesy

Mis 6 D T nQ w

Sam Ie z'sworth SGD use AD to

gradients easily

Convergence/Comments

I Does it converge?

Subtle: we are not ”hill climbing” on an on an objective.

I at best, we can get to an equilibrium.

I Comparison to EM and likelihood based approaches:

I Computing the the probability of x under G is di�cult.

di�culty for EM.

I “mode collapse” with GANs

sampling distribution not reflective of the truth.

I NLP generative methods do not use GANs!

(better results with direct training approaches)

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Whichfaceisreal.com

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We can get creativeStyle transfer. From the “cycleGAN”

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Thank you!!

Thank you for the hard work!

I Good luck on the final and have a great spring break.

I You have a good toolkit.

Please participate in the larger ML community!

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