Metody Deep Learning - Wykład 6

Jun 3, 20150 likes1,007 views

Szósta część wykładów na temat deep learning i uczenia maszynowego. Prowadzone były na AGH, przez firme Craftinity (Craftinity.com), razem z kołem naukowym BIT (http://knbit.edu.pl/pl/)

1.Feed Forward NN
2. NN - training
3. Probabilistic
graphical models
4. Restricted
Boltzmann machines
5. Autoencoders
6. Deep learning
7. Convolutional
NNs

Autoencoder
W
W⇤
= WT
Decoder
Encoder
ˆx = sigm(c + W⇤
h(x))
h(x) = sigm(b + Wx)x
h(x)
ˆx

Loss function
• dla danych binarnych
• dla danych liniowych
l(x, ˆx) =
X
k
(xk log (ˆxk) + (1 xk) log (1 ˆxk))
l(x, ˆx) =
1
2
X
k
(xk ˆxk)2

Trenowanie
• możemy minimalizować koszt metodą gradient descent
• dla obu przypadków funkcji kosztu gradient względem
aktywacji ma taką samą formę:
Oa(x)l(x, ˆx) = ˆx x
• gradienty wag oraz biasów możemy uzyskać propagacją
wsteczną

Adaptacja do wejścia
• wybieramy łączny rozkład nad wejściem p(x | µ)
gdzie µ to wektor parametrów tego rozkładu
• wybieramy relację pomiędzy wektorem µ
i ukrytą warstwą h(x)
• użyj jako funkcji kosztu:
l(x) = log p(x | µ)

Undercomplete Hidden
Layer
• warstwa ukryta kompresuje wejście
W
W⇤
= WT
• warstwa ukryta dobrze modeluje dane
treningowe, ale źle inne wejścia

Overcomplete Hidden Layer
W
W⇤
= WT
• nie ma kompresji w warstwie środkowej
• warstwa ukryta może nauczyć się identyczności
• nie ma gwarancji, że ukryte jednostki nauczą się
znaczącej reprezentacji

Denoising autoencoder
W
W⇤
= WT
x
h(x)
ˆx
˜x
p(˜x | x)
• dodajemy szum do
wejścia
• rekonstrukcja obliczana z
zaszumionego wejścia
• loss function porównuje
rekontrukcję z
autentycznym wejściem

Intuicja
x
x˜x
˜x
ˆx = sigm(c + Wh(˜x))
p(˜x | x)

• Stacked Denoising Autoencoders: Learning
Useful Representations in a Deep Network with a
Local Demonising Criterion - Vincent, Larochelle,
Lajoie, Bengio Manzagol, 2008
• A Connection Between Score Matching and
Denoising Autoencoders - Vincent, 2011

Filtry
(Vincent, Larochelle, Bengio i Manzagol, ICML 2008)
• bez szumu

Filtry
(Vincent, Larochelle, Bengio i Manzagol, ICML 2008)
• 25% szumu

Filtry
(Vincent, Larochelle, Bengio i Manzagol, ICML 2008)
• 50% szumu

Idea: karanie
modelowania wszystkich
danych

Contractive Autoencoder
W
W⇤
= WT
h(x)
ˆx
˜x
• dodajemy składnik do funkcji kosztu,
który penalizuje nieinteresujące nas
rozwiązania
• chcemy ekstrachować tylko cechy, które
odzwierciedlają wariacje danych ze
zbioru treningowego
• model ma być inwariantny na inne
wariacje

Contractive Autoencoder
l(x, ˆx) + kOxh(x)k
2
F
Nowa funkcja kosztu:
Dla binarnych obserwacji:
l(x, ˆx) =
X
k
(xk log (ˆxk) + (1 xk) log (1 ˆxk))
kOxh(x)k
2
F =
X
j
X
k
(
@h(x)j
@xk
)2

Intuicja
encoder musi być wrażliwy
na takie wariecje, żeby
dobrze rekonstruować dane
encoder nie powinien być
wrażliwy na wariację nie
zaobserwowaną w zbiorze
treningowym

Contractive Auto-Encoders:
Explicit Invariance During Feature
Extraction - Rifai, Vincent, Muller,
Glorot, Bengio, 2011

Demo
https://github.com/Craftinity/DA-
AGH

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Metody Deep Learning - Wykład 6

1. Metody Deep Learning

2. Autoencoders

3. 1.Feed Forward NN 2. NN - training 3. Probabilistic graphical models 4. Restricted Boltzmann machines 5. Autoencoders 6. Deep learning 7. Convolutional NNs

4. Dlaczego?

5. Przykład: redukcja wymiarowości - PCA

6. Przykład: redukcja wymiarowości - DAE

7. Autoencoder W W⇤ = WT Decoder Encoder ˆx = sigm(c + W⇤ h(x)) h(x) = sigm(b + Wx)x h(x) ˆx

8. Loss function • dla danych binarnych • dla danych liniowych l(x, ˆx) = X k (xk log (ˆxk) + (1 xk) log (1 ˆxk)) l(x, ˆx) = 1 2 X k (xk ˆxk)2

9. Trenowanie • możemy minimalizować koszt metodą gradient descent • dla obu przypadków funkcji kosztu gradient względem aktywacji ma taką samą formę: Oa(x)l(x, ˆx) = ˆx x • gradienty wag oraz biasów możemy uzyskać propagacją wsteczną

10. Adaptacja do wejścia • wybieramy łączny rozkład nad wejściem p(x | µ) gdzie µ to wektor parametrów tego rozkładu • wybieramy relację pomiędzy wektorem µ i ukrytą warstwą h(x) • użyj jako funkcji kosztu: l(x) = log p(x | µ)

11. Jaka może być warstwa ukryta?

12. Undercomplete Hidden Layer • warstwa ukryta kompresuje wejście W W⇤ = WT • warstwa ukryta dobrze modeluje dane treningowe, ale źle inne wejścia

13. Overcomplete Hidden Layer W W⇤ = WT • nie ma kompresji w warstwie środkowej • warstwa ukryta może nauczyć się identyczności • nie ma gwarancji, że ukryte jednostki nauczą się znaczącej reprezentacji

14. Jak zapobiec uczeniu się ��Գٲ⳦��Դ�ś��?

15. Idea: reprezentacja odporna na szum

16. Denoising autoencoder W W⇤ = WT x h(x) ˆx ˜x p(˜x | x) • dodajemy szum do wejścia • rekonstrukcja obliczana z zaszumionego wejścia • loss function porównuje rekontrukcję z autentycznym wejściem

17. Intuicja x x˜x ˜x ˆx = sigm(c + Wh(˜x)) p(˜x | x)

18. • Stacked Denoising Autoencoders: Learning Useful Representations in a Deep Network with a Local Demonising Criterion - Vincent, Larochelle, Lajoie, Bengio Manzagol, 2008 • A Connection Between Score Matching and Denoising Autoencoders - Vincent, 2011

19. Filtry (Vincent, Larochelle, Bengio i Manzagol, ICML 2008) • bez szumu

20. Filtry (Vincent, Larochelle, Bengio i Manzagol, ICML 2008) • 25% szumu

21. Filtry (Vincent, Larochelle, Bengio i Manzagol, ICML 2008) • 50% szumu

22. Idea: karanie modelowania wszystkich danych

23. Contractive Autoencoder W W⇤ = WT h(x) ˆx ˜x • dodajemy składnik do funkcji kosztu, który penalizuje nieinteresujące nas rozwiązania • chcemy ekstrachować tylko cechy, które odzwierciedlają wariacje danych ze zbioru treningowego • model ma być inwariantny na inne wariacje

24. Contractive Autoencoder l(x, ˆx) + kOxh(x)k 2 F Nowa funkcja kosztu: Dla binarnych obserwacji: l(x, ˆx) = X k (xk log (ˆxk) + (1 xk) log (1 ˆxk)) kOxh(x)k 2 F = X j X k ( @h(x)j @xk )2

25. Intuicja encoder musi być wrażliwy na takie wariecje, żeby dobrze rekonstruować dane encoder nie powinien być wrażliwy na wariację nie zaobserwowaną w zbiorze treningowym

26. Contractive Auto-Encoders: Explicit Invariance During Feature Extraction - Rifai, Vincent, Muller, Glorot, Bengio, 2011

27. Demo https://github.com/Craftinity/DA- AGH

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Metody Deep Learning - Wykład 6

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