深層生成モデルを用いたマルチモーダルデータの半教師あり学習

¤
¤ [Guillaumin+ 10] [Cheng+ 16]
¤ end-to-end
¤ VAE [Kingma+ 14][Maaløe+ 16] GAN
[Salimans+ 16]
¤ JMVAE[Suzuki+
16]

¤ Guillaumin [Guillaumin+ 10]
¤
¤ 2
¤ MKL
¤
¤ Cheng [Cheng+ 16]
¤ RGB-D
¤ Co-training
¤
¤ ->

¤ Semi-Supervised Learning with Deep Generative Models
[Kingma+ 14]
¤
¤
!
"
#
ℒ = ℒ " + ℒ ", # + ( ) *[−log01 # " ]
34 " #, !
01 ! ", #
01 # "

¤ Joint multimodal variational autoencoders (JMVAE)[Suzuki+ 16]
¤ joint 3(", 6)
¤ " 6 ! joint representation
¤
それらの生成過程を次のように考える.
z ∼ pθ(z) (1)
x, w ∼ pθ(x, w|z) (2)
，それぞれのドメインのデータについて条件付き独立と仮定する．
pθ(x, w|z) = pθx (x|z)pθw (w|z) (3)
x
z
w
図 1 両方のドメインが観測されたときの TrVB
モデルの変分下界 L は，次のようになる．
2
01 ! ", #
34 ", 6 !
34 ", 6 ! = 34("|!)34(6|!)

¤
¤
¤
¤
¤
Sea
[blue, sky, sand,…]

SS-MVAE
¤ Semi-Supervised Multimodal Variational AutoEncoder (SS-MVAE)
¤ JMVAE
¤
L = {(x1, w1, y1, ), ...,
xi wi
∈ {0, 1}C
N , wN )}
q(y|x, w)
(a) SS-MVAE (b) SS-HMVAE
1:
2
34 ", 6 #, !01 # ", 6
34 ", 6 #, ! = 34 " #, ! 34 6 #, !
01 ! ", 6, #

SS-MVAE
¤ SS-MVAE
¤
¤
= µ + σ2
⊙ ϵ
12
Maddison 16]
1
y)dz
Ll(x, w, y) = L(x, w, y) − α · log qφ(y|x, w) (4)
α
α = 0.5 · M+N
M
J =
(xi,wi,yi)∈DL
Ll(xi, wi, yi) +
(xj ,wj )∈DU
U(xj, wj) (5)
JMVAE φ θ
qφ(y|x)
Semi-Supervised Multimodal
Variational AutoEncoder SS-MVAE
3.4 SS-HMVAE
SS-MVAE
a p(x, w, y) =
pθ(x|a)pθ(w|a)pθ(a|z, y)p(z)p(y)dadz 1
(a) (b) SS-MVAE y z x w
y z a x w
|z)pθ(z)dz
θ
z)pθ(z)
w)
]
(1)
µ + σ2
⊙ ϵ
12
ddison 16]
log p(x, w) = log pθ(x, w, z, y)dzdy
≥ Eqφ(z,y|x,w)[log
pθ(x|z, y)pθ(w|z, y)pθ(z)
qφ(z, y|x, w)
]
≡ −U(x, w) (3)
qφ(z, y|x, w) = qφ(z|x, w, y)qφ(y|x, w)
qφ(y|x)
2
Ll(x, w, y) = L(x, w, y) − α · log qφ(y|x, w) (4)
α
α = 0.5 · M+N
M
J =
(xi,wi,yi)∈DL
Ll(xi, wi, yi) +
(xj ,wj )∈DU
U(xj, wj) (5)
JMVAE φ θ
qφ(y|x)
Gumbel softmax[Jang 16, Maddison 16]
φ θ 1
3.3 SS-MVAE
JMVAE
y
p(x, w, y) = pθ(x|z, y)pθ(w|z, y)p(z)p(y)dz
1(a)
log p(x, w, y) = log pθ(x, w, z, y)dz
≥ Eqφ(z|x,w,y)[log
qφ(z|x, w, y)
]
≡ −L(x, w, y) (2)
∗1 C
JMVAE
qφ(
Se
Variational AutoEncoder SS-M
3.4
SS-MVAE
a
pθ(x|a)pθ(w|a)pθ(a|z, y)p(z)
(a) (b) SS-MVAE
q(a, z|x, w, y) =
q(z|x, w, y) =
p(z|x, w, y)
Gulrajani 16]
2
12
φ θ 1
3.3 SS-MVAE
JMVAE
y
1(a)
qφ(z|x, w, y)
]
≡ −L(x, w, y) (2)
∗1 C
(xi,wi,yi)∈
Variational Au
3.4
S
a
pθ(x|a)pθ(w
(a) (b)
p(z|x, w
Gulrajani 16]
2
φ θ 1
3.3 SS-MVAE
JMVAE
y
1(a)
qφ(z|x, w, y)
]
≡ −L(x, w, y) (2)
∗1 C
Va
3.
a
(a
G
1:
qφ(y|x, w)
qφ(z, y|x, w)
]
≡ −U(x, w) (3)
qφ(y|x)
2
x1, w1, y1, ), ...,
xi wi
q(y|x, w)
oder JMVAE
x w
pθ(w|z)pθ(z)dz
θ
(w|z)pθ(z)
1:
qφ(y|x, w)
qφ(z, y|x, w)
]
≡ −U(x, w) (3)
qφ(y|x)
[Kingma 14a, Rezende 14]
12
φ θ 1
3.3 SS-MVAE
JMVAE
y
1(a)
qφ(z|x, w, y)
]
J =
(xi,wi,yi)∈
Variational Au
3.4
S
a
pθ(x|a)pθ(
(a) (b)
= {(x1, w1, y1, ), ...,
xi wi
{0, 1}C
wN )}
q(y|x, w)
utoencoder JMVAE
x w
pθ(x|z)pθ(w|z)pθ(z)dz
θ
)dz
(x|z)pθ(w|z)pθ(z)
qφ(z|x, w)
]
1:
qφ(y|x, w)
qφ(z, y|x, w)
]
≡ −U(x, w) (3)
qφ(y|x)
2
0

1:
SS-HMVAE
¤ Semi-Supervised Hierarchical Multimodal Variational AutoEn-
coder (SS-HMVAE)
¤
¤
2
34 9 #, !
34 ", 6 9
01(9|", 6)
01(!|9, #)
01(#|", 6)

2
¤ SS-HMVAE 9
¤ auxiliary variables
¤
¤
[Maaløe+ 16]
DL = {(x1, w1, y1, ), ...,
xi wi
y ∈ {0, 1}C
, (xN , wN )}
N
q(y|x, w)
ional autoencoder JMVAE
x w
w) = pθ(x|z)pθ(w|z)pθ(z)dz
θ
E(x, w)
1:
qφ(y|x, w)
qφ(z, y|x, w)
]
L = {(x1, w1, y1, ), ...,
xi wi
∈ {0, 1}C
N , wN )}
q(y|x, w)
l autoencoder JMVAE
x w
= pθ(x|z)pθ(w|z)pθ(z)dz
θ
w)
1:
qφ(y|x, w)
qφ(z, y|x, w)
]
≡ −U(x, w) (3)
SS-MVAE SS-HMVAE
q(z|x, w, y) =
Z
q(a, z|x, w, y)da

¤
¤
¤
¤ Gumbel softmax[Jang+ 2016]
¤
15,000 10,000
975,000
M = 15, 000 N = 975, 000
4.2
x w
R3857
{0, 1}2000
pθ(x|z, y) = N(x|µθ(z, y), diag(σ2
θ (z, y))) (8)
pθ(w|z, y) = Ber(w|πθ(z, y)) (9)
pθ(x|a) = N(x|µθ(a), diag(σ2
θ (a))) (10)
pθ(w|a) = Ber(w|πθ(a)) (11)
y {0, 1}38
qφ(y|x, w) = Ber(y|πθ(x, w)) (12)
SS-MVAE SS-HMVAE
∗2 http://www.flickr.com
∗3 http://www.cs.toronto.edu/ñitish/multimodal/index.html
SS-HMVAE
MC=10
SS-MVAE
MAP
MAP
HMVAE
5.
2
∗4 https://github.com/Thean
∗5 https://github.com/Lasag
∗6 https://github.com/masa-
∗7 [ 16] LRAP
MAP
3
4.2
x w
R3857
{0, 1}2000
pθ(x|z, y) = N(x|µθ(z, y), diag(σ2
θ (z, y))) (8)
pθ(w|z, y) = Ber(w|πθ(z, y)) (9)
pθ(x|a) = N(x|µθ(a), diag(σ2
θ (a))) (10)
pθ(w|a) = Ber(w|πθ(a)) (11)
y {0, 1}38
qφ(y|x, w) = Ber(y|πθ(x, w)) (12)
SS-MVAE SS-HMVAE
∗2 http://www.flickr.com
∗3 http://www.cs.toronto.edu/ñitish/multimodal/index.html
MAP
MAP
HMVAE
5.
2
∗4 https://github.com/Thea
∗5 https://github.com/Lasag
∗6 https://github.com/masa
∗7 [ 16] LRAP
MAP
3
Semi-
ultimodal Variational AutoEn-
|a)pθ(w|a)pθ(a|z, y)p(z)p(y)
qφ(a, z|x, w, y)
]
(6)
p(z) = N(z|0, I) (13)
p(y) = Ber(y|π) (14)
pθ(a|z, y) = N(a|µθ(z, y), diag(σ2
θ (z, y))) (15)
qφ(a|x, w) = N(z|µθ(x, w), diag(σ2
θ (x, w))) (16)
qφ(z|a, y) = N(z|µθ(a, y), diag(σ2
θ (a, y))) (17)
rectified linear unit
Adam [Kingma 14b]

¤ Tars
¤ Tars
¤
¤
¤ Github https://github.com/masa-su/Tars
P(A,B,C,D)=P(A)P(B∣A)P(C∣A)P(D∣A,B)

Tars
¤ VAE
x = InputLayer((None,n_x))
q_0 = DenseLayer(x,num_units=512,nonlinearity=activation)
q_1 = DenseLayer(q_0,num_units=512,nonlinearity=activation)
q_mean = DenseLayer(q_1,num_units=n_z,nonlinearity=linear)
q_var = DenseLayer(q_1,num_units=n_z,nonlinearity=softplus)
q = Gauss(q_mean,q_var,given=[x])
0(!|")
z = InputLayer((None,n_z))
p_0 = DenseLayer(z,num_units=512,nonlinearity=activation)
p_1 = DenseLayer(p_0,num_units=512,nonlinearity=activation)
p_mean = DenseLayer(p_1,num_units=n_x,nonlinearity=sigmoid)
p = Bernoulli(p_mean,given=[z])
3("|!)
model = VAE(q, p, n_batch=n_batch, optimizer=adam)
lower_bound_train = model.train([train_x])

Tars
¤
¤
z = q.sample_given_x(x) #
z = q.sample_mean_given_x(x) #
log_likelihood = q.log_likelihood_given_x(x, z)
•
•
!~0(!|")
log 0 (!|")

¤ Flickr25k
¤
¤ 38 one-hot
¤ 3,857 2,000
¤
¤ 100 2 5000
-> 97 5000
desert, nature, landscape, sky rose, pink
clouds, plant life, sky, tree flower, plant life

¤
¤ SS-MVAE
¤ SS-HMVAE
¤
¤ SVM DBN Autoencoder DBM JMVAE
¤ mean average precision (mAP)
¤
3.
3.1
DL = {(x1, w1, y1, ), ...,
(xM , wM , yM )} xi wi
y ∈ {0, 1}C
∗1
DU = {(x1, w1, y1, ), ..., (xN , wN )}
M << N
q(y|x, w)
3.2 JMVAE
joint multimodal variational autoencoder JMVAE
[Suzuki 16][ 16]
z x w
p(x, w) = pθ(x|z)pθ(w|z)pθ(z)dz
VAE JMVAE θ
θ −UJMV AE(x, w)
log p(x, w) = log pθ(x, w, z)dz
≥ Eqφ(z|x,w)[log
pθ(x|z)pθ(w|z)pθ(z)
qφ(z|x, w)
]
≡ −UJMV AE(x, w) (1)
qφ(z|x, w) φ
1:
qφ(y|x, w)
qφ(z, y|x, w)
]
≡ −U(x, w) (3)
qφ(y|x)
2
3.
3.1
DL = {(x1, w1, y1, ), ...,
(xM , wM , yM )} xi wi
y ∈ {0, 1}C
∗1
DU = {(x1, w1, y1, ), ..., (xN , wN )}
M << N
q(y|x, w)
3.2 JMVAE
joint multimodal variational autoencoder JMVAE
[Suzuki 16][ 16]
z x w
p(x, w) = pθ(x|z)pθ(w|z)pθ(z)dz
VAE JMVAE θ
θ −UJMV AE(x, w)
log p(x, w) = log pθ(x, w, z)dz
≥ Eqφ(z|x,w)[log
pθ(x|z)pθ(w|z)pθ(z)
qφ(z|x, w)
]
≡ −UJMV AE(x, w) (1)
qφ(z|x, w) φ
1:
qφ(y|x, w)
qφ(z, y|x, w)
]
≡ −U(x, w) (3)
qφ(y|x)
2
SS-MVAE SS-HMVAE

mAP
SVM [Huiskes+] 0.475
DBN [Srivastava+]* 0.609
Autoencoder [Ngiam+]* 0.612
DBM [Srivastava+]* 0.622
JMVAE [Suzuki+] 0.618
SS-MVAE (MC=1) 0.612
SS-MVAE (MC=10) 0.626
SS-HMVAE (MC=1) 0.632
•
• SS-HMVAE
•
•
•
• *
• MC

¤ mAP validation curve
MAP
0.618
SS-MVAE (MC=1) 0.612
SS-MVAE (MC=10) 0.626
2: MAP
Flickr retrie
internation
trieval, pp.
[Ioﬀe 15] Ioﬀe
Acceleratin
covariate sh
[Jang 16] Jan
cal Repara
preprint ar
[Kingma 13]
Auto-encod
arXiv:1312
[Kingma 14a]
and Wellin
generative
Processing
[Kingma 14b]
stochastic o
(2014)
[Maaløe 16] M
• SS-HMVAE
• SS-MVAE JMVAE

¤ MIR Flickr25k
¤
¤
¤
¤
¤
¤ RGB-D

¤
¤ JMVAE SS-HMVAE SS-MVAE
¤ Tars
¤
¤ SS-HMVAE
¤
¤
¤
¤ GAN VAT

深層生成モデルを用いたマルチモーダルデータの半教師あり学習

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深層生成モデルを用いたマルチモーダルデータの半教師あり学習