Original: For q ψ ( s, z | x, d s ) , we concatenate outputs of feature extractors of X and d s : the feature extractor for x is composed of four Convolution-Batch
Revised: For q ψ ( s, z | x, d s ) , we concatenate outputs of feature extractors of X and d s : the feature extractor for x is composed of four Convolution-Batch

Original: Normalization-ReLU (CBNR) blocks and four Convolution-Batch Normalization-ReLU-MaxPooling (CBNR-MP) blocks with structure 64 BNR → 128 CBNR-MP → 128 CBNR → 256 CBNR-MP → 256 CBNR → 512 CBNR-MP → 512 CBNR → 1024 CBNR-MP; the feature extractor of c is composed of three Fully Connection-Batch Normalization-ReLU (FC-BNR) blocks with structure 128 → 256 → 512.
Revised: Normalization-ReLU (CBNR) blocks and four Convolution-Batch Normalization-ReLU-MaxPooling (CBNR-MP) blocks with structure 64 BNR → 128 CBNR-MP → 128 CBNR → 256 CBNR-MP → 256 CBNR → 512 CBNR-MP → 512 CBNR → 1024 CBNR-MP; the feature extractor of c is composed of three Fully Connection-Batch Normalization-ReLU (FC-BNR) blocks with structure 128 → 256 → 512.

Original: The concatenated features are further transformed by four 64 FC-BNR to generate µ s,z
Revised: The concatenated features are further transformed by four 64 FC-BNR to generate µ s,z

Original: ( x, d s ) and log σ s,z ( x, d s ) .
Revised: ( x, d s ) and log σ s,z ( x, d s ) .

Original: For the prior model p θ ( s, z | d s ) , it shares the same structure without feature extractor of x .
Revised: For the prior model p θ ( s, z | d s ) , it shares the same structure without feature extractor of x .

Original: For p φ ( x | s, z ) , the network is composed of three DeConvolution-Batch
Revised: For p φ ( x | s, z ) , the network is composed of three DeConvolution-Batch

Original: Normalization-ReLU (DCBNR) blocks and three Convolution-Batch Normalization-ReLU (CBNR) blocks, followed by a convolutional layer, with structure 256 DCBNR → 256 CBNR → 128 DCBNR → 128 CBNR → 64 DCBNR → 64 CBNR → 48 Conv.
Revised: Normalization-ReLU (DCBNR) blocks and three Convolution-Batch Normalization-ReLU (CBNR) blocks, followed by a convolutional layer, with structure 256 DCBNR → 256 CBNR → 128 DCBNR → 128 CBNR → 64 DCBNR → 64 CBNR → 48 Conv.

Original: For p φ ( y | s ) , the network is composed of
Revised: For p φ ( y | s ) , the network is composed of

Original: FC-BNR → 512 FC-BNR → 3 FC-BNR.
Revised: FC-BNR → 512 FC-BNR → 3 FC-BNR.

Original: For prior model p φ ( s, z | d s ) N ( µ s,z ( d s ) , diag( σ 2 s,z ( d s )))
Revised: For prior model p φ ( s, z | d s ) N ( µ s,z ( d s ) , diag( σ 2 s,z ( d s )))

Original: the µ s,z ( x, d s ) and log σ s,z ( x, d s ) are parameterized by Multi Perceptron Neural Network (MLP).
Revised: the µ s,z ( x, d s ) and log σ s,z ( x, d s ) are parameterized by Multi Perceptron Neural Network (MLP).

Original: The decoders p φ ( x | s, z ) are p φ ( y | s ) parameterized by Deconvolutional neural network.
Revised: The decoders p φ ( x | s, z ) are p φ ( y | s ) parameterized by Deconvolutional neural network.

Original: For all methods, we train for 200 epochs using SGD with weight decay 2 × 10 − 4 and learning rate 0. and is multiplied by 0.2 after every 60 epochs.
Revised: For all methods, we train for 200 epochs using SGD with weight decay 2 × 10 − 4 and learning rate 0.01 and is multiplied by 0.2 after every 60 epochs.

Revised: The batch size is set to 4.

Original: For each variable in biomarker vector C ∈ R 9 , each person may have multiple records, and we take its median as representative to avoid extreme values due to device abnormality.
Revised: For each variable in biomarker vector C ∈ R 9 , each person may have multiple records, and we take its median as representative to avoid extreme values due to device abnormality.

Original: As for LaCIM- d , we adopt the same decoder p φ ( x | z, s ) and classiﬁer p φ ( y | s ) .
Revised: As for LaCIM- d , we adopt the same decoder p φ ( x | z, s ) and classiﬁer p φ ( y | s ) .

Original: For q ψ ( s, z | x, d ) , we adopt the same network for the shared part; for the part speciﬁc to each domain, µ s,z ( x, d ) and log σ s,z ( x, d ) are generated by the sub-network which is composed of 1024 FC-BNR →
Revised: For q ψ ( s, z | x, d ) , we adopt the same network for the shared part; for the part speciﬁc to each domain, µ s,z ( x, d ) and log σ s,z ( x, d ) are generated by the sub-network which is composed of 1024 FC-BNR →

Original: FC-BNR → q z,s FC-BNR.
Revised: FC-BNR → q z,s FC-BNR.

Original: The z, s can be reparameterized by µ s,z
Revised: The z, s can be reparameterized by µ s,z

Original: ( x, d ) and log σ s,z ( x, d ) are fed into a sub-network which is composed of q z,s FC-BNR → 1024 FC-BNR → q z,s FC-BNR to get rid of the constraint of Gaussian distribution.
Revised: ( x, d ) and log σ s,z ( x, d ) are fed into a sub-network which is composed of q z,s FC-BNR → 1024 FC-BNR → q z,s FC-BNR to get rid of the constraint of Gaussian distribution.

Original: Then the reconstructed images and predicted label are computed by p φ ( x | z, s ) and p φ ( y | s ) which have the same network structure of LaCIM-C with the z, s .
Revised: Then the reconstructed images and predicted label are computed by p φ ( x | z, s ) and p φ ( y | s ) which have the same network structure of LaCIM-C with the z, s .

Original: [Table]
Revised: [Table]

Original: The d s variable in training and test.
Revised: The d s variable in training and test.

Original: The selected attributes include Education Years, Age, Gender (0 denotes male and 1 denotes female), AV45, amyloid β and TAU.
Revised: The selected attributes include Education Years, Age, Gender (0 denotes male and 1 denotes female), AV45, amyloid β and TAU.

Original: We split the data into m =training environments and test according to different value of d s .
Revised: We split the data into m =training environments and test according to different value of d s .

Original: The Tab. 7.13 describes the data distribution in terms of number of samples, the value of d s (Age and TAU).
Revised: The Tab. 7.13 describes the data distribution in terms of number of samples, the value of d s (Age and TAU).

Original: 7.13. E XPERIMENTS WITH C OMPLETE O BSERVABLE S OURCE V ARIABLE
Revised: 7.13. E XPERIMENTS WITH C OMPLETE O BSERVABLE S OURCE V ARIABLE

Original: In image-based diagnosis, the personal attributes, genes and biomarkers are often available.
Revised: In image-based diagnosis, the personal attributes, genes and biomarkers are often available.

Original: Therefore, we consider the setting when d s can be fully observed.
Revised: Therefore, we consider the setting when d s can be fully observed.

Original: In this case, the value of d s is person-byperson.
Revised: In this case, the value of d s is person-byperson.

Original: Therefore, the number of environments m is equal to the number of samples.
Revised: Therefore, the number of environments m is equal to the number of samples.

Original: In this case, the dataset turns to { x i , y i , d is } ni =1 .
Revised: In this case, the dataset turns to { x i , y i , d is } ni =1 .

Original: The expected risk turns to:
Revised: The expected risk turns to:

Original: [Equation] [Equation]
Revised: [Equation] [Equation]

Original: And the corresponding empirical risk is:
Revised: And the corresponding empirical risk is:

Original: [Equation]
Revised: [Equation]

Original: The d s here is re-deﬁned as the 9-dimensional vector that includes all attributes, genes and biomarkers mentioned above.
Revised: The d s here is re-deﬁned as the 9-dimensional vector that includes all attributes, genes and biomarkers mentioned above.

Original: We re-split the data into 80% train and 20% test, according to different average value of speciﬁc variable in the whole vector d s .
Revised: We re-split the data into 80% train and 20% test, according to different average value of speciﬁc variable in the whole vector d s .

Original: The d s variable in training and test We implemented OOD tasks in which the value of d s is different between training and test.
Revised: The d s variable in training and test We implemented OOD tasks in which the value of d s is different between training and test.

Original: Speciﬁcally, we repeatedly split the dataset into the training and the test according to a selected attribute in d s for three times.
Revised: Speciﬁcally, we repeatedly split the dataset into the training and the test according to a selected attribute in d s for three times.

Original: The average value of these attributes in train and test are recorded in Table 7.13.1.
Revised: The average value of these attributes in train and test are recorded in Table 7.13.1.

Original: Experimental Results We conduct OOD experiments with source variables Age, Gender, amyloid β and TAU different between training data and the test.
Revised: Experimental Results We conduct OOD experiments with source variables Age, Gender, amyloid β and TAU different between training data and the test.

Original: The results are shown in Table 12.
Revised: The results are shown in Table 12.

Original: 7. S UPPLEMENTARY FOR D EEPFAKE
Revised: 7. S UPPLEMENTARY FOR D EEPFAKE

Original: Implementation Details.
Revised: Implementation Details.

Original: We implement data augmentations, speciﬁcally images with 30 angle rotation, with ﬂipping horizontally with 50% probability.
Revised: We implement data augmentations, speciﬁcally images with 30 angle rotation, with ﬂipping horizontally with 50% probability.

Original: We additionally apply random compressing techniques, such as JpegCompression.
Revised: We additionally apply random compressing techniques, such as JpegCompression.

Original: For inference model, we adopt Efﬁcient-B

Revised: For inference model, we adopt Efﬁcient-B

Original: Tan and Le (2019), with the detailed network structure as: FC(2048, 2048) → BN → ReLU → FC(2048, 2048) → BN → ReLU → FC(2048, q t =
Revised: Tan and Le (2019), with the detailed network structure as: FC(2048, 2048) → BN → ReLU → FC(2048, 2048) → BN → ReLU → FC(2048, q t =

Original: s,z ).
Revised: s,z ).

Original: The structure of reparameterization, i.e. , ρ t = s,z is FC( q t =
Revised: The structure of reparameterization, i.e. , ρ t = s,z is FC( q t =

Original: s,z , 2048)
Revised: s,z , 2048)

Original: → BN → ReLU → FC(2048, 2048) → BN → ReLU → FC(2048, q t = s,z ).
Revised: → BN → ReLU → FC(2048, 2048) → BN → ReLU → FC(2048, q t = s,z ).

Original: The network structure for generative model, i.e. , p ψ ( x | s, z ) is TConv-BN-ReLU( q t
Revised: The network structure for generative model, i.e. , p ψ ( x | s, z ) is TConv-BN-ReLU( q t

Original: = s,z , 256) →
Revised: = s,z , 256) →

Original: TConv-BN-ReLU(256, 128)
Revised: TConv-BN-ReLU(256, 128)

Original: → TConv-BN-ReLU(128, 64) → TConv-BN-ReLU(64, 32)
Revised: → TConv-BN-ReLU(128, 64) → TConv-BN-ReLU(64, 32)

Original: → TConv-BN-ReLU(32, 32) →
Revised: → TConv-BN-ReLU(32, 32) →

Original: TConv-BN-ReLU(32, 16) → TConv-BN-ReLU(16, 16) → Conv-BN-ReLU(16, 3)
Revised: TConv-BN-ReLU(32, 16) → TConv-BN-ReLU(16, 16) → Conv-BN-ReLU(16, 3)

Original: → Sigmoid,
Revised: → Sigmoid,

Original: [Table] [Table]
Revised: [Table] [Table]

Original: T a b l e 13 :
Revised: T a b l e 13 :

Original: G e n e r a l fr a m e w o r k t a b l e f o r ou r m e t h od a nd b a s e li n e s on
Revised: G e n e r a l fr a m e w o r k t a b l e f o r ou r m e t h od a nd b a s e li n e s on

Original: D a t a ∈ {
Revised: D a t a ∈ {

Original: C M
Revised: C M

Original: N I S
Revised: N I S

Original: T , N
Revised: T , N

Original: I C O ,
Revised: I C O ,

Original: ADN
Revised: ADN

Original: I , D ee p F a k e }
Revised: I , D ee p F a k e }

Original: D a t a s e t .
Revised: D a t a s e t .

Original: W e d e no t e t
Revised: W e d e no t e t

Original: h e d i m e n s i on o f
Revised: h e d i m e n s i on o f

Original: z o
Revised: z o

Original: [Table]
Revised: [Table]

Original: z s a
Revised: z s a

Original: [Table]
Revised: [Table]

Original: d i m z , z s .
Revised: d i m z , z s .

Original: W e li s t t h e ou t pu
Revised: W e li s t t h e ou t pu

Original: t d
Revised: t d

Original: i m e n s i on ( e .
Revised: i m e n s i on ( e .

Original: g .
Revised: g .

Original: t h e c h a nn e l nu m
Revised: t h e c h a nn e l nu m

Original: [Table]
Revised: [Table]

Original: e
Revised: e

Original: [Table] [Table]
Revised: [Table] [Table]

Original: f
Revised: f

Original: [Table]
Revised: [Table]

Original: m odu l e , i f it
Revised: m odu l e , i f it

Original: [Table]
Revised: [Table]

Original: i ff
Revised: i ff

Original: [Table]
Revised: [Table]

Original: e n
Revised: e n

Original: [Table]
Revised: [Table]

Original: e i
Revised: e i

Original: [Table]
Revised: [Table]

Original: a t a :
Revised: a t a :

Original: [Table]
Revised: [Table]

Original: M N I S
Revised: M N I S

Original: [Table]
Revised: [Table]

Original: E n c D a t a x
Revised: E n c D a t a x

Original: F C (, d i m z )
Revised: F C (, d i m z )

Original: D ec - C E
Revised: D ec - C E

Original: D a t a y
Revised: D a t a y

Original: E n c D a t a x ; E n c D a t a d
Revised: E n c D a t a x ; E n c D a t a d

Original: F C (, d i m z )
Revised: F C (, d i m z )

Original: D ec - C E
Revised: D ec - C E

Original: D a t a y
Revised: D a t a y

Original: E n c D a t a x
Revised: E n c D a t a x

Original: F C - B N - R e L U ( 256 , 256 )
Revised: F C - B N - R e L U ( 256 , 256 )

Original: F C (, 256 ) →
Revised: F C (, 256 ) →

Original: z
Revised: z

Original: D ec D a t a y ; D ec D a t a x
Revised: D ec D a t a y ; D ec D a t a x

Original: E n c D a t a x
Revised: E n c D a t a x

Original: DANN - C L
Revised: DANN - C L

Original: S D a t a y ;
Revised: S D a t a y ;

Original: DANN - C L
Revised: DANN - C L

Original: S D a t a y p D a t a θ ( x | z d , z x , z y )
Revised: S D a t a y p D a t a θ ( x | z d , z x , z y )

Original: p D a t a θ d ( z d | d ) p D a t a θ y
Revised: p D a t a θ d ( z d | d ) p D a t a θ y

Original: ( z y | y )
Revised: ( z y | y )

Original: q D a t a φ d ( z d | x ) q D a t a φ x ( z x | x ) q D a t a φ y
Revised: q D a t a φ d ( z d | x ) q D a t a φ x ( z x | x ) q D a t a φ y

Original: ( z y | x )
Revised: ( z y | x )

Original: E n c D a t a x ; E n c D a
Revised: E n c D a t a x ; E n c D a

Original: [Table]
Revised: [Table]

Original: a d
Revised: a d

Original: F C
Revised: F C

Original: [Table]
Revised: [Table]

Original: N
Revised: N

Original: [Table]
Revised: [Table]

Original: F C (
Revised: F C (

Original: [Table] [Table]
Revised: [Table] [Table]

Original: m
Revised: m

Original: [Table]
Revised: [Table]

Original: s )
Revised: s )

Original: [Table]
Revised: [Table]

Original: a
Revised: a

Original: [Table]
Revised: [Table]

Original: p
Revised: p

Original: [Table]
Revised: [Table]

Original: i
Revised: i

Original: [Table]
Revised: [Table]

Original: E
Revised: E

Original: [Table] [Table]
Revised: [Table] [Table]

Original: m
Revised: m

Original: [Table] [Table]
Revised: [Table] [Table]

Original: m
Revised: m

Original: [Table]
Revised: [Table]

Original: # o f P a r a m s 1 .
Revised: # o f P a r a m s 1 .

Original: 12 M 1 .
Revised: 12 M 1 .

Original: 16 M
Revised: 16 M

Original: [Table]
Revised: [Table]

Original: M
Revised: M

Original: [Table] [Table]
Revised: [Table] [Table]

Original: M
Revised: M

Original: [Table]
Revised: [Table]

Original: M 1 .
Revised: M 1 .

Original: [Table]
Revised: [Table]

Original: M
Revised: M

Original: [Table]
Revised: [Table]

Original: M hyp e r- P a r a m s l r : 0 .w
Revised: M hyp e r- P a r a m s l r : 0 .w

Original: d : 0 .
Revised: d : 0 .

Original: l r : 0 .w
Revised: l r : 0 .w

Original: d : 0 .
Revised: d : 0 .

Original: l r : 0 .
Revised: l r : 0 .

Original: 01 w d : 0 .
Revised: 01 w d : 0 .

Original: l r : 0 .w
Revised: l r : 0 .w

Original: d : 0 .
Revised: d : 0 .

Original: l r : 0 .
Revised: l r : 0 .

Original: w d : 0 .
Revised: w d : 0 .

Original: 000l r : 0 .w
Revised: 000l r : 0 .w

Original: d
Revised: d

Original: [Table]
Revised: [Table]

Original: l r
Revised: l r

Original: [Table] [Table]
Revised: [Table] [Table]

Original: D a t a : N I
Revised: D a t a : N I

Original: C O
Revised: C O

Original: E n c D a t a x
Revised: E n c D a t a x

Original: F C ( 1024 , d i m z )
Revised: F C ( 1024 , d i m z )

Original: D ec - C E
Revised: D ec - C E

Original: D a t a y
Revised: D a t a y

Original: E n c D a t a x ; E n c D a t a d
Revised: E n c D a t a x ; E n c D a t a d

Original: F C (, d i m z )
Revised: F C (, d i m z )

Original: D ec - C E
Revised: D ec - C E

Original: D a t a y
Revised: D a t a y

Original: E n c D a t a x
Revised: E n c D a t a x

Original: F C - B N - R e L U (,)
Revised: F C - B N - R e L U (,)

Original: F C ( 1024 , 1024 )
Revised: F C ( 1024 , 1024 )

Original: → z
Revised: → z

Original: D ec D a t a y ; D ec D a t a x
Revised: D ec D a t a y ; D ec D a t a x

Original: E n c D a t a x
Revised: E n c D a t a x

Original: DANN - C L
Revised: DANN - C L

Original: S D a t a y ;
Revised: S D a t a y ;

Original: DANN - C L
Revised: DANN - C L

Original: S D a t a y p D a t a θ ( x | z d , z x , z y )
Revised: S D a t a y p D a t a θ ( x | z d , z x , z y )

Original: p D a t a θ d ( z d | d ) p D a t a θ y
Revised: p D a t a θ d ( z d | d ) p D a t a θ y

Original: ( z y | y )
Revised: ( z y | y )

Original: q D a t a φ d ( z d | x ) q D a t a φ x ( z x | x ) q D a t a φ y
Revised: q D a t a φ d ( z d | x ) q D a t a φ x ( z x | x ) q D a t a φ y

Original: ( z y | x )
Revised: ( z y | x )

Original: E n c D a t a
Revised: E n c D a t a

Original: [Table]
Revised: [Table]

Original: ; E n c D a t
Revised: ; E n c D a t

Original: [Table]
Revised: [Table]

Original: d
Revised: d

Original: F C (
Revised: F C (

Original: [Table] [Table]
Revised: [Table] [Table]

Original: m
Revised: m

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table]
Revised: [Table]

Original: #o f P a r a m s ( m = 8 ) 18 .
Revised: #o f P a r a m s ( m = 8 ) 18 .

Original: 08 M 19 .
Revised: 08 M 19 .

Original: M
Revised: M

Original: [Table]
Revised: [Table]

Original: 70 M 19 .
Revised: 70 M 19 .

Original: 13 M
Revised: 13 M

Original: [Table]
Revised: [Table]

Original: 86 M 16 .
Revised: 86 M 16 .

Original: 31 M
Revised: 31 M

Original: [Table]
Revised: [Table]

Original: 25 M #o f P a r a m s ( m = 14 ) 18 .
Revised: 25 M #o f P a r a m s ( m = 14 ) 18 .

Original: 08 M 19 .
Revised: 08 M 19 .

Original: 01 M 19 .
Revised: 01 M 19 .

Original: 70 M 26 .
Revised: 70 M 26 .

Original: 49 M 14 .
Revised: 49 M 14 .

Original: 87 M 18 .
Revised: 87 M 18 .

Original: 08 M
Revised: 08 M

Original: [Table]
Revised: [Table]

Original: 70 M hyp e r- P a r a m s l r : 0 .
Revised: 70 M hyp e r- P a r a m s l r : 0 .

Original: 01 w d : 0 .
Revised: 01 w d : 0 .

Original: l r : 0 .
Revised: l r : 0 .

Original: 0w d : 0 .
Revised: 0w d : 0 .

Original: l r : 0 .w
Revised: l r : 0 .w

Original: d : 0 .
Revised: d : 0 .

Original: l r : 0 .
Revised: l r : 0 .

Original: 05 w d : 0 .
Revised: 05 w d : 0 .

Original: l r : 0 .
Revised: l r : 0 .

Original: w d : 0 .
Revised: w d : 0 .

Original: l r : 0 .
Revised: l r : 0 .

Original: 01 w d : 0 .
Revised: 01 w d : 0 .

Original: l r : 0 .
Revised: l r : 0 .

Original: 01 w d : 0 .
Revised: 01 w d : 0 .

Original: D a t a :
Revised: D a t a :

Original: ADN I
Revised: ADN I

Original: E n c D a t a x
Revised: E n c D a t a x

Original: F C ( 1024 , d i m z )
Revised: F C ( 1024 , d i m z )

Original: D ec - C E
Revised: D ec - C E

Original: D a t a y
Revised: D a t a y

Original: E n c D a t a x ; E n c D a t a d
Revised: E n c D a t a x ; E n c D a t a d

Original: F C ( 1536 , d i m z )
Revised: F C ( 1536 , d i m z )

Original: D ec - C E
Revised: D ec - C E

Original: D a t a y
Revised: D a t a y

Original: E n c D a t a x
Revised: E n c D a t a x

Original: F C - B N - R e L U (,)
Revised: F C - B N - R e L U (,)

Original: F C ( 1024 , 1024 )
Revised: F C ( 1024 , 1024 )

Original: → z
Revised: → z

Original: D ec D a t a y ; D ec D a t a x
Revised: D ec D a t a y ; D ec D a t a x

Original: E n c D a t a x
Revised: E n c D a t a x

Original: DANN - C L
Revised: DANN - C L

Original: S D a t a y ;
Revised: S D a t a y ;

Original: DANN - C L
Revised: DANN - C L

Original: S D a t a y p D a t a θ ( x | z d , z x , z y )
Revised: S D a t a y p D a t a θ ( x | z d , z x , z y )

Original: p D a t a θ d ( z d | d ) p D a t a θ y
Revised: p D a t a θ d ( z d | d ) p D a t a θ y

Original: ( z y | y )
Revised: ( z y | y )

Original: q D a t a φ d ( z d | x ) q D a t a φ x ( z x | x ) q D a t a φ y
Revised: q D a t a φ d ( z d | x ) q D a t a φ x ( z x | x ) q D a t a φ y

Original: ( z y | x )
Revised: ( z y | x )

Original: E n c D a t a x ; E n c D a t a d
Revised: E n c D a t a x ; E n c D a t a d

Original: F C ( 1536 , d i m z s )
Revised: F C ( 1536 , d i m z s )

Original: D ec D a t a y ; D ec D a t a x p r i o r : E n c D a t a d
Revised: D ec D a t a y ; D ec D a t a x p r i o r : E n c D a t a d

Original: E n c D a t a x
Revised: E n c D a t a x

Original: E n c D a t a z , s × m Φ D a t a z , s × m
Revised: E n c D a t a z , s × m Φ D a t a z , s × m

Original: D ec D a t a y
Revised: D ec D a t a y

Original: [Table] [Table]
Revised: [Table] [Table]