Learning Domain-Agnostic Representation for Disease Diagnosis
Authors: Churan Wang
Jing  Li
Xinwei Sun
Fandong Zhang
Yizhou Yu
Yizhou Wang
Venue: ICLR 2023 poster (2023)
Keywords: multi centers disease diagnosis
mammogram classification

Abstract: In clinical environments, image-based diagnosis is desired to achieve robustness on multi-center samples. Toward this goal, a natural way is to capture only clinically disease-related features. However, such disease-related features are often entangled with center-effect, disabling robust transferring to unseen centers/domains. To disentangle disease-related features, we first leverage structural causal modeling to explicitly model disease-related and center-effects that are provable to be disentangled from each other. Guided by this, we propose a novel Domain Agnostic Representation Model (DarMo) based on variational Auto-Encoder. To facilitate disentanglement, we design domain-agnostic and domain-aware encoders to respectively capture disease-related features and varied center-effects by incorporating a domain-aware batch normalization layer. Besides, we constrain the disease-related features to well predict the disease label as well as clinical attributes, by leveraging Graph Convolutional Network (GCN) into our decoder. The effectiveness and utility of our method are demonstrated by the superior performance over others on both public datasets and inhouse datasets.

Published as a conference paper at ICLR 2023
LEARNING DOMAIN-AGNOSTIC REPRESENTATION FOR DISEASE DIAGNOSIS
Churan Wang Jing Li', Xinwei Sun? Fandong Zhang?, Yizhou Yu?, Yizhou Wang
1 School of Computer Science, Peking University
2 CFCS, School of CS, Inst. for AI, Peking University
3 Nat'l Key Lab. of GAI & Beijing Institute for GAI (BIGAI)
4 Nat'l Eng. Research Center of Visual Technology
5 AI lab, Deepwise, Beijing, China
6 Department of Computer Science, The University of Hong Kong
7 School of data Science, Fudan University
chhranwang, liging yizhou. @pku. edu. en
z langfandonggdeeeee com, sunx nwei @ wudan.edu.an.mm yizhouyGacn.org
ABSTRACT
In clinical environments, image-based diagnosis desired achieve robustness on multi-cente samples. Toward this goal, natural way is to capture only clinically disease-related features. However, such disease-related features are often entangled with center-effect, disabling robust transferring to unseen centers/domains. To disentangle disease-related features, we first leverage structural causal modeling to explicitly model disease-related and center-effects that are provable to be dis- entangled from each other. Guided by this, we propose novel Domain Agnostic Representation Model (DarMo) based variational Auto-Encoder. To facilitate disentanglement, we design comain-agnostic and domain- aware encoders to respec- tively capture disease-relatee features and varied center effects by incorporating a domain-aware batch normalization layer. Besides, we constrain the disease-related features to well predict the disease label well clinical attributes, by leveraging Graph Convolutional Network (GCN) into our decoder. The effectiveness and utility of our method are demonstrated by the superior performance over others on both public datasets and in- houh datasets.
INTRODUCTION
A major barrier to the deployment of current deep learning systems to medical imaging diagnosis lies in their non- robustness to distributional shift between internal and external cohorts (Castro et al.,
2020 Ma et al. 2022 Lu et al. 2022), which commonly exists among multiple healthcare centers (e.g. hospitals) due to differences in image acquisition protocols. For example, the image appearance can vary lot among scanner models, parameters setting, and data preprocessing,
shown in Fig. [] (a.b,c). Such a shift can deteriorate the performance trained models, as manifested by a nearly 6.7 % AUC drop of empirical risk minimization (ERM) method from internal cohorts (source domain, in distribution) to external cohorts (unseen domain, out of distribution), as shown in Fig. (bar graph).
To resolve this problem, existing studies have been proposed to learn task-related features (Castro) et al. 2020 Kather et al. 2022 Wang et al. 2021b) from multiple environments of data. Although capture lesion-related information, it is not guaranteed that such features can be disentangled from the center effect, i.e., to variations in image distributions due to domain differences in acquisition protocols (Fang al.) 2020 Du al. 2019 Garg al. 2021) The mixtures of such variations lead to biases in learned features and final predictions. Therefore, a key question in robustness
the learned representation
in which way can the fissese-rrelted features be disentangled from center-effect? Recently, (Sun et al. 2021) showed that the task-related features can be disentangled from others, but requires that the input X and the output Y are generated simultaneously. However, this requirement often does not satisfy disease prediction scenarios, e.g., Y can refer to ground-truth disease labels acquired from pathological examination, which can affect lesion patterns image X.
indicates corresponding author

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Cases From Different Centers (0)
AUC Evaluation under Infernal Cobort and External Cobort
3.97
3.5
lnnercal Calort (Source Denail)
0:51
0.6
Exceraal Coboit (Urseea Donaii)
3.91
037
335
6,22
Center1
Centerz
Cemerd
Centent
3.1
Oura
Frous
From Biffereut Couters
Contert
Center3
Centerd
Domain differences between multi centers (Cases-a,b,c) and AUC evaluation of Ours/ ERM (training by Empirical Risk Minimization) under internal/exteral cohort. Cases-a.b.c: similar cases in different centers (red rectangles: lesion areas). The bar graph: in the external cohort (unseen domain) ERM performs a large drop on AUC, instead, our proposed method performs stable.
Figure I:
To achieve this disentanglement, we build our model in Fig. 2 (b), via structural causal modeling (SCM) that can effectively encode prior knowledge beyond data with hidden variables and causal relations. As shown, we introduce mm and Umi to respectively denote macroscopic and microscopic parts of disease-related features that often employed in clinical diagnosis. Specifically, the macro- scopic features encode morphology-relatee attributes (Surendiran & Vadivel 2012) of lesion areas, as summarized in American College of Radiology (ACR) (Sickles et al. [213); while the microscopic features are hard to observe but reflect subtle patterns of lesions. Taking the mammogram in Fig. P (a) as illustration, the macroscopic features refer the margins, shapes, and speculations of the masses; while the microscopic features refer to the textures, and the curvatures contours (Ding et al. 2020a). As these disease- related patterns vary between malignancy and benign, they are determined by the disease status Y and we have - (Uma, Umi) in Fig. 2 (b) correspondingly. Besides, the Uma differs from Umi. it is related to clinical attributes A that are easy observe from the image. In addition to disease-relaee related features, we also introduce center effect in the image. Note that given the image (i.e., condition X), the va correlated to (Vma, fmi). making them entangled with each other. This entanglement can cause bias and thus unstable prediction behaviors when transferred to unseen centers/domains.
to account for domain gaps from the
Equipped with this causal modeling, can observe that the distributional shift of data is mainly accounted for by the variation of 0a across domains. Moreover, we can theoretically prove that when this variation is diverse enough, the disease-relatee effect. To the best of our knowledge, we are the first to prove that this disentanglement is possible, in the literature imaging diagnosis. Inspired by this result, propose disentangling learning framework, dubbed as Domain Agnostic Representation Model (DarMo), to disentangle disease- related features for prediction. Specifically, adopt variational auto-encoder framework and decompose the encoder into domain-agnostic and dowain-aware branches, which respectively encode disease-related information (Vma: Una) and domain effect vg. To account for the variation of ua across domains, we propose to incorporate domain- -warr batch normalization (BN) layer into the domain- aware encoder, well capture the effect in each domain. To capture disease-related information, we use disease labels to supervise (#ma. Umi) and additionally constrain Vina to reconstruct clinical attributes with Graph Convolutional Network (GCN) to model relations among attributes.
features can be disentangled from the center
To verify the utility and effectiveness of our method, we perform our method on mammogram benign/malignant classification. Here the clinical attributes are those related the masses, which are summarized in ACR (Sickles et al. 2013) and are easy to obtain. We consider four datasets (one public and three in noushuse) that collected from different sources. The results unseen domains show that our method can outperform others by 6.2%. Besides, our learned disease-related features can successfully encode the information the lesion areas.
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In summary, contributions mainly three-fold: a) We leverage SCM to encode medical prior knowledge, equipped with which we theoretically show that the disease-related features can be disentangled from the domain effect; b) We propose novel DarMO framework with domain-agnostee and domain-aware encoders, which facilitates the disentanglement of disease-related features from center effect achieve robust prediction; e) Our model can achieve satte-of-the-arn performance in terms of robustness to distributional shifts across domains in breast cancer diagnosis.
RELATED WORK
Domain Domain-AAnostie Agnostic Representation Learning for Disease Diagnosis. The multi-center study is important for clinical diagnosis Liu al. (2020); Kather et al. 2022); Caattro al. (2020); (Pollard et al. 2018). It considers multiple domains (centers) and aims improve the diagnosis performance in unseen domains. However, under unseen domains, previous methods will lead to a dramatic performance decrease when testing data from different domain with different bias (Ilse et al.)
2020; Sattitratanacheewiin et al. 2020 Zhang et al. (022a).. Thus such previous models are not robust enough to the actual task (Azulay & Weiss |020|Cheng al., (022). An intuitive idea to solve domain gaps among multi-centers is learning domain domain-agnostic representation. Progress has been made can be roughly divided into three classes: (i) Learning the domain-specific constraints, e.g. (Chattopadhyay et al. 2020) aim to learn domain-specift masks but fails in medical images for suitable distinguish different domains based on masks. (ii) Disentangle-
e.g., (IIse et al.) 2020) model three independent latent subspaces for the domain, the class, and the residual variations respectively. They do not make use of the medical attribute knowledge which is important in our mammogram classification. (iii) Design invariant constraints, e.g., (Arjovsky et al. 2019 /Zang ict al. 2022b) aim to learn invariant representation across environments by minimizing the Invariant Risk Minimization term. (Ganin et al. 2016) and (Li et al. 2018) use adversarial way with the former performing domain-adversari training to ensure a closer match between the source and the target distributions. Lack of disentanglement and the guidance of medical prior knowledge limits their performance on unseen domains.
METHODOLOGY
Melignent
Problem Setup Notations. Denote X E X, E V,AE A respectively as the image, be- nign/malignant label, and clinical attributes. We here formulate different centers different do- mains and collect datasets {a vf 1 from multiple domains (healthcare centers) E D. Our goal is to identify causal features from training domains (centers) Drr that the in- duced disease predictor can generalize well to new unseen domains (external cohort) Dre. Let m = |Dr, be the number of training domains (centers) and n = Σ un be the total train- ing samples.
Todtre willer Hikee
Microccopic
Murgi Groomsottdd Shape
Macresoople Features
y
In the following, we first introduce our causal model that incorporates medical priors regard- ing heterogeneous data from multiple domains in Sec. 3.1 With this modeling, show that the domain-agnostic causal features can dis- entangled from domain- fit distributions of each domain well. Guided by this result, we in Sec. 3.2 propose variational auto-encoder based method as a gener- ative model fit these distributions, so as to learn causal features for disease prediction.
d
mmi
Ema
A
X
(b)
features if we can
Causal Graph of model. For Uma Umi, 02 that respectively denote macroscopic, microscopic, and center-dependent features, the (Uma; Umi) are associated with the disease status and Va is affected by domain variable d.
Figure 2:
3.1 DOMAIN-AGNOSTI CAUSAL MODEL FOR MEDICAL IMAGE We first formally define the notion of domain-aware features and domain-agnoste casual features, in the framework of proposed structural causal model in Fig. (b). In this model, roughly
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(DADI)
Medical
Image
Decoder
Layer
Doman-Aware BN Layer
Demain-Agnostic (DADR)
Disease-Altrbuue Gemerative Models
Mass Benign/Malignant Classifier
Figure 3: Overview of our VAE-based method, which is composed of two-branch encoder: Domain- Agnostic Relevat Encoder (DADR) to extract macroscopic features Uma+ microscopic features Umi and Domain-Aware Disease-Irrelevant Encoder (DADI) to extract domain-speen -specic effects Ud- In DADI, images from different centers fed into corresponding domain-aware layers respectively, to model the variation of domain effects. In DADR, we implement graph convolution Attribse-Atribute Generative Model) capture relations among clinical attributes.
decompose latent factors v of the input image into domain-agnostic causal features (Uma; Umi) that are determined by the disease status y. and other domain-aware features V. affected by the domain variable d. For domain-agnostte casual features, we further denote Uma macroscopic features that generate clinical attributes Ema (such as shapes, margins (Sickles et al. 2013) Wang et al. 2021b Zhao et al., 2022) that normally utilized by clinicians for disease prediction, and Umi as microscopic features (such as textures, curvatures of contours (Ding et al.) (020a)) that may be difficult to observe but can encode the high-frequency patterns of lesions. For va it can encode biases introduced during the imaging acquisition process from different centers/medical devices.
If we directly train predictor p(yla)) using neural network, the extracted representation from entangle the causal features (Uma: Ums) and center effects va because conditioning on x can induce the spurious path from Va to (Uma: Umi), making va and (Umas Umi) correlated with each other. Such an entanglement makes it hard to generalize well on new centers' data. Specifically, if we denote as the learned representation from training domains' data, then S's distribution of the diseased group can be affected by which is domain- on another domain's 's data, which may cause difficulty in discriminating the diseased group from the normal one in terms of S's distribution.
Therefore, this distribution can change lot
To remove this domain dependency, it desired to disentangle causal features from domain-awane features. Indeed, this disentanglement can be achieved via acquisition from multiple domains with diverse distributions. Specifically, the difference between (Umor Ums) and Va mainly lies in whether this feature is domain-invarian The diversity among domains invariant information, i.e., (Umas Ems) in our scenario, as shown in the following theorem:
thus provide a clue to identify
Theorem 3.1 (Informal), Suppose that multiple domains are diverse enough. Then long fil each domain's 's distribution well, then.frr each image I 4- fa Vina )²), the learned factors (Ūmis Umay Ud) has Ū.i hyme (omi(Utn)) (vrn),
can
ha(v)), Uma hmma
( (Vina) for some henis hmay ha-
The diversity condition means the extent of dependency Ua on and (Umas Ummi) on are large enough, which can be shown to hold generically in the appendix.
Remark 3.1.
This theorem informs that as long as we can fit data well, we can identify each factor, particularly domain-agnosti causal features (Uma, Umi) up the transformation that does not depend on ug- In this regard, the learned domain-agnoss Guided by this analysis, we propose a variational auto-encoder (VAE)- based method, as generative model to fit data from each center.
causal features are disentangled from domain effects.
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3.2 GENERATIVE MODELING FOR AANOSTIC CAUSAL FEATURES
In this section, we first obtain the objective function via reformulating the Evidence Lower BOund (ELBO) in VAE, which are composed Domain-Aware Prior Models, Donain-AwarreAAgoosti Inference Models to learn latent factors, and DiseaseAAtrribtte Generative Models to reconstruct X, A and to predict y.
Objective Function of VAE. To learn p A) for each domain d, decompose the whole log- log-likelihood into log p (z. y, A) = log (x) + log (y. A Ar)), in which the term log (x)
can be replaced by the ELBO of VAE (Kingma & Welling 2013). ; i.e, (vz (log p5(2,)) agd (v)()))))
that is I log (x). Here, the "=" can only be achieved once the variational distribution que (elaz) equals to the ground-truth posterior pg(v)z). In this case, we have PV A|z) = Po (A(pma)) (oou))o(y((uun U/ma Umi ( Umii, Udd (r))dd maddddmddmmaade since A -. O'm, Vel Umm and 1 Mal (Umas Umi) according to Fig. 2(b). The empirical loss for data in domain d is:
(5 (() = ndd
1
nh
log Ag(x,) + (aguetllz) (log
Pa 1)) qud qud (0/xx) ))
na
(lg (Fage (po Aelmma )oo Uma: umi))
1dd
Eg Roi (v)))) (log pogppo())))) - KL (olxs)) P((1))
(I)
with Za- (u/2z) learned approximate p/ (v]zr) To optimize the loss, we need respectively parame- terize the prior models p (Dmay Ums: va) = po (va (ald))(((u (al/dd((@mma Umii), inference models qu (v)xx)) (i.e.. encoder) and generative models (o P'ma Umi. v2). (A Uma), Po(3] Emaa Umi) (i.e., decoder). In the following, we will introduce our implementation for these models. As illustrated in Fig. 3 we propose a two-branch encoder: Domain-A Aarnt--gnn Encoder to extract (Uma: Umi) and Domain-Aware Encoder to extract Va. For the latter, we incorporate a domain-awee aware BN to capture the variation of multiple domains. With learned causal features, we implement graph convolution network to capture relations among clinical attributes.
Domain-Aware Prior Models. Following the causal graph in Fig. 2 we factorize (5 (Uma: Umis va)
into pr (maa Umi: va) = p( (lumas Umi Pe (Pald), where the p( p(Uma: Ums) can be modeled as isotropic Gaussian while pa, (Vald) is dwwain-aware, and is parameterized as a Multilayer Perceptron (MLP) with one-hot encoded vector d R.m input.
To disentangle causal features (Uma: Ums) from domain effects, we adopt mean-field feead approximation to factorize (Us, Uma: Umai (z) Toh (Umas Umad xx) Ayg (valx)) with qu (1ma; Unile (x) and ((val22, 2 d) respectively implemented via a domain-agnosiic disease-relevant encoder (DADR) and a domain-aware disease-irrelevant encoder (DADI). This parameterization is inspired by the attributing the domain-aware effects to feature va while sharing parameters of the domain-agnostic encoder 1/ for all centers, the domain-aware effects can be removed in learned macroscopic and microscopic information, leading to robust generalization ability across domains.
Domain-Awaare/Annosii Inference Models.
properties of (Umay Umi) and va- By
With shared parameters of the Nomainn-gnnosie encoder, we have
A = / pe ( (A) [A|mma)) PPma)Pol Uma: Uni Ng (Umay Uma (z) dd
(2)
which hence does not depend on the domain index d. To reflect the variety of different domain effects, the domain-aware encoder contains a Domain-Aware Layer (DAL), which composed of m batch-normalization (BN) layers with (7a,, 32) for each center: fa = , (f) = Taal + 3a. with ui denoting the normalized features by the mini-batch mean and variance 8g-
Aitribe-Attriuute Generative Models. To learn Umay Umis Vd, we constrain them to well recover x and predict A, y. respectively via Po_ (x|u), pe, (yl Pmaa Ums) and pe (Al (A]ema). Specifically, to capture macroscopic patterns in Uma- constrain
estimate the clinical attributes A that include macroscopic information such as shape, margins, lobulation, etc. As correlations among clinical attributes can be helpful for disease diagnosis, we propose reconstruct A via Graph Convolutional
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Table 1: AUC evaluation of public/in- datasets on external cohorts (unseen domains), i.e..
training and testing data are from different domains, O: domains for testing, domains for training).
InHl
InH2
InH3
DDSM
FRM (He 2016
0.822
0,758
0.735
0.779
Chen et al. 2019
0.827
0,804
0.830
Guided-Vaa VAL (Ding et al.
2020b
0.872
0.811
0.779
0.811
IAIA-BL BL (Barnett of al.
202T
0.861
0.803
0.767
0.782
ICADx (Kim et 2018
0.882
0.802
0.777
0.826
(Li
2019
0.848
0.794
0.769
0.815
DANN (Gannn et al.
DANNTGannun
0,857
0.811
0.781
0.813
MMD-AÄE (Li ct al 2018
0.860
0.783
0.770
0,786
DIVA (lse et al. 20200
0.865
0.809
0.784
0.813
IRM (Arjovsky et al.
2019
0.889
0.830
0.795
0.829
Chatlopadhyay
2020
0,851
0.796
0.772
0.797
DDDG iZhang
0.867
0.811
0.778
0.802
EFDM Zhang et al.
2022c
0.864
0.812
0.765
0.796
Ours
0.948
0.874
0.858
0.892
Ours (2/3 DAL)
0.946
0.874
0,853
0.889
Ours (1/2 DAL)
0,942
0.871
0.847
0.883
Ours (1/3 DAL.)
0,930
0.863
0,842
0.871
Ours (one layer DAL)
0.926
0.857
0,835
0,864
Ours (DAL ME)
0.946
0.873
0,855
0.891
Ours (DAL GL)
0.947
0.872
0.854
0.887
Network (GCN) Kipi & Welling (016)) that is flexible to capture the topological structure in the label space. More details are left the appendix.
Training and Testing, With above parameterizations, we optimize prior parameters ppri := {0a): inference parameters zi := {eid] with vid == (11, vid) such that vig includes (7d, 3a) and other layers' parameters that do depend d, and generative parameters 0gen == (0z, fy Oa) via L(6 pri: v., 6 ggen) En (82, did 9gen) with ed defined in Eq. During testing stage for new im- age x, we first extract causal features (Uma. Ums) from æ, followed by prediction via pe, (v/ Umas Umi).
EXPERIMENTS
Datasets and Implementation. To evaluate the effectiveness of our model, we apply our model on mammogram mass benign/malignnnt classification, which drives increasing attention recently (Wang
et al. 2021a] Zhao et al. 2018 Wang et al.] 20216 Lei et al. 2020; Wang et al. 2020 2022) due to its clinical use. Public dataset (DDSM (Bowyer et al. 1996)) and three in-house datasets (InH1, InH2, and InH3) what we use are from different centers (center4, 1, 2, 3 respectively). Different medical devices, different regions/countries, and different image formats cause domain gaps. For each dataset, we randomly split it into training, validation, and testing sets with an 8:1:1 patient-wise ratio. The inputs of network are resized into 224 x 224 with random horizontal flips and fed into networks. To verify the effectiveness of multi-center benign/malignant diagnosis, performances on the external cohort (unseen domains) in Tab. T (training data and testing data are from different domains). To remove the randomness, values. To further validate our effectiveness, we also give internal cohort (source domain,i.e, the same domain as training domain) results of each dataset which can be seen as the upper bounds of each dataset. For fair comparison, the number of above-all training sets all keep the same. Area Under the Curve (AUC) is used as the evaluation metric image-wise. More details of datasets and implementation are shown Appendix.
show
for 10 times and report their average
4.1 RESULTS
Compared Baselines. We compare model with the following methods: a) ERM (He et al. 2016) directly trains the classifier via ResNet34 by Empirical Risk Minimization; b) Chen et al. Chen et al. 2019) achieves multi-label classification with GCN for attributes prediction; Guided VAE

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Table 2: AUC evaluation of public/in-house datasets on internal cohorts (source domains, i.e. in-distribution: training and testing data are from the same domains. - do not use, O: the same domain for training and testing).
InHl
InH2
InH3
DDSM
HRM (He et al.,
2016
0.888
0.847
0.776
0.847
Chen ct al.. 2019
0.924
0.878
0.827
0.871
Guided- VAE (Ding ct al.
2020b
0.921
0.867
0.809
0.869
ICADx KK Kim et al. 2018
0.911
0.871
0.816
0.879
Li a1
20191
0.908
0.859
0.828
0.875
IAIA-BL Barnett
2021
0.910
0.865
0.821
0,856
Ours-single
0.952
0.898
0.864
0.919
Ding et al. 2020b) also implements disentangle network but lacks the medical prior knowledge of attributes during learning; d) Li al. (Li al. 2019) improve performance by generating more benign/malignan images via adversarial training; e) ICADx (Kim et al. (018) also proposes the adversarial learning method but additionally introduces shape/mmargins information for reconstruction; f) DANN (Ganin et al. 2016) uses an ad adversarial way to ensure closer match between the source and the target distributions; g) MMD-AAE (Li et al.) 2018) extends adversarial autoencoders by imposing the Maximum Mean Discrepancy (MMD) measure; h) DIVA (llse et al. (020) proposes generative model with three independent latent subspaces; i) IRM (Arjovsky et al. 2019) designs Invariant Risk Minimization term to learn invariant representation across environments; j) Prithvijit et al. Chattopaahyyy et al., 20200) add domain-speciff masks learning for better domain generalization. k)LAIA-BL (Barnett et al. 2222] diagnoses based pixel-level prediction. 1) DDG (Zhang et al. 2022b) formulates a constrained optimization to solve domain generalization. m) EFDM Zhang al.
2022c) matches empirical distribution functions.
Results & Analysis on external cohorts (unseen domains). To verify the effectiveness of our train our model the combination of three
method under unseen domains (out-of-distribution)) datasets from three different centers and test on the external cohort (another unseen dataset from other centers). As shown in Tab. (Lines 1-18), our methods can achieve state-of-the-art results under unseen domains in all settings.
Specifically, the first six lines are the methods based on different representation learning and we extend them to our domain generalization task. The next seven lines are the methods aiming at domain generalization. (Li et al. 2019) generates more data under the current domain, the larger number of data improves the performance compared with ERM (He et al., 2016) but the augmentation for the current domain greatly limits its ability of domain generalization. (Chattopadhyay et al.. 2020) learns domain-specific masks (Clipart, Sketch, Painting), however, the gap that exists in medical images can not balance through mask learning. DANN (Ganin et al. 2016). DDG (Zhang al. 2022b), EFDM (Zhang et al.) 2022c) and MMD-AAE L et al. 2018) design distance constraints between the source and the target distributions. However, simple distance constraints are not the key cancer diagnosis and not robust enough. The advantage of Guided-VA VAE (Ding et al. 2020b) and DIVA (Iise et al. 2020) over mentioned methods above may be due to the disentanglent the former methods. IRM (Arjovsky al. (2019) learns invariant representation across environments by Invariant Risk Minimization. However, lacking the guidance of the disentanglement learning limits their performance. Guided-VAE (Ding et al. 20205) introduces the attribute prediction which improves their performance more than DIVA ilse et al. 2020). The improvements in ICADx (Kim) al.) 2018), Guided- VAE (Ding et al. learning. Although ICADx (Kim et al. correlations between attributes and diagnosis, which limits their performance. With further exploration of attributes via GCN, method can outperform ICADx (Kim et al. 2018), Guided-VAL (Ding ct al. 2020b). Compared to (Chen et al. (2019) and IAIA-BL (Barnett et al. (021)) that also implement attribute learning, additionally employ disentanglement learning with variance regularizer which can help to identify invariant disease-related features during prediction.
learning in
2020b) prove the importance of the guidance of attribute 2018) uses the attributes during learning. it fails to model
Comparisons on internal cohorts (source domains). We further compute the in-distribution AUC performance of every single dataset under internal cohorts (Tab. 2). Our method shows stable performance while other methods drop a lot under external cohorts compared with Tab.
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Table 3: Overall Prediction Accuracy (ACC) of Multi Attributes (Mass shapes, Mass margins) on external cohorts (unseen domains, i.e. out-of-distributns training and testing data are from different domains). Testing names are noted in the table.
Methodology MaM-muatitask Chen et al. (Chen et al. 2019
InHl
InH2
InH3
DDSM
0.618
0.560
0.596
0.662
0.827
0.795
0.748
0.842
ICADX (Kim et al. 2018
0.743
0.647
0.612
0.739
Proposed Method
0.914
0.877
0.858
0.934
Specifically, we implement the methods which aim at representation learning on internal cohorts, i.e. training and testing on the data from the same domain. Such in-distribution results can serve as the upper bounds of our generalization method. To adapt our proposed mechanism the in-distribution situation, we change our network with two branches without domain- for extracting features into a, S, since training data only from one center center(Ours-sing Ours-single), i.e. one domain without domain influence. As shown in Tab. 2 based on the disentanglement mechanism and the guidance of attribute learning, Ours-single still gets the state-of-art performance. We argue that the disentangling mechanism with the guidance of attributes helps effective learning of discasc-related features under a single domain. Results in Tab. Caan be seen as the upper bound results of each setting in Tab I Our results in Tab. Tare slightly lower than results in Tab. 2 by 0.4% to 2.7%. We argue that based on our mechanism for domain generalization, our method can get evenly matched performance compared under external cohorts
BN layers accordingly
with internal cohorts (in-distribution). For example, as shown when testing on DDSM (Bowyer et al.) 1996), performances of our model training on InHl InH2+InH3 and training on DDSM itself are comparable.
4.2 ABLATION STUDY
Ablation study on each component. To verify the effectiveness of each component in our DarMo, we evaluate some variant models on external cohorts as shown in our appendix-Tabe Tab.4.
To abate the impact of the combination of training domains, we also train our model under different training combinations and show results in Appendix. Results indicate that influences between different domains are not obvious and three domains are sufficient to achieve comparable results.
Ablation study on the ratio of using domain-aware layers. To verify the effectiveness of the ratio of using DAL, we replaced the original BN layer with DAL in different ratios. The results are shown in Tab. 1innc18-21, specifically, 1/3 means only 1/3 BN layers in the network are replaced, others, and so Torth. As shown, under the lower ratio, the performance drops due to the poorer domain interpretability. The higher ratio can get better performance.
Ablation study on Domain-Aware Mechanism To deeply investigate the proposed domain-awar BN layer, we analyze various implementation forms of multiple domains as follows: a) Multiple Encoders(ME). Since the irrelevant encoder contains the information of domain environments, an intuitive idea is directly. b) Grouped Layer(GL). To reduce the parameter quantity of ME, we consider several groups of blocks with each group containing two blocks in the same structures. Each group only responds to one block each time, and different domains are different block combinations. The number of groups n that satisfies 2n m (m denotes the number of domains, if m is not the exponential power of 2, find m that is larger than m and is the least number that satisfies 2n rit). Thus each domain is a permutation combination based on each group choosing one block. e) Domain-Aware BN Layer(DAL). To further reduce the parameter quantity and achieve domain generalization, we propose the domain-aware BN layer for each domain. The scaling and shifting parameters in each layer are learned adaptively.
multiple irrelevant encoders so to each domain has one irrelevant encoder
We conduct experiments under the mechanisms above and the results are shown in Tab. Linel8-22 Three different kinds of mechanisms have comparable performance. Since BN can usually be used as an effective measure for domain adaptation (Toffe & Szegedy] (2015), DAL can be slightly better than the others with lighter computation, especially compared to ME.
4.3 PREDICTION ACCURACY OF ATTRIBUTES
We argue that attributes can be the guidance of cenign/maliinnat classification. the current domain generalization task, under external cohorts (unseen domain), we also calculate the prediction accuracy
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Validation
Test
Input
3]
IPLLE
Reconstucion
Resorsttuctoon of Mea
Recondnctior of Mi
Resonstructon of
Recenstrctin
Yiu
Raosnntruction
Predkcted Atybutes
RREEJLAR Marghn
ROUND Margin
OHII
Nargins
Staps
Shape Margins SP CULATED
Shape Margine OBSCURED
Shape
AtHiutes
Mangins
IUL GEFEENED
CIRCUMSCRIRED
Figure 4: Visualization on (atid(int and test(external) cohorts. Red rectangles: lesion regions; green rectangles: white dots caused by machine shooting. Each row: the reconstruction of different latent variables. Validation: 1st and 4th columns are from the center2, the 2nd column is from the centerl, and the 3rd column is from the center3. Test: columns are from center Note that there are no reconstruction results of va at the test stage because the test domains have corresponding domain-awasd aware encoders.
of attributes in ours and other attribute-based representative methods in Tab. Our method gets the best prediction accuracy on the attributes over other methods under out-of-distribution.
4.4 VISUALIZATION
We visualize reconstruction results of all latent factors and the predicted attributes of the current image in Fig. 4 to validate that our model successfully disentangle latent factors Umas Umis and Vd. Since the DADI Encoder is partially fomain-dependerd sets are from the same domain, but the testing set (Right in Fig. is from different unseen domain. As we can see, the disease-related features Umm + Uni mainly reflect the disease-related information since they mainly reconstruct the lesion regions without mixing others. The disease-irrelevant va features mainly learn features such as the contour of the breasts, pectoralis, and other irrelevant glands without lesion information. caused by machine shooting are learned by ny visualization. This means that through the ability of domain generalization, our method can disentangle the irrelevant part successfully and prevent it from predicting the disease. Moreover, the macroscopic features Uma capture the macroscopic attributes
validating (Left in Fig. 4 and training
worth noting that the white dots on the image which are
lesions, egg., shape and density; while microscopic features Umi learn properties like global context, texture, or other invisible features but related to disease classification. These results further indicate the effectiveness and interpretability of our DarMo.
CONCLUSION
We propose a novel Domain Agnostic Representation Model (DarMo) on domain generalization for medical diagnosis, in order achieve robustness to multi centers. We evaluate our method on both public and in-house datasets. Potential results demonstrate the effectiveness of our DarMo, we will try to generalize this method other medical imaging problems such as lung cancer, liver cancer, elc.
ACKNOWLEDGEMMEN
This work was supported by MOST-2022ZDD 14900, NSFC-6206113600) Hong Kong Research Grants Council through General Research Fund (Grant 17207722).

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A FORMAL DESCRIPTION OF THEOREM 3.1
In this section, we present the formal version and the proof of theorem 3.1, which claims the disentanglement between disease-related features and center effects. In the following, we first introduce model assumptions, followed by definition of disentanglement; finally, we present the formal version of theorem 3.1 and its proof.
Model Assumptions and Notations. According to the causal graph in Fig. 2 the joint distribution over (y, vg. Umi: Uma- 2, given each domain can be factorized as conditional factors Pearl (2009)
Schölkopf et al. 2021:
ply, Vd; Umi, Uma, Ad - p(y) ( (y)pplpppppp) (ema 1)p(p(((( Md, Umi; Uma )ma)p(( A(ema)
In the following, we will introduce the assumption of each conditional factor. Specifically, for latent variables ua, Veni, Uma: we assume that Umi yy, Umaly yy and vald belong to the following exponential families:
p(vald)= == Pry. aa (Dald), Pr Pgm (Ume (), Proma rimm (Umal
(3)
where
9uc
Ay Thy (u:) o,. + BB((s)) - Cu.s)
PT-ryy(uo)) = exp
for any (Umii Uma } with y. and u va with o d. The (TT) [u:)], (To denote the
sufficient statistics and natural parameters, {B,) and {C,,, denote the base measures and normalizing
constants to ensure the integration of distribution equals to 1. Let ((xx)== = (u1). (u, au
X0u (u.) = (u.), ..., T.M.. (u.)), Vi E [g.l). r == [_,,,,... To _o E R (T% :=
[T b. Vi E [gu)). This assumption has been widely assumed in the literature of causal representation learning and causal learning Khemakhem et al. (2020): Sun et al. (202T)
For 2, A, we assume the following additive noise model (ANM):
I = fa(Um (Umis Uma, Ud) + Ez; A = (A(mma)+As
(5)
where EA denote the exogenous variables of X and A, respectively.
Definition of Disentanglement. With such model assumptions and formulations, we introduce our for- mal definition of disentanglement. First, we denote == (TTM., Tea, Tume, Tyms r r fa fA
in the above models. We define the disentanglement as follows:
Definition A.1 (Disentanglement of Latent Space). We say that the Umis Bmaa Da are disentangled
with each other under 0, if for any 0 == (T Twv Twom froms, Prmm 1 So, [A} that giving rise to the same observational distributions: pa(x, A, uly)d = pggar, A, yld) for any x, y, A and d, there exists invertible matrices Mynss M Myma> Me, and vectors bys Domes Dyma such that:
T(( = My ((1=))2(11) + beme? T( = Myme
(6)
+ byma?
(7)
T(TE" (D()) = M,,,, (([==" + b
(8)
where the I, A,D DD denote the space of the latent variables Meni; Ud, Uma- Correspondingly, for ( that transforms x into the latent space (I, A, A,D). (z=))(()), is= lA(x) and [f=))((z) respectively denote the elements of (x) in the space I, A and D.
Remark A.1. This definition is a variation of A A-identifiability of Khemakhem et al. identifiability in Sun et al.) (202T). which means the latent variables can be determined up to affine transformation with an invertible transformation matrix. Specifically, for any x +- Sa Umaa v2), the (x(x,, (==)(())))))))))))))(()) and [S= 1== ((x) respectively return true latent variables w V Uy. Then if the model 0 can perfectly fit the joint distribution over each domain, i.c., p0 Ald), (f=")z(x), [f= (A()) and If= (I()) can recover Vinis Vmna Di up to linear transformations with invertible matrices Momo Mrma and Mag
(020) and the
Formal Version of Theorem 3.7 We present the formal version of theorem 3.1 follows:
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Theorem A.2 (Formal version of theorem 3.1. Under the causal model in Fig. 2 with Eq. 3 and Eq. for any 8 we have that Umá, Ud, Uma are disentangled, under following assumptions:
1. The characteristic functtoo of Ex, EA are almost everywhere nonzero.
2. fax fA are bijective functions;
3. The sufficient statistics are differentiable almost everywhere; besides, (Th hiisk.. are linearly independent in I. A or DD for each i E for any u = Umit Umay Vd.
4. There exists mn different values of domain variable d, (i.e., d1, dmd and K different values of disease label y, (i.e., "1,... yK)))))))))))))) such that [
The
r di
da
I mmx maxxa xhrug) and 1/2 max xku) have full column rank.
Umn Pu=mmis Ummm Vmna
mommemiiee mmm
Pu=emi Mana 17]
91
UK
91
Remark A.2. These assumptions have been widely assumed in the literature of independent com- ponent analysis and representation learning Khemakhem el al.) (2020); [Sun el al.) (2027): [L et al. (222). Assumptions 1-3 is easy to satisfy. Specifically, the characteristic functions of e and E are almost everywhere non-zeros for most discrete (such as binomial, Poisson, geometric) continuous variables (such as Gaussian, student-t). For assumption 2, as has been empirically verified Kramer (199T) that the extracted low dimensional embedding is able to recover the original image, it is natural for fa to be bijective. The bijectivity of fA is to ensure the disentanglement of Uma (up to affine transformation), similarly adopted in Li et al. (2027).
For assumption 4, is required that distribution across domuins and disease status are diverse enough, which is easy to satisfy. Based on this assumption, m (the number of domains) and K (the number of disease statuses) are respectively required to be larger than the dimension of Va. and the dimension of (Umi, Uma). This suggests that we should collect data from as many domains as possible, although empirically we find that three domains are enough to achieve disentan glement and generalization (as shown in Tab. [and Tab. that out-of-domain performance is comparable to nn-distribution performance). For disease label, we can access a more finer label, e.g. breast cancer stage D D'Orsi al.) (2018), although empirically we find that binomial benign/malignancy label is able to disentangle disease-related features.
Proof. For simplicity, we penote = Pi (ulo). Since po (xld, y) = Pa (x/ld, v). then we have
J Pse (al Uma: va)p(Umé: Uma (p) ual dd
f Pj. (Ir/mmi, Uma, Va ( Umi, Umn (ol (d)ddmddd
According to the chain rule of changing from Vmmis Uma Dd to Ja (Umis Uma va), we have that J Pe, (x- 2)p(f= (z) d.
f 1 F)p( f (z) y) dd) where Jy (x) denotes the Jacobian matrix of f on x. Denote p'(zld, y) == (zldd ( Applying Fourier transformation to both sides, we have Flp'((w)p: (w) = FlFT()) (w), where Ps. denotes the characteristic function ez. Since they are almost everywhere nonzero, we have that Flp/(w)) = Fl which means that pi (d, y) = (øld, dd y). This is equivalent to the following:
log volJ
Σ
(log Bi B, - log C. (v)
k.
Aua
(z)) +
(log Ba B:((
km
log C.adl (d) +
Ty
qu (log (:(1F - log (7)
log vol. j. (x) +
Σ
U= Sma
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4ra
(
(x)) + Σ (log B.(())ll(x))
Noa
log Cra (d) + Σ
Tyy (o.
(9)
Subtract the Eq. 9 with y = y/1 from Eq. 9 with y yke for l # 1, have that
(r
Σ
(x()),, (Ux)) + Σ log (y
(T=((==))())) I (yx)) + log (11)
Σ
(10)
for all & E [m]) where [ Tly) T(v)). Denote (k)
E
n 2 E C (s ) for
C 3
k * 1. Similarlly,, by subtracting the Eq. 9 witt d = d, from Eq. 9
with d = for I 1, we have
(T (V="(\])>>x)) (di) + Σ log C. (d1)
(r,(
(r
(T" (o()), (di)) + Σ log
(11)
C (di)
C (d
for all [m]] where [(d) r(d) I(d1). Denote (0) E.
for I # 1, we
C (d))C
have that:
T (I (b(x)) = Va. ( (l(x))) + boer
(12)
T T Temi ([fu] (x)) Pmaa. T Tuma ([falá((z)
T ([Fa (x)) UmaiT T Time ([fe)ā(())) + Bema + beme
(13)
Similarly, we also have (A(y) 5 (lyy), which means that
asmo
log volJ
(log
log logC. (d)
koma
+
Tomo (If (If (A:(A)) (I))
Pema
log vol. fA (A) +
(log B (.((fT))A log C. (d)
koma
+
Ti. (If (A)( (A)),
(14)
f=1
which has that
T
Fume
Tema ((fā))a(A)) = Tume ((T=))((A)) + i i.me
(15)
Denote == ToTTAAIT AT... == trick above, we have that
I TTT .h(v)= = =[fa] (x) (A(A))TT Applying the same
F T Uma ([fa)
Time (If2) 8
(16)
Combining Eq.
16 we have that
va, Tua ([5=') =F vo. T (f==([=²)) D
=
(17)
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Pimes Thme (IfolA (2))
Omai
Tume ([f2Az bymn..
(18)
r Pmiii Teme ([ (x))
Tmas T ([fo) (x)) + beme.
(19)
Applying the same trick in (Sun et al. 2021 Theorem 7.9) due to assumption 3, 4, we have that invertible for Umiis mma Vd- The proof is completed by setting Mus by in
T
A.1 as F" and by for u Umis Umna Ud-
Def.
B OBJECTIVE FUNCTION
B.1
FINAL Loss
Our final loss function is the summation of the loss in Eq. 1 i... En ld Ed C4 .8), where each
ed (a "0 .g)) is:
[og Pog As(aza) B (olas) (log (3(2, u)
Fud (1l (222) ))
e (1 .p8)
Tid
(log (Bquaclos)) (Ai: up (M Jimas Ummi)
1=1
prodiction A,
(vlz.) (logpo(zs(v))
KT (olas))
7d 1=1
reconstruction
Kl. divergence
The first term to the cross entropy loss for A and y; for each sample Is, we first generate Umii Uma from 2; via 9 (v) then feed Umis Uma into po (3sl Emas Umi) and Uma into pe (Aj Ummuma to predict and A, respectively. The second and third terms are respectively reconstruction loss and KL divergence loss in VAE.
B.2 DERIVATION OUR OBJECTIVE
The log- ligeliidddood over the observations (x,, y, A) in the Bayesian network is given by:
log p(x, y, A; A) log p(;; 0) + log p(A|;; 0)
+ logp(y/zz, A;
(20)
which forms the learning objective of problem. Next, give the details about how the loss functions for optimization are derived from the likelihood.
For the likeliiod p(r; 8) of each domain, have the ELBO as lower bound the log-likelihood:
log p(x; 0) = K KLgg(ua Umis Uma (t)(lp((a Umis Umalat (x))+
E Egloss Fma (r) log ((u: Vmiis Umas I))
log q(Ud, Umis Uma (z)
pl Uaa Umis Umaas x.)
E Egglvasms Pma Pma
log
q( Ud, Umss Vma (x))
KL(g(ua, Umis Uma x)) [p(dd, Urnis Uma))
+ Ems (x) log (p( (2r Umis Uma))
(21)
where 4(122)) denotes q(02, Umis Umal for simplicity. Specifically, we use 0 to parameter- ize p(Ud, Umis v:) and to parameterize q(ua, Umi, Umal (z). The prior joint distribution
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Po(Ud, Umiy Uma, 1) can be factorized into pbl (2)))pp) po Uma (2g Umis Uma). Under mean- mean-field approximation, the posterior qá (Vd, Umis Uma 1) can be factorized into Le (Vaal () (Omis Um (z)). Note that the index is added since and æ are domain-varian and Umi, Uma are nomain-invvrrian The final two terms in Eq. 21 are the KL loss and reconstruction loss in the loss functions.
For the conditional log- log-likeldhood log (2 0), we have:
log p(A]2; log / pe (e(AAmmma )po (Umal (2) d2
(22)
where pa(Uma (r) is re-parameterized by the posterior model go (ommmll (2) in the variational framework above. Under one-time sampling, we have log (pA((aza 0) log pog (P) Uma ) (Uma (2r). Since the
different attributes are independent in A, and each attribute Nete E A [[C] = (1,-. CP) obeys binomial distribution, we can rewrite the oog-likelhhoo as:
logp(( (A]2; 0) = logp(g . -0cl:;
C
log II
p( 0)
<=1
C
log
g 9: (1 -:)
i=1
Σ log D: + (1 -g:) --:::logg log(1 5:)
(23)
where 9 denotes the probability of that the sample contains attribute i (i.e. &r being under the prediction of pe (a(AApu (AAluma Me (vmauallzz) 22)). Thus we derive the multi-label loss for the Graph Convolutional Network.
For the conditional log- likelihood log p(y|2, A; have: log plyla, A;
log po(y/umi,, Uma ) (Umi, Uma (r, A ddddda
(24)
where (p Umalzs xx, A) is re-parameterized by the posterior model go (Umi: Uma (x) in the variational framework above. Under one-time sampling, have log p(ylar A; 0) log (3 Umis Uma (maa)g((n (Umis Um)lz). Since y obeys binomial distribution, we can rewrite the log- likelihood as:
log Dgyl(y/z,44 A: = log 8" 9) (1-9)
= ylog + (1 v) log(1 9)
(25)
where i denotes the probability of y being under the prediction of pe (ylums Uma 2o (Umsés Uma (z)).
Thus we derive the loss function for the binary classification of benign/mmalignan.
C ABLATION STUDY ON EACH COMPOMENT
Here are some interpretations for the variants: a) DADI denotes whether using DADI encoder during the reconstructing phase, while DAL denotes using domain-aware layers for distinguishing multiple domains in DADI encoder; b) Attribute Learning denotes the way to predict attributes: x means no predictions of attributes, multi-task means using fully connected layer predict the multiple attributes, and yen means using our Disease-Autriuu Generative Model to predict attributes; c) Umi denotes whether split the latent factor Umi out for disentanglement in training: d) Medical Image Decoder denotes whether use the reconstruction loss in training.
As shown in Tab. 4 every component is effective. is worth noting that using naive GCN also leads boosting of around 5% in average. Such result demonstrate that the attributes guide the
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Table Ablation Study: AUC evaluation of public/in-house datasets on external cohorts (unseen
domains, ie., out-of-distriuttion: training and testing data are from different domains, testing on
InH1//nH2//nH//DDDSS while training on the other three). Testing names are noted the table.
DADI
Attribute Learning
Umii
Medical Image Decoder
InH1
InH2
InH3
DDSM
0.822
0.758
0.735
0.779
multi-task
0.851
0.793
0.775
0.801
X
Eyen
X
X
0.877
0.827
0.804
0,830
X
Egen
0.911
0.846
0.816
0.844
DAL
Lgenn
0.931
0.862
0.841
0.878
DAL
0.913
0.840
0.823
0.852
Egen
0,916
0.851
0.821
0.859
DAL
Eyen
0.948
0.874
0.858
0.892
Table 5: Ablation study the combination of training data sets. Take testing on the public dataset DDSM as an example. (OOD settings)
train on InH(1.2) 0.885
train on InH(1,3)
train on InH(3,2) 0.887
train on (nH(1,2,3) 0.892
0.881
learning of discase-related features. Meanwhile, disentanglement learning also causes noticeable promotion, which may be due to that the disease-related features can be easier identified through disentanglement learning without mixing information with others. Moreover, Lines 5-6 validate that disease-related features can be disentangled better with the guidance of exploring attributes. Lines 7-8 validate that distinguishing multiple domains improves the generalization performance.
D MORE ABLATION STUDY
We also explore the impact of the combination of training domains and try different training combina- tions for unseen test domains. Take testing DDSM (Bowyer et al. 1996) example. As shown in Tab 5] the more types of domains the better effect of our model. Due to the different correlations between different domains, the effect will be different under different combinations. But based the inter mechanism of our model, influences between different domains are not obvious and three domains are sufficient to achieve comparable results.
Under the setting: testing on DDSM (Bowyer et al.) 1996) (OOD) while training on InH1 InHH+HHHHH, also list the results of our invariant model DarMo (OOD model) under testing on the testing set of InH HDHI/InH2/InIH (in-distribution) as shown in Tab, 6 We also do experiments under the setting: training on MuI1--InDD2IIIIDDDDDSS and testing InH1/InH2//nH//DDDM In addition, under the same setting, we also test our variant model Ours-single (in-distribution model). The results of testing on unseen DDSM (Bowyer et al.) 1996) (OOD) is 0.861, testing on InH1//H2/InHH (in- distribution) which are from the same training sets (IHHI+IHH2+IIH33 are 0.944, 0,880, and 0.853 respectively. The variant model testing on InH1/HHH2/mHH3 (the same domain as the training set) behaves comparably with ours Tab. and is slightly better since our DarMo split some inter-domain correlation which can decent performance under domain generalization. Thus, the variant model faces larger drop over invariant model DarMo when generalizing to the unseen DDSM dataset (0.892 vs 0.861).
E
MORE DETAILS OF DISEASE ATTRIBUTE GENERATIVE MODELS.
To capture macroscopic patterns in Cra, we constrain it to estimate the clinical attributes A that include macroscopic information such as shape, margins, lobulation, etc. Besides, we constrain and Umi to predict the disease label y, with Umi accounting for additional microscopic information of lesions. We note that such constraints align with the causal graph in Fig. 2 as only Uma + A and y I Un/un Umi- Finally, constrain all factors to reconstruct the input with Uy responsible for the domain-aware effects in x (Medical Image Decoder ). Indeed, such asymmetric roles of Umma, mii Ve in terms of relations with y, A, additionally help to disentangle them from
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Table 6: AUC of testing data set InHH///mHH2///H33DDDDS while training InH1 InHI+InHH2++nHH
test
test on
test
test
InHI
InH2
InH3
DDSM
0.939
0,874
0.852
0.892
InH1
InH3
dug
rskic Ioee
riece irre
tacmon Mie
InH2
DDSM
dapp
eskipe lite
vilce inmo
rerncle bl
emmpli,
efror
Figure 5: Distribution of lesions' characteristics in each center (dataset).
each other, on the basis of the two-branch encoder. We parameterize pe(y, A, rlr) as pa_ (zlv), pe, (y/Umar Umi) and рed (Aluma))
To utilize these relations, we parameterize the Pa(A(mma by a Graph Convolutional Network (GCN) which is flexible way to capture the topological structure in the label space. Along with (Chen et al.) 2019), we build graph G (V, E) with twelve nodes and consider each attribute as a node, e.g., Shape-circle, Margin-clear. Each node V/2 E V represents the word embedding of the attributes. Each edge E F. represents the inter-relevance between attributes. The inputs of the graph are feature representations H' and corresponding correlation matrix which is calculated the same way Wang et al. (2021b). For the first layer, Hd E Rexe' denotes the one-hot embedding matrix of each attribute node where is the number of attributes. c' is the length of embeddings. Then, the feature representation the graph at every layer (Kipf Welling 2016) can be calculated via H'+ 5( W(BH. where 5(.) is LeakyRelu (Maas al. al.] 2013). W is the transformation matrix which is is
the parameter be learned in the Ith layer. The output {A*}, ) leamed to approximate attributes {A*t
(|Causal-Encoderre)
F MORE DETAILS OF IMPLEMENTATION AND DATASETS.
External cohorts are unseen before testing, i.e., have not been used in the training phase. For each dataset, the region interest (ROIs) (malignant/benign masses) are cropped based on the annotations of radiologists the same as Kim et al. 2018). The training/validee waapin////avi//eseinnggg samples we use contain 1165 ROIs from patients/ 43 ROIs from 68 patients/1 147 ROIS from 75 patients DDSM (Bowyer al.) 1996). 684 ROIs from 292 patients/87 ROIs from 38 patients/83 ROIs from 33 patients InHI, 840 ROIs from 410 paticnts/104 ROIs from 50 patients/ 105 ROIS from 52 patients in InH2, and 565 ROIs from 271 patients/70 ROIs from 33 patients/70 ROIs from 34 patients in InH3. The distribution of lesions' characteristics in each center (dataset) we use is shown Fig. 5 And the distribution of is shown in Fig.
ages in each center
For fair comparison, all methods are conducted under the same setting and share the same encoder backbone, i.e., ResNet34 (He et al. 2016). Meanwhile, the decoder is the deconvolution network of
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InH1
InH3
1
InH2
DDSM
10
8 9
9
Figure 6: Distributions of ages in each center (dataset).
the encoder. For attribute annotations, in DDSM (Bowyer et al. 1996) annotations can be parsed from the ".OVERLAY" file. The third line the ".OVERLAY" file has annotations for types, shapes, and margins of masses. And in our in-house datasets, we obtain attribute annotations from the verification of one director doctor based on the annotations of three senior doctors. We implement all models with PyTorch. We implement Adam for optimization. The weight hyperparameter in variance regularizer in our experiments.
The clinical attributes contain circle, oval, irregular, circumscribed, obscured, ill-defined, is-lobulated, not-lobulated, is-spiculated, not-spiculated. We add additional benign and malignant nodes to learn the correlation between the combination of attributes and benign/mallinnatt For the implementation of compared baselines, we directly load the published codes ERM (He et al. 2016). Chen et al.
(Chen et al. 2019), DANN (Ganin et al. 2016), MMD-AAE (Li et al. 2018). DIVA (llse et al. 2020). IRM (Arjovsky et al. 2019) and Prithvijit et al (Chattopadhyay et al. 2020) during the test stage; while we re-implement methods of Guided-VAB (Ding al.] (2220b), ICADx (Kim et al. 2018 and
Li et al. (Li et al. 2019) for lacking published source codes.
G TEST SET OF DDSM
We use the same To provide convenience for the latter works, we publish the list of our test division on the public dataset DDSM (Bowyer et al. 1996).
benign_12 case 888
Senign_04_case333
cancer_01_casee300 benign_05_caselln
04
cancer_08 caaer__0__aseellll
464 1464
Sancer_09_casell
cancer_ll_case1673
cancer_04_case 1090
cancer_05 Lincer_55ccase055 benign_06_case0366
benign_04_case020
benign_02_case1 cancer_05_casee11e
cancer 05 case0127
1ancer_55_case0127
venign_04___ 04_case3103
cancer_07_casee
cancer_00e 1
benign_ 11_casel792
sancer_15_ce cancer_15_case3371
benign_07_ 10____00__sseee
benign_099 000g___00
cancer_02_casedu
cancer_15_casee
cancer_0l_case3027
cancer_07_case ll14
cancer_03 Lancer_03_casel077
benign_03_casee
cancer_06_camt 1182
cancer 05_ c5__ass0110
benign 12 12_casel947
benign_ Bonign_12__00 12_caseeee___e_ee 1922
cancer 0steer_05__00 05_ 00__21002100
cancer 08 c40
cancer 05 05_005__c___ 05_case0173
senign_02_casee111 0l__g_0200ss
benign_ll 1836
cancer_05 Lincer_05_case0222
cancer_ 1ncer__8_ccase1333
benign_06_ccaee077
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Published as a conference paper at ICLR 2023
cancer 02_ case0077
benign 11 _1_casel855
cancer cancer_05_cae _5_ccse0__
benign 08 case1786
cancer 07 _0__0_ee_______________
cancer_10 1ancer_0__case1573
cancer 05 05_cas00181
benign 09_case4038
cancer_053 Siccer_0S_case0192
benign_06_caseoln
cancer_06_casel11
benign_01_case311
senign_09_case4003
Denign_06_case0366 cancer_12_case4139
cancer_ Suncer_14_case198 cancer_ Mance__05ccacO133
Luncer_10_cass 642
cancer_O$_casecll
cancer_ cancer_03_casee000
caner__22_case4108
cancer cancer_09_cant 09_ce_0300 2aiig_00_ccaee412 cancer_05_caseeie
benign_09 0066
benign_03_caaee
benign_09__cae4022
benign_13_case544
benign_09__case4090
21


Reviews:
[{"review_id": "J_Vtq6y6zRB", "reviewer": "Reviewer_RBtC", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "In this study, the authors proposed Domain Agnostic Representation Model (DarMo) based on variational auto encoder, a learning framework to disentangle disease-related features from domain-related (center-related) effects to achieve robust prediction. They claimed that their work is the first to prove the disentanglement is feasible and their model can achieve state-of-the-art performance in terms of robustness to distributional shift for breast cancer detection using a public (DDSM) and three in-house datasets. ", "summary_of_the_review": "In general, their work and claim are well explained and verified with experimental results, ablation studies, and visualizations. However, some additional experiments might be needed to improve the quality of their study. ", "strength_and_weaknesses": "Strength\n•The authors implemented lots of prior works as baselines and evaluated their performances using the public and three in-house datasets to compare with their proposed model. \n•The main problem they are interested in, causal relationships between domain, macroscopic, and microscopic dependent features, and their proposed model based on VAE are well described with appropriate example images, sufficient explanations, informative diagrams, and equations. \n•They performed ablation studies to verify the effectiveness of each component in their DarMo, which helped the reviewer understand why each element is needed.\n•They shared visualizations of reconstructions of latent variables to show that their proposed model learned disentangled features.\nWeakness\n•Can you elaborate how the domain-aware BN layer is implemented? If there are 4 domains (centers), each center image is fed into each layer of DADI encoder (that means 4 channels)? Is the BN layer just the regular BN layer without modification? \n•In Figure 3, the latent variables extracted from DADI encoder are just combined with the features extracted from DADR encoder to generate input images using “medical image decoder”. The reviewer is not sure how the domain-aware disease-irrelevant features affect the classification of benign and malignant masses which is the main output of this model.\n•Can the authors provide more details on how the four datasets are different in terms of domain effects including imaging acquisition, manufacturer, patient population, etc. It would be more interesting to see visualizations for each domain effect.\n•Is the input data to the model a mammogram image or a patch of lesion region? Are the evaluation based on study level or image level? If all the results reported in this study are image-level, the reviewer would suggest that study-level results are better to be used for comparisons as study-level interpretation are usually needed in a clinical setting. \n•In addition to the empirical results, it would be good to show an analysis on disentanglement using simplified datasets like different manufacturers including Hologic and GE machines. With DarMo, the domain-specific features (of each manufacturer) can be visualized and more informative to the potential reader. Visualization results shown in Figure 4 do not give the reader what domain-aware features are learned. \n•The reviewer might miss it, but did the authors evaluate performance of conventional CNNs (like ResNet50) as results shown in Table 1? Also, it would be good to show performance of model trained on all datasets (InH1+InH2+InH3+DDSM) and evaluated on each dataset. If their proposed model performance is comparable or superior to it, it would be nice to demonstrate the robustness of the proposed model to distributional shift. \n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "Fqbxg0V0ud", "reviewer": "Reviewer_eNnv", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper proposes a model DarMo to disentangle disease-related features from domain-related effects to achieve robust prediction in the healthcare domain. \nThe proposed model is guided by structural causal modeling to explicitly model disease-related and center effects. \nExperiments on four real-world datasets demonstrate the effectiveness of DarMo.\n", "summary_of_the_review": "Above the acceptance threshold. \nPlease see Strength And Weaknesses for detail.\n", "strength_and_weaknesses": "S1: The methodology part is written in a clear way and well addressed the main claims in the introduction part. \n\nS2: It is an interesting idea to apply structural causal modeling to encode medical\nprior knowledge and to disentangle disease-related features from the domain effect.\n\n\nW1: It is better to provide complexity analysis. On top of accuracy and AUC, time efficiency should be considered in practical application.\n\nW2: It is better to involve more components, e.g., loss functions, in Section 3.2 to make it clearer.\n\nW3: Sun et al., 2021a is duplicated.\n\nW4: The source codes are not available to validate the experimental results.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "0s1FyqlK5Jc", "reviewer": "Reviewer_kDRU", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper proposes a variational autoencoder strategy to offer robustness to hospital-specific X-ray characteristics. The methodology aims to disentangle these centre-specific measurement characteristics from the features predictive of the condition. The paper presents theoretical intuition and evidence of the stronger robustness of malignancy classification on 4 mammogram datasets by demonstrating how their model trained on a subset of these datasets generalizes better to a dataset external to the training set.", "summary_of_the_review": "Good paper, clear with great experimental and technical work. Would benefit from clearer proofs of the main theoretical result.", "strength_and_weaknesses": "The paper clearly presents the motivation and the studied problem, which is highly relevant to the medical community. The paper is well structured and written which makes the proposed model clear even if complex. Moreover, the authors propose relevant ablation studies and thorough evaluation against state-of-the-art methodologies. \n\nThe main weakness of this work is the mathematical proofs, particularly the one in Appendix. Specifically, the theorem in the main text is not quite precise, nor particularly intuitive. It is also not easy to connect with the provided proof (the comment following 3.1 is much more valuable). The notations (such as log vol) should also be introduced and simplified as much as possible. References to equations should be numbered, instead of ‘the one with y_k’, ‘the one with d_t’ which makes it difficult to follow.\n\nMinor updates that could improve the paper: \n- Displaying confidence in the tables (it is currently not clear if the results are significantly better)\n- Adding in Appendix a robustness metric, i.e. the difference in performance when trained in the same set and transferred. The performances should be computed on exactly the same test set.\n- Adding reference to graph convolutional network (also it is referenced once as 'graph convolution network'),\n\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works."}, "extra_text": {}}]

Author rebuttal:

Decision: Accept: poster