COSDA: Counterfactual-based Susceptibility Risk Framework for Open-Set Domain Adaptation
Authors: Wenxu Wang
Rui Zhou
Jing Wang
Yun Zhou
Cheng Zhu
Ruichun Tang
Bo Han
Nevin L. Zhang
Venue: ICML 2025 poster (2025)
Keywords: Domain adaptation
Open-set
Causality
Primary area: theory->domain_adaptation_and_transfer_learning

Abstract: Open-Set Domain Adaptation (OSDA) aims to transfer knowledge from the labeled source domain to the unlabeled target domain that contains unknown categories, thus facing the challenges of domain shift and unknown category recognition. While recent works have demonstrated the potential of causality for domain alignment, little exploration has been conducted on causal-inspired theoretical frameworks for OSDA. To fill this gap, we introduce the concept of *Susceptibility* and propose a novel **C**ounterfactual-based susceptibility risk framework for **OSDA**, termed **COSDA**. Specifically, COSDA consists of three novel components: (i) a *Susceptibility Risk Estimator (SRE)* for capturing causal information, along with comprehensive derivations of the computable theoretical upper bound, forming a risk minimization framework under the OSDA paradigm; (ii) a *Contrastive Feature Alignment (CFA)* module, which is theoretically proven based on mutual information to satisfy the *Exogeneity* assumption and facilitate cross-domain feature alignment; (iii) a *Virtual Multi-unknown-categories Prototype (VMP)* pseudo-labeling strategy, providing label information by measuring how similar samples are to known and multiple virtual unknown category prototypes, thereby assisting in open-set recognition and intra-class discriminative feature learning. Extensive experiments demonstrate that our approach achieves state-of-the-art performance.

COSDA: Counterfactual-based Susceptibility Risk Framework for Open-Set Domain Adaptation
Wenxu Wang" 1
Rui Zhou 2
Jing Wang? Yun Zhou?
Cheng Zhu
Ruichun Tang'
Bo Han
Nevin L. Zhang*
Abstract
Cantal relation
Spurious reation
Obeerved factor
Uixcbeeved
Intervened factor
Factir
Open-Set Domain Adaptation (OSDA) aims transfer knowledge from the labeled source do- main to the unlabeled target domain that contains unknown categories, thus facing the challenges of domain shift and unknown category recogni- tion. Little exploration has been conducted on causal-inspired theoretical frameworks for OSDA. To fill this gap. we introduce the concept Sus- ceptibility and propose novel Counterfactual- based susceptibility risk framework for OSDA, termed COSDA. Specifically, COSDA consists of three novel components: (i) a Susceptibility Risk Estimator (SRE) for capturing causal infor- mation, along with comprehensive derivations the computable theoretical upper bound, forming risk minimization framework under the OSDA paradigm; (ii) a Contrastive Feature Alignment (CFA) module, which is theoretically proven based on mutual information to satisfy the Ex- ogeneity assumption and facilitate cross-domain feature alignment; (iii) a Virtual Multi- -nnuii-unknow--- categories Prototype (VMP) pseudo-labeling strat- egy, providing label information by measuring how similar samples are to known and multiple virtual unknown category prototypes, thereby as- sisting in pet recognition and intra-class dis- criminative feature learning. Extensive experi- ments demonstrate that our approach achieves state-of-the art performance.
E
E
X
X
X
(a) SCM for data generation
(b) SCM for CSDA
(c) SCM for OSDA
Source
Target (OSDA)
KIKwai Cleeves
Uniianvn Clesse
Known Clases
(d) Open- Set Domain Adaplation Problem
Iea (f(s))) # wi)+ - - (7 (G (xx,) Giz)))
(e) Risk Paradigm for OSDA
Figure (a) Causal graph for data generation, (b) causal graph for domain shift, where red arrows describe the distribution of data (X,Y) is shifted because environment variables E are intervened in unseen domain, and (c) causal graph for OSDA, where red arrows indicate and intervened causal variables C lead unknown classes; (d) shows how images changed with the interventions on C:; (e) the risk paradigm for OSDA, including source supervised risk. feature alignment risk, and open set space risk.
intervened environment variables
1. Introduction
Traditional supervised learning algorithms heavily rely the in-distribution assumption (Murphy, 2012), which as- sumes that training and test data are sampled from the same distribution. However, this assumption is not consistent in wild environments, where domain shift (Zhang et al., 2013) and category shift (Qu et al., 2023) lead to the failure of supervised learning algorithms. Considering domain shift, Close-Set Domain Adaptation (CSDA) aims to transfer model from labeled source domain to unlabeled target domain under the assumption of shared label space (Ganin & Lempitsky, 2015; Cui et al., 2024). Existing domain adap- tation methods can broadly categorized into two main streams: metric learning (Long et al., 2016; Wei et al., 2024) and adversarial learning (Ganin al.; Li et al., 2018).
Equal contribution 'College of Computer Science and Tech- nology, Ocean University of China. Qingdao, China NNational Key Laboratory of Information Systems Engineering, National University of Defense Technology, Changsha, China 'Deparmmnnt Mechanical Enginecring, University British Columbia, Van- couver, Canada "Department of Computer Science, Hong Kong Baptist University, Hong Kong. China Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Hong Kong, China. Correspondence to: Ruichun Tang <tangruichun @ ouc.edu.en">.
Proceedings of the ndnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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COSDA: Counterfactual-basee Susceptibility Risk Framework for Open-Set Domain Adaptation
However, in test environments, encountering novel classes is common, exposing the limitations of the shared label space assumption. To address both domain shift and class shift, researchers have begun to explore a different learning setting known as Open-Set Domain Adaptation (OSDA) (Saito et al., 2018; Wang et al., 2024; Fang et al., 2020), which integrates CSDA with open-set recognition. OSDA assumes that the label space of the source domain is subset of that of the target domain, meaning that the model is expected to encounter unseen classes during real-world applications.
inspired Feature Alignment (CFA) optimization objective to align cross-domain features and pseudo-labeling strategy with Virtual Mulli-unknown--ategoriiss Prototypes (VMP) instead of treating the unknown class as single category.
The main contributions of this paper are as follows:
Promising Way: We propose a structural causal model within the OSDA paradigm and perform theoretical deriva- tions and algorithm design centered the counterfactual probability of susceptibility. This addresses its optimiz- ability, evaluability, and identifiability, thus presenting a principled causal framework for OSDA tasks.
A body of work has focused on OSDA, and the risk for- mation of these studies is illustrated in Fig. 1 (e). Here, E
E,~S [I (z,) + yo)] aims at unbiased supervised learn- ing of source domain (Bucci et al., 2020: Li et al., 2023); E E (T (I.) + G (1a))] denotes feature align-
Systematic Theoretical Framework: We introduce a novel counterfactual-basee risk Susceescciiiiilitty risk-alon with its evaluator. A theoretically computable upper bound for the target domain's 's susceptibility risk is derived within the OSDA paradigm.
a. (TASS
ment to address domain shift (Ganin et al.; Luo al., 2020; [I (h (Ix) * K + 1)] repre-
Wei et al., 2024); and E
xte (T(s)
Innovative Techniques: We identify an optimization objec- tive that satisfies the Exogeneity causal assumption, which is recognized as maximizing the mutual information between the target sample and the source domain prototype. Based on this, we propose Virtual Mulli-unknown-categorr Pro- totype (VMP) pseudo-labeling strategy and a Contrastive- inspired Feature Alignment (CFA) module.
sents the minimization of open-set risk to achieve unknown class recognition (Saito et al., 2018), where most methods re- quire the design of unknown class recognition strategies (Liu et al., 2019; Saito, 2021: Qu et al., 2023).
Causal models have been widely utilized to achieve domain alignment (Arjovsky et al., 2020; Lu et al., 2021; Yuan et al., 2024; Yue et al., 2021) due to the invariance of causal features. Most causal models divide latent features into cevironment--speiife features (E) and causal features (C), assuming that F. I. C' and F Y C (Yang et al., 2024; Lv et al., 2022), as shown in Fig. (bb). Domain shift in causal diagrams arises from interventions on domain-specific vari- ables, which alter their distributions and consequently affect the joint distribution of the dataset, while P(Y C') remains stable( Yuan et al., 2024). However, for OSDA, there has been little exploration of causal graphs and a comprehensive causal-based risk theory. This is the gap that we aim to fill.
Comprehensive Experiments: We validate the effective- ness of the model on three benchmark datasets, achiev- ing improvements of 2.9%. 2.2% and 1.0%, respectively, compared to of-tho----e-rrr (SOTA) algorithms. Ablation studies and experiments on synthetic datasets confirm the effectiivnesss of each proposed module.
2. Preliminaries
Causal inference based on counterfactual distributions in- volves evaluating the effects of interventions on outcomes and seeks identify variables whose alterations signifi- cantly influence the actual values of outcomes. To quantify this influence, we introduce the concept of Probubility of Counterfactual, which is formally defined as below.
We argue that causal features still play a crucial role in OSDA. When causal features are not intervened, the condi- tional probability of the label P(Y|C) will remain stable. However, significant shifts in causal features can lead to category shifts, explaining the emergence of new categories. Therefore, the model must be sufficiently concentrated on core causal features. Based on this, we propose a promising OSDA method using essential causal information, which builds upon the probability of Susceptibility. First, we model an evaluator to assess and optimize the susceptibility of fea- tures. Second, to assess risk with limited data, an OSDA risk framework is provided through theoretical analysis. For the identifiability of counterfactual-bat baase susceptibil- ity risk, characteristics must fulfill two causal assumptions: Exogeneity and Monotoniciry. To ensure that extracted fea- tures fit these causal assumptions, we propose two novel strategies: mutual information theory-based Contrastive-
Definition 1 (Probability of Counterfactual (Pearl, 2009));
Let the invariant representation of causal variables C for
label y be c, and e' is the specific implementation of C, where C & c'. The probability that Y changes from + y
to Y = y when C is altered from c' to c is
PC = Pr(Yao(C=o) =y)
(l)
Two causal definitions, Exogeneity and Monotonicity, have been introduced by Pearl (Pearl, 2009) for identifiability. Exogeneity represents condition of no confounder, ensur- ing the vanishing of differences between the intervention distribution and the conditional distribution. Monotonicity further elucidates the monotonic direction of causal effects. The definitions of Exogeneity and Monotonicity are detailed
2

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COSDA: Counterfactual--aaee Susceptibility Risk Framework for Open-Set Domain Adaptation
in Appendix B.
3.2. Susceptibility Risk Modelling
Based on Exogeneity and Monotonicity, the identifiable dis- tribution of Eq. (1) is described by the following lemma, which is defined as susceptibilityy
This section presents the Susceptibility Risk Estimator (SRE) for representation learning in the target domain. First, introduce concept, Probability of Intervention Relevance (PIR), which is used to quantify the probability of Y after C has been intervened.
Lemma (Probability of susceptibility ((Pearl, 2009))). If C is exogenous relative to Y, and Y is monotonic relative to C, then the probability that Y is susceptible C is
Definition 2 (Probability of Intervention Relevance (PIR)).
Given a test domain T. if E T C. and E 1 Y C, the probability of intervention relevance (PIR) is defined as:
PS Pr(Y = y/ = c) Pr(Y = =ycC==
(2)
- Pr(Y = y/c c')
(c)) = P. y|C = d'),
(4)
and the Probability of Observational Relevance (POR) is
The proof of lemma 1 is established by the logical analysis carried out by Pearl (Pearl, 2009). A characteristic with higher PS typically encompasses more significant causal information. Appendix A presents examples to illustrate where the susceptibility is high and where it is low. Fur- thermore, susceptibility risk, compared to traditional causal effect evaluations (Pearl, 2009), proves to be more effee- tive in identifying core causal features. This indicates that susceptibility risk functions for identifying causal links, hence improving the model's I's capacity to concentrate on critical causal information.
defined as: POR = Pi(Y - C c).
(5)
Then, we define the estimation of Susceptibility risk.
Proposition (Susceptibility Risk (SR)), Observational relevance risk Ox(c) and the intervened relevance risk O,(c') are defined as:
Oc(c)= E
E. (X.U)~T en P((()))
P(Y xvlc),
(6)
more discerning indicator
E O,(c') = (x.9)~T ((
P(Y + y ())).
(7)
Then, susceptibility risk SR, based on Lemmas 1 is formally defined and we derived a new formulation of SR, as: SRy(c, c') = - PS == O₂(c) - O((').
Additionally, causality posits the Semantic Separability as- sumption of features, meaning that features with distinct semantics maintain a certain distance and a certain feature does not correspond to multiple semantic meanings simulta- neously. To meet this condition, we define the stability loss LSTA (Yang et al., 2024) as follows:
(8)
The induction is detailed in Appendix B.1.
3.3. OSDA Risk Framework with Susceptibility
LSTA = E ||c 1cc-c'll22 c'122
(3)
In this section, we introduced several theorems to gain an evaluable upper bound for SR,-
where represents the degree of intervention on the causal features. LSTA indicates that the semantic meaning is dis- tinguishable between and c', requiring that the degree of intervention must be sufficiently large to induce semantic changes in features, thereby avoiding inherently unstable learning.
Linking open-set recognition risks and closed-set classi- fication risks.
Assume supp(S) is the shared support set; the target do- main in OSDA has subsample set {X, YJ & supp(S). Therefore. SR, can be rewritten as:
Theorem 1.
Given the source domain distribution S and the target domain distribution Tx, the susceptibility risk on the test domain SR,(c, c') can expressed as:
3. Methoodooogy
3.1. Learning Setup
SR3 (c,c')=
[T(x,)) v) supp(S)]
Assume that we have the labeled source data D,- S and unlabeled target
(x.9)~T
(X,, Y2} {(xii, Bed) The ~ Tx. where S is the data D,- = [X.)= = {x> joint probability distribution of the source domain, T is the marginal distribution of the target domain, with n,, and ny indicating the size of the source and target datasets, re- spectively. Open-set Domain Adaptation (OSDA) allows the source label space V/ = f1,..., K} and the target label space }/- = ()),, K + 1}. where K +1 1 denotes the un- known class. Given the i.i.d. samples drawn from S and Tx, the goal of OSDA is to train a model that can classify the samples from the known classes and recognize the samples from the unknown class correctly.
E P(Y # C = c) d-P,:e' x-x)
P(Y # y C' -'==0 + ((x,))-(((xxx9)) & supp(S))
E [x)x(())-x))
P(Y # K1 C C=
E d'P(CI(Ex)
P(Y + K K+1|
:= -ina
(X. Y)
(9) where (Sp is the support set of the source domain dis- tribution. Px Y & supp(S)) shares the same idea as the Open Space Risk (Scheirer et al., 2012), quantifying how
3

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COSDA: Counterfactual-basce Susceptibility Risk Framework for Open-Set Domain Adaptation
Susceptibilitt Risk Evaluation
Souree
C
Lx (o
Pc
Abaet Linkoon
sample
MLP
Optmizing SR
Target
sample
Classifier
Embedding Layer
C
N (((e
Lei (oc)
Feature Extractor
(b) Satisfaction for Exogeneity
Distribution by source model
1. define positive instances pt
get unknown class prototype pi
4. get pesudo lahel by (q.)
3 CFA
far for
!
misuio
Iareel
Distribution after adaptation
2. known class prototype pf
Source
(ot Ne
Mean(
Target Known
Target Unknown
The label of is
(p Ten
Mean(
Prototypes
The label of is unlanann
Figure 2. An overview of our proposed COSDA, (a) describes the deployment of feature interventions. We add intervention module utilizing Multi-I Mayr Perception (MIP) following feature C, executing an intervention via nonlinear transformation feature C. The feature distribution is Gaussian distribution with parameterized mean and variance, popularized by VIB (Kingma et al., 2015). (b) The VMP and CFA are proposed to address Exogeneity. The central idea of VMP (1.-4.) is to build the centroids all known and unknown classes, and then generate the pseudo label for samples by comparing the distance between samples and the centroids. CFA (5.) introduces the concept of feature alignment, which reduces the distance to the appropriate class centroid while maximizing the distance the centroids of other classes, establishing class-lcvel cross-domain feature alignment. Through adaptation, we align the features of known classes while also lcarning the decision boundary for unknown classes.
open the OSDA problem setting is. (X, Y) accumulates the open-set recognition error.
where
== dTx (c) - drx + (X,
(11)
L. == :=:=e5(c)) cc(c) es (c').
(12)
Linking Target Risks and Source Risks.
In the OSDA task, only the labeled observations of the source domain and the unlabeled observations of the target domain Tx are provided. Consequently, direct assessment of susceptibility risk in the target domain is unattainable. To resolve this issue, we introduce the expected disagreement dr, and the expected joint erгоr és (Lacasse et al., 2006), which needs no label information of the target domain. Then, we propose Thcorem 2 using 3-divergence (Germain et al., 2016) and Hölder's ' Inequality. Proof for Theorem is provided in Appendix B.3.
Linking Empirical Risks and Expected Risks. The ex- pected risk SR(c, c') cannot be calculated since the distribu- tions S and Tx are not provided. We define the estimation distributions on the available data D as P(Y y C = c). P(Y y C' c'). P(Y y C c). P(Y = C' = c'), then the empirical risks with respect to SR(c, c') are defined as Eq. (13) below.
SR(c, c') == ED EDEE- = C c) C' c'). (13)
- -EDBE-PIIXX-
P(Y P(Y
Theorem 2. Given the source domain distribution S and the target domain distribution Tx. an invariant represen- tation inference model G, an intervention model G', and classifier h, the susceptibility risk on the test domain SRe(c, c²) is upper bounded by:
To address the issue that the estimation of expected risk is not available, we propose Corollary using the Variational Inference, Hoeffding inequality, Markov inequality, and Jensen inequality following (Yang al., 2024) to ensure the expected risk can be upper bounded by the empirical risk.
ex
SRT (c,c')
_ (d (c) drx (c'))
+ lim {r(T][)(es(()) - es(c')) (10) 000
Corollary 1. Suppose prior distributions for the represen- tations "cc := P(C), jo := P(C'). With probability 1-8 over the choice of samples X D, for every parameter
+ (X,),
4

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COSDA: Counterfactual- Susceptibility Risk Framework for Open-Set Domain Adaptation
combination, SR - c upper bounded by CRL = -log(oc) + log(
prototypes by these positive instances. Subsequently, these affirmative instances of known classes are eliminated, and the remaining samples are subjected to clustering algo- rithm in order to estimate the prototypes of U unknown classes. The pseudo-labels for the samples are determined by calculating and comparing the distances between each target domain sample and all prototypes.
(14)
Corollary 1 indicates that the error between the empirical risk and expected risk can be minimized as the KL diver- gences decrease. Proof for Corollary is provided in Ap- pendix B.4.
Specifically, given the scores of x; after the softmax func- tion {(h(G(x))) for the k-th known class, we first define the Top-M (x(((G(x)))) scores represented as positive in- stances Pt, and let the positive prototype representation p²:
3.4. Satisfaction of Causal Assumptions
In this section, we concern the satisfaction of causal as- sumptions, Exogeneity (Assumption 1) and Monotonicity (Assumption 2).
As for Monotonicity, emphasizes the value of y given that should be larger than given any other intervened feature c'. This objective can be formulated as:
= 1 Σ G(x))) MM Pe
(17)
= max P( y/C - P c')= (15)
For the unknown classes, remove all positive instances of known classes and use the K-means algorithm to generate
which is equal to minimizing the susceptibility risk. There- fore, we can naturally introduce the Monotonicity measure- ment into the estimation of susceptibility risk.
U negative prototypes for the unknown classes.
{p") X.EDA((P (
K-means (G(x:)).
(18)
As for Exogeneity, we first rewrite the assumption using information theory (Kraskov al., 2004).
Here we set U = K, M = N + K). For sample X the o-th element of its pseudo label ÿ is defined as follows:
Proposition 2. (Mutual Information Equivalence) The Exogeneity condition in Assumption can be equivalently represented with the Mutual Information I(::)):
1. if (G (xxx) .P() max {s (G (x)))p()) p0)
G.
O, if sG (G (xa). p8) < max {s (G (xt). P8) K+U
Pr(Y k.C, E = es/a)) Pr(Y =CC)
(19)
max E. T(CHsCt))
(16)
where s(a.b) measures the similarity between and b. Based on Eq. (19), we obtain the pseudo labels ÿt for all categories o E [V.,1) = {l..... K, K + 1,..,, K + U}. Then, the samples with pseudo label {K + 1, 1.., K + U} are defined as unknown class samples.
Xi:Ek
where Cu represents sample features in the target domain G(xx)) and C² represents the center point representation in the source domain G(x,:)). Both C, and C² belong to the k-th category. If Pr(Y E|C, = e1/=)= = Pr(Y = k C), then certain domain traits are unnecessary for identifying Y. Maximizing E. T(C,;; C+) mitigates domain changes on
Contrastive-inspired Feature Alignment (CFA). To fully leverage the labeled knowledge from the source domain, this paper adopts contrastive learning strategy to align the feature space of shared classes across domains. Unlike the contrastive learning strategy in CSDA, the prototypes for comparison in this work include not only the source domain prototypes d but also the virtual unknown class prototypes p (estimated by Eq. (18)). The prototypes of known classes in the source domain are defined as:
Ek causal features, ensuring resilient and trustworthy represen- tation. Proposition 2 is proven in Appendix B.5.
To achieve E CCC we introduce an innovative xx:Ek
and efficient pseudo-labeling strategy termed Virtual Multi- unknown--ategorris Prototype pseudo-labeling (VMP) for classifying samples from the target domain, subsequently maximizing the feature information shared between the tar- get domain and source domain through contrastive-inspired Feature Alignment (CFA).
= n 1=1
G(xx))
(20)
To prevent negative effects from pseudo label noise, the target domain samples used for contrastive learning are filtered by I(xx): ): (i) the pseudo label obtained based on the highest logit is aligned with the label obtained through the VMP strategy, and (ii) the value of the highest logit is higher than 0.7.
Prototype pseudo- labeling (VMP). Unlike previous clustering-bis algo- rithms, which group unknown classes into a unique class, this paper presupposes the existence of U' unknown classes in the representation space. The fundamental concept of this approach is to initially identify positive instances of recog- nized classes using confidence scores and compute positive
Virtual
{ 1, (mxx((((((((xx)))) A A5=1 =1
I(x:)
{
(21)
clse
5

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COSDA: Counterfactual--asee Susceptibility Risk Framework for Open-Set Domain Adaptation
Table 1. Comparison results (%) of Image-CI.R. (Best in bold and second hest in underline)
Average UNK
B--C UNK
B-I UNK
B-P UNK
C-B UNK
C-I
OS*
HOS
O5
HOS
OS*
HOS
OS*
HOS
OS
HOS
OS
UNK
HOS
OSNN (Mendes et al., 2017)
77.0
50.4
60.4
92.3
63.0
74.9
79.6
61.0
69.1
68.3
59.3
63.5
65,3
47.3
54.9
84.3
47.0
60.4
OSRP (Saito al. 2018)
74.4
70.2
71.5
87.0
85.3
65.7
74.3
66.3
66.7
66.5
58.0
59.9
89.0
80.0
84.3
STA (Liu al. 2019)
81.3
55.1
65.0
93.3
51.7
66.5
86.0
00.7
71.2
27.2
48.7
59.8
61.3
09.7
65.2
91.7
66.7
77.2
(Bucci et 2020)
69.9
76.9
78.3
73.0
74.6
68.3
63.3
68.3
63.3
78.3
DAOD (Fang et al., 2020)
71.1
75.8
73.3
79.4
82.0
80.7
78.4
90.9
81.3
72.1
80.8
76.3
$1.3
17.1
49.1
79.0
$8.6
83.6
ANNA (Li 2023)
78.2
85.6
83.0
75.0
74.5
83,0
68.3
87.0
89.9
Ours
81.0
XX.3
84.3
95.0
97.9
96.4
87.4
K8.9
W8.1
78.5
82.5
80.5
61.5
80.5
69.7
900.8
93.88
92.3
Method
C-PP UNK
1-18
L-SC
I-PP
P-BB
P.-C
P--1
OS
HOS
OS*
UNK
HOS
OS
UNK
HOS
OS*
UNK
HOS
OS
UNK
HOS
OS*
UNK
HOS
OS*
UNK
HOS
OSNN
75.3
46.3
57.3
62.0
41.6
49.8
92.0
41.3
57.0
81.3
40.6
54.2
55.0
49.6
52.2
86.0
55.3
67.3
82.0
52.6
64.1
OSRP
87.7
53.7
66.7
55.7
64.7
58.
80.7
92.7
86.3
66.3
74.3
70.
52.3
61.0
56.3
68.01
78.9
66.0
80.7
72.6
STA
$4.0
54.0
65.7
62.3
54.0
57.9
94.0
53.7
68.4
80.7
59.0
68.2
61.3
43.7
51.0
93.7
47.7
63.2
90.0
51.0
66.1
78.7
73.3
58.0
59.7
88.7
78.0
77.0
59.3
52.7
90.3
79.7
79.7
DADO
74,5
78.9
76.7
51.5
56.9
55.7
80.3
82.0
81.2
73.3
80.8
76.9
51.7
51.0
51.3
79.0
82.0
80.5
79.6
$6.6
83.9
ANNA
84.0
56.0
65.2
80.7
62.3
85.0
83.3
Ours
80.9
84.5
82.7
60.8
79.4
68.9
94.5
97.9
96.2
82.4
87.2
84.7
58.9
78.2
67.2
94.0
97.01
95.5
87.2
91.7
W9.4
The optimization objective of our proposed contrastive learn- ing is
domain using predicted pseudo-labels. LKL. is used to reduce the error between the expected risk and the empirical risk. Luxo is for satisfaction of the Exogeneity assumption, and
(G((x)) x I(x())
Levo
S(G(x.:) (p)) 5(G((x)) (p
CSTA tends to sufficiently large intervention operations to ensure that the learning parameters of the model are stable.
(22)
where
4. Experiments.
K p((x)))
S(G(x)), (p*)) (p.)*)
(23) In this section, we verify the effectiveness of COSDA using real-world and synthetic datasets.
K+U
S(G(xi), (ettxx))pP)))))) (
Σ
s(G(x)),P.)
(24)
4.1. Experiment Setup
Benchmark Dataset Settings. Extensive experiments are conducted on five benchmarks following the stan- dard setting (Qu et al., 2023; Bucci et al., 2020): Office- Home (Venkateswara et al., 2017), Office-31 (Wang et al., 2019), Image-CLEF (Li et al., 2023), DomainNer (Wen Brbic, 2024), and VisDA (I.i et al., 2021).
where s(a, b) denotes the similarity between a and b. nē denotes the number of samples in the target domain with label k.
Our proposed contrastive-inspired Lexo comprises two ef- fects: (i) For the source-share (known) categories, Cewo operates the domain alignment with intra-class compact- ness and inter-class separability; (ii) for the target-private (unknown) categories, Lero increases the discrepancy be- tween private-class samples and the source domain features, enabling the model to better recognize unknown classes.
Evaluation Metries. Following the main OSDA stream (Qu et al., 2023; Li et al., 2023), we utilize four widely used measures, i.e., UNK, OS", OS, and harmonic mean accu- racy (HOS). Among them, HOS is regarded as the most equitable evaluation criterion.
HOS- 2 x OS x UNK
(26)
OS + UNK
3.5. Model Optimization
Implementation Details. We adopt the same network ar- chitecture as mainstream OSDA methods (Qu et al., 2023; Li et al., 2023). All experiments are conducted using the ImageNet (Deng et al., 2009) pre-trained ResNet-50 (He et al., 2016) feature extractor. First, we train a source model the source domain. During target model adaptation, we apply the SGD optimizer with a momentum of 0.9 and batch size of 32 for all benchmark datasets, following (Li et al., 2023). We set the learning rate to 1 x 10-3 for Office-31, Image-CLED and Office-Home For hyperpa- rameters, X,=0.2, A1 All experiments are conducted
During the adaptation stage of the proposed COSDA, we implement the optimization objective as follows:
L Le
+
C.
+ Aexo Levo
+
LKL
+
LSTA
(25)
Eq. (11)
Eq. (12)
Eq. (22) Eq. (14)
Eq. (3)
where A. is from the OSDA theory framework. Intuitively, C, measures the empirical susceptibility risk of the source domain using source domain labels, while L, measures the empirical susceptibility risk of the target
6

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COSDA: Counterfactual-basee Susceptibility Risk Framework for Open-Set Domain Adaptation
Table 2. Comparison results (%) of Office-311. 31. (Best bold and second best underline)
Method
Average
A-D
A-W UNK
D--A
D-W UNK
W-3A
W-I
OS
BOS
UNK
HOS
OS
HOS
OS*
UNK
HOS
OSBP (Satto et al., 2018)
87.2
80.4
83.7
90.5
75.5
82.4
86.8
79.2
82.7
76.1
72.3
75.1
97.7
96.7
97.2
73.0
74.4
73.7
99.1
84.2
91.1
STAsum cI 2019)
94.6
50.5
65.5
95.4
61.6
58.0
71.0
55.0
69.4
49.7
65.5
92.1
46.
96.6
64.4
LAN (You 2019)
93.4
40.3
55.1
95.6
24.4
38.9
95.5
31.0
46.8
93.5
53.4
68.0
99.8
52.5
68.8
94.1
38.8
54.9
81.5
41.4
53.0
ROS (Bucci al., 2020)
86.6
85.8
85.9
87.5
77.8
82.4
88.4
76.7
82.1
74.8
81.2
77.9
99.3
93.0
96.0
59.7
86.6
77.2
100.0
99.4
99.7
ANNA (Li st al., 2023)
87.8
90.0
88.6
93.2
76.1
53.8
82.8
88.4
85.5
75.4
91.1
52.5
99.4
99.6
99,5
76.0
57.9
87.6
100.0
96.8
98.1
GLCC (Qu ol., 2023)
89.0
OSLPP (Wing al., 20124
89.3
85.6
92.6
91.5
89.5
88.4
89.0
76.6
79.3
96.9
92.3
78.9
78.5
78.7
98.8
98.6
GLC++ (Qu et al., 2024)
90.4
93.9
38.6
86.7
89.1
93.4
94.7
96.5
95.9
Table 3, Ablation study results (%) on Office-Homee Home with four different sub-tasks. (Best in bold and second best in underline)
Office Home
A-R
R-P
P-C
C-A
Average UNK
OS
UNK
OS
HOS
OS
UNK
OS
HOS
OS
UNK
OS
HOS
OS*
UNK
OS
HOS
OS*
OS
HOS
Causal Assumption
w/o Cexo
75.6
80.0
75.8
22.2
73.6
82.6
74.0
77.8
56.9
74.8
57.6
64.6
52.2
25.0
53.1
61.6
64.6
78.1
65.1
20.4
OSDA Theory Framework
w/o C.
89.0
0.0
85.6
0.0
82.9
0.0
79.7
0.0
49.8
0.0
47.9
0.0
61.5
0.0
59.1
0.0
20.8
0.0
68.1
0.0
w/o
72,9
85.2
73:1
78.6
71.1
87.2
71.7
78.3
51.5
77.9
52.5
62.0
49.8
77.6
50.9
60.7
64.6
82,0
62.1
69.9
Pscudo labelling Stratogy
with MLP
84,3
0.0
81.1
0.0
83.1
0.0
79.9
0.0
55.7
0.0
53.6
0.0
66.6
0.0
64.1
0.0
72.4
0.0
69.7
0.0
with
77.2
82.9
77.2
77.0
73.6
84.0
74.0
78.4
51.5
75.5
52.5
61.3
50.7
74.1
51.6
60.2
63.3
78.7
63.8
69.2
Ours
80.3
79.5
80.2
79.9
81.1
77.3
80.9
79.1
58.5
69.9
58.9
63.7
57.9
74.0
58.6
65,0
69.4
75.2
69.6
71.9
on an RTX-4090 GPU with PyTorch-1.10. We compare our method with recent works that adopt the same OSDA settings. All baseline scores are directly taken from their publicly reported results. A detailed review of the base- lines is provided in Appendix C. The code is available at http://gghllbboomm////UUUo600000 maste.
surpasses it with 3.6% OS*, 3.9% UNK, and 4% HOS, respectively, verifying the effect of our method.
Office-Home. Comparison results on Office-Home are shown in Table 6. COSDA gives the best average HOS (71.6%) evaluated over 12 tasks. Specifically, our method outperforms OSBP, ROS, and OSLPP with 7.0%, 5.5%, and 4.7% HOS, and surpasses them by 8.0%, 1.9% and, 2.6% in UNK comparison, demonstrating the robustness of our unbiased OSDA framework.
4.2. Benchmark Comparison
Image-CLEF. We report the comparison results of the real- world benchmark Image-CLEs CLEF in Table 1. We observe that COSDA achieves the best results in 11 of 12 sub-tasks for the HOS comparison and 10 of 12 tasks for the UNK comparison, verifying our great potential for more complex real-world scenes. Moreover, COSDA achieves the best 84.3% average HOS, which yields 2.9% gains over the state- of-the-art work ANNA, 11 11.0% over DADO (Fang et al., 2020), 12.8% over OSBP, and the best 88.3% average UNK, which outperforms ANNA by 2.7%, DADO by 12.5%, and OSBP by 18.1%, verifying the effectiveness of our method.
4.3. Efficiency of Susceptibility Risk
In this section, we conduct synthetic experiments to evaluate the effectiveness of susceptibility risk. The effectiveness of susceptibility risk is demonstrated by examining whether it can learn the essential causal relationships. To this end, we designed a synthetic data generator based on Fig. 3 and created a sample set {X, Y). where X is generated from three causal factors C and a spurious association factor S.
Office-31. Comparison results on Office-3/ are shown in Ta- ble 2. The proposed method achieves the best average HOS (92.6%) over all 6 tasks, outperforming OSBP (Saito et al., 2018), ROS (Bucci et al., 2020), and OSLPP (Wang et al., 2024) with 8.9% 6.7%, and 5.2% HOS and 13.5%, 8.1 1., and 8.3% UNK, respectively. Compared with the state-of- the-art OSDA (source-free) work GLC++ (Qu et al., 2024), our method comprehensively surpasses it with 2.2% HOS. Compared with the state-of-the-art OSDA (source-support) work ANNA (Li et al., 2023), our method comprehensively
noise
noise
B
Aps
Psc
S
C
Y
Figure 3. Causal graph for Synthetic Data Generation: Y 1. SSS C
We use a parameter Xpsc to distinguish the importance of causal factors. When Apec is closer to 0 or 1, the causal association is stronger to Y; Conversely, the closer Apsc is to 0.5, the weaker the causal association is. Then we introduce
7

---

COSDA: Counterfactual-basce Susceptibility Risk Framework for Open-Set Domain Adaptation
parameter 3 to represent the noise intensity in the data. We set Apuc (0.15, 0.25, 0.35) and 8 {0.1, 0.4, 0.7, 1.1).
for unknown classes, while its ability to recognize known categories declines. Overall, removing the risk from either domain negatively impacts the model's performance, with the OS dropping by 1.5% and 7.5%, respectively.
10
Efficiency of VMP. To assess the effectiveness of VMP, we compare it to the logit-based pseudo-labeling strategy (MLP) (Wang et al., 2022) and the Global Clustering pseudo- labeling strategy (GC) (Qu et al., 2023; Saito, 2021). The comparison illustrates that MLP (row 8) has virtually no discriminative ability for unknown categories. This is most likely because it relies heavily on source domain knowl- edge and lacks unknown class information. Furthermore, our technique outperforms GC by 2.7%, demonstrating the usefulness of VMP.
Distarge Couslation
0.6
044
A=11
8=07
0.2
#=04
B-01
0.0
7/0= =0.15
Auc
=0.25
2x
=0.35
Spurious
Radors
4.5. Qualitative Results
Figure 4. Results of Suscepetibility risk yellow and Vanilla risk
orange
Trade-off Analysis. To analyze the impact of parame- ters in Eq. (25) on COSDA performance, we define X = {0.1, 0.5, 0.8, 1.0} and Aezo {0.1, 0.2, 0.5, 0.8, 1.0}.
Besides, Aper denotes the spurious degree. When Aper gets higher, the spurious correlation stronger in data X. We set Aper 0.4, and the dimension of the factors d = 64. Then we develop a non-linear function to generate X from (Co.15: Co.25. ST. We use Distance Correlation to evaluate the correlation between the learned representation and these factors. A higher Distance Correlation indicates a better representation of factors. In Fig. 4, we compare the performance of the susceptibility risk evaluator with that of a standard empirical risk evaluator. For critical causal factors (Apsc = 0.15), our method achieved distance cor- relation higher than the standard risk. For factors with lower causal relevance (Apec = 0.25, Apsc- = 0.35). For spurious factors, our method yielded a lower Distance Correlation compared to the standard risk. These results verified that by incorporating susceptibility risk evaluation, models can reduce the learning of spurious correlations and maintain focus critical causal factors. Due page limitations, ad- ditional details and results regarding synthetic experiments are provided in the Appendix D.
Fig. 5 shows that the proposed technique has good parameter stability across datasets.
S1.0
Far
1591
1126
Figure 5. The sensitivity analysis ()e, dezo) of COSDA on P-1 (eeoge-CLEF)) task (left) and Rw-Pt (Office- task (right) terms of parameter variations.
Feature-level Analysis. To illustrate the success of our strategy, we compare the characteristics recovered by the baseline algorithms and our approach to the t-SNE. Fig. 6 shows the t-SNE visualization of feature distributions on the W + D task (Office-31, left) and Ar + Rw task (Office- Home, right) with the ResNet-50 backbone. Comparative methods include OSBP, ANNA, and COSDA. The gray node denotes the unknown target sample, the red node denotes the known source sample, and the blue node denotes the known target sample. Compared with OSBP, our method clusters class characteristics more compactly, which indicates the improvement of the decision border between known and unknown classes. Since both OSBP and ANNA utilize ad- versarial training and share the same underlying framework. their feature spaces exhibit similar characteristics. Com- paratively, ANNA better delineates the boundaries between known and unknown classes, as only small number of gray points overlap with the blue and red points. Due to their similar performance, we cannot clearly exhibit COSDA's ad- vantage at the feature level compared with ANNA. However,
4.4. Ablation Study
In this part, we conducted detailed ablation studies on four subtasks in Office-HHe Home and summarized the efficiency of different parts of COSDA.
Efficiency of CFA. As shown in Table 3, compared to the complete COSDA, removing Lero (row 3) results a 1.5% decrease in average HOS, with a particularly notable 4.8% reduction in O This indicates that the CFA significantly enhances the model's 's ability recognize known categories.
Efficiency of the Evaluation on Source/Target Risks. As shown in Table 3, when L, is removed (row 5), the model fails to recognize unknown classes. Conversely, when the f. is removed (row 6), the model becomes overconfident
8

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COSDA: Counterfactual-basee Susceptibility Risk Framework for Open-Set Domain Adaptation
(a) OSBP (Office-Home)
(b) ANNA (Office-Home)
(c) Ours Coffice-Home
(d) OSBP (Office-31)
ANNA (Office-31)
(f) Ours (Office-31)
Figure 6. The t-SNE visualization of feature distributions on the W with the R0 backbone.
D task (Office-31, left) and Ar - Row task (Office-Home, right)
the clustering tendency of local unknown classes suggests that VMP's approach of considering unknown classes as multiple distinct groups is beneficial.
5. Conclusion
This paper establishes theoretical framework for OSDA grounded in the classical concept of Susceptibility to address the OSDA problem. We further present two modules, des- ignated as CFA and VMP, to fulfill causal assumptions and mitigate both feature alignment risk and open-set risk. Ex- periments show that COSDA outperforms the competition on all three benchmarks.
Table Comparison results on DomainNet and VisDA with CLIP backbone (All baseline results are obtained from Reference (Deng
Jia, 2023)).
DomainNe((73//13)
VisDA(6/6)
Method
OS*
UNK
HOS
OS*
UNK
HOS
DCC (Li al., 2021)
50.2
45.1
47.5
75.3
46.2
$7.3
UNIOT (Deng & Jia. 2023)
59.2
51.2
75.7
49.4
59.8
Acknowledgements
CROW (Wen & Brbic, 2024)
70.3
50.9
59.0
77.0
62.8
69.2
COSDA-CLIP
72.0
76.2
73.9
85.2
72.6
78.4
This work was supported by the National Key Re- search and Development Program of China (Grant No. 2022YFB3305803). BH was supported by the NSFC Gen- eral Program No. 62376235, GDST Basic Research Fund Nos. 2022A151501 1652 and 2024A 12441115001399, Rui Zhou was supported by the National Natural Science Founda- tion of China under Grant 62276272, the Training Pro- gram for Excellent Young Innovators of Changsha under Grant KQ2009009, and the Postgraduate Scientific Re- search Innovation Project of Hunan Province under Grant XJJC2024022.
Comparison on more datasets and more backbones. We
implemented additional experiments on VisDA (Li et al., 2021) and DomainNet (Deng & Jia, 2023; Wen & Brbic, 2024) and discovered that method demonstrates good performance on both CNN-based and CLIP-based architec- tures. Considering both time constraints and GPU mem- ory demands (particularly for the larger models), we uti- lized six 40GB NVIDIA 100 GPUs to execute the new experiments. NemainNet and VisDA use the same hyper- parameter settings as smaller-scale datasets, specifically
A, 0.2, Aezo 1. But the learning rate has been reduced, specifically Ir 5e 4. On DomainNet, COSDA-CIL - achieves 73.9% HOS, outperforming CROW by 14.9%. On VisDA, COSDA-CLIP reaches 78,4% HOS, outperforming CROW by 9.2%. With CLIP, COSDA particularly further enhances known-class classification and unknown-clan de- tection (UNK).
Impact Statement
This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here.

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COSDA: Counterfactual-basel Susceptibility Risk Framework for Open-Set Domain Adaptation
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COSDA: Counterfactual-baser Susceptibility Risk Framework for Open-Set Domain Adaptation
Appendix
The structure of the Appendix is as follows
Appendix A gives examples to illustrate where the susceptibility is high and where it is low.
Appendix contains all missing proofs in the main manuscript.
Appendix C contains the extended related work.
Appendix details the dataset, implementation details and additional experimental results.
A. Understanding Susceptibility
As fundamental concept in causal inference, susceptibility pertains to determining whether event (cause) leads to another event (effect). The average causal effect (ACE) is classical metric for quantifying the strength of causal relationships, defined as:
ACE = P(B))) - P(B)
(27)
where the first term represents the probability of event B occurring given that event A occurs, and the second term measures the probability of B occurring the absence of A. By intervening on causal variable (i.e., altering their states), we can observe changes in the outcome B. In the complex physical world, event often has multiple causes, and it is crucial to evaluate their causal significance. Generally, larger ACE indicates stronger causal relationship, implying more significant influence of the cause on the effect and greater mutual information between the cause and the effect.
The probability of susceptibility (PS) is defined as:
equal to ACE
P(B[A) P(B) -A) PS
(28)
1- P(B)-A)
the association between AA and B after intervention
Here, the numerator is identical Eq. 27, while the denominator quantifies the association between events A and B after intervention. When interventions of the same magnitude on A produce equivalent changes in B, the average causal effect treats them equal. However, a higher P(B| -A) indicates stronger susceptibility, guiding us to pay greater attention to it, which is intuitively more reasonable. We provided three examples to illustrate the effectiveness of susceptibility.
For the label "maple", we define four relevant characteristics: (I) palmately lobed leaves, (2) larger leaves with a few prominent teeth, (3) palmate veins, and (4) orange or red color. The conditional probabilities between these characteristies and the label (i.e., whether a leaf belongs to a maple tree) are summarized in Fig. 7, When comparing a certain feature, we presume that information regarding other features is inaccessible.
Example 1. (with same ACEE The characteristic "palm-shaped lobes" is regarded as the most distinguishing feature of maple leaves, whose presence firmly signifies a maple leaf. Conversely, the distinguishing of "palmate veins") is another relative trait of maple leaves, albeit less pertinent than "palm-shaped lobes." Given these assumptions, the average causal effect (ACE) for both features is determined to be identical, at 0.5. Nonetheless, susceptibility risk directs the model to emphasize the characteristic "palm-shaped lobes" owing to its elevated A)B) This underscores the superiority of the susceptibility model detecting more distinetive causal factors.
Example 2. (with same P ((B|-A) ) For the label "maple", the feature "orange or red"' is not causally relative "maple". Therefore, given C = 0 or C C=11 1, the conditional probability P(Y(C') remains unchanged, so we assume it to be 0.3 in both cases. Under these assumptions, P(B|-A -A) is equal for "orange or red" and "palace-shaper lobes". Relying solely on P(B may lead to misguided attention, as it fails to distinguish between causally relevant and irrelevant features. By calculating the PS xe 0.43, we find that the feature "prominent teeth" is more significant than "orange or red", which aligns with the results of comparing ACF.
12

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COSDA: Counterfactual-basce Susceptibility Risk Framework for Open-Set Domain Adaptation
label (Y)
feature (C)
P(YC- -
P(YIC - 0)
ACE
PS
0.8 0.3
ACE = 0.8 01.
PS
1 - 0.3
0.5
palm- shaped lobes
P(YIC = 1) 0.8
P(VCC = 0) = 0.3
0.7
maple
0.6 0.3
ACE = 0.6 (1.
PS
1 1 0.3
0.3
prominent teeth
P(УCC 1) 0.6
POIC 0) 0.3
PS 0.6 - 0.1
ACE 0.6-0.. - 0.1
0.1
0.5
palmate veins
P(Y|C- = 1) = 0.6 P.ICC = 1) 0.1
0.56
0.3 0.3
ACE 0.3
PS
0.3 0
=
orange, yellow
P(Y 0.3 P(Y = 0) 0.3
Figure 7. Examples understanding susceptibility image classification problem
Example 3. (with same P(BIA) ) The feature "prominent teeth" is assumed to be third-relative characteristic of maple leaves. If leaf lacks "prominent teeth", it is highly unlikely to be maple leaf. However, the presence of "prominent teeth" does not exclusively indicate a maple leaf, as other species may also exhibit this trait. Therefore, we assume - 0.6, P(Y = 1/C = 1) = 0.3. Under these assumptions, P(B[A) is equal for "prominent teeth" and "palace-shaped lobes". However, susceptibility risk guides the model to prioritize the feature "palm- lobes", which exhibits a greater difference than ACE. This result highlights the superiority of the susceptibility model in identifying more discriminative causal features.
In summary, susceptibility provides more robust measure of the causal relationship between features and the target. This work proposes a susceptibility risk estimator derived from this principle, aiming to guide the model in learning more causally relevant features and improving its generalization capabilities across domains.
The connections of SRE, CFA, and VMP. SRE quantifies causal feature representation ability via susceptibility analysis. Direct SRE estimation in the target domain is infeasible due to label scarcity. To resolve this problem, first decompose target-domain expected risk into open-set and closed-set, then bridge source/target risks using iamain-invariant represen- tations, and finally derive generalization bounds narrow the gap between empirical and expected susceptibility risks (Theorems 2 & Corollary 1). To satisfy the exogeneity assumption for causal identifiability, we propose CFA, which encourages independence across causal features belonging to different categories via information bottleneck (Proposition 2) and then introduces the VMP pscudo-label strategy.
B. Proofs
Assumption ((Exogeneity (Causality (Pearl, 2009)))). The Exogeneity of holds if the following invariant conditions are satisfied in Fig. I(b): L C, 1 YY C, which can be equivalently represented using the probability: Pr(Y cx/a)= = Cr)Y(C), where Ct/a is the domain-spectie feature.
Assumption 2 (MMonotonicity (Causality (Pearl, 2009)))). If the causal feature of is Y is monotonic relative to X if and only if v/c A Ye = false.
In this section, we provided theoretical proofs. Theorem 2 and Corollary follow the PAC-Bayesian theory frame- work (Catoni, 2007; Germain et al., 2016). Proposition 2 is based on Mutual Information theorey (Kraskov et al., 2004). The proof of Monotonicity is built upon Causality theory (Pearl, 2009).
13

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COSDA: Coutteracctull-baset Susceptibility Risk Framework for Open-Set Domain Adaptation
Algorithm 1 Overall Training Process of COSDA
Input: source domain Ds, target domains Dr; pretrained source model fg. number of epochs E, batch size B, Trade-off hyperparameters X, Aezo. a blank Memory M.
Initialize parameters randomly; M + f
for epoch to E do
Compute prototypes Pt for 1 to max//22 I.I... do
k/u by VMP (Eq. (17), (18)).
Sample mini-batch B, (Xeb. rbb B, {8+b) from Ds. Dr.
Forward pass: ys : of 2 int, = =f(B,; f), where int, denotes the intervention on Z
Compute loss: Lu, (xT(s)) (STA(S) -sb- 85 o0,0
of int,, (Eq. (12), (14), (3))
Get pesudo labels Sig of Bi by VMP with P. k/a (Eq. (19))
Forward pass: Df: Dr of int, = O)
Compute loss: Lt, LKL()); ESTACO) + Yo. Se. St of of int, (Eq. (11), (14), (3))
Update M Z.
Get P. by .M. (Eq. (21))
Compute loss: Lezo Yob, p Př. (Eq. (22)) Calculate the overall loss, L + Eq. (25) Backward pass: compute gradients VoL. Update parameters: 0 = - VoL. end for
end for
Output: Final Optimized Models fū-
B.1. Proof of Proposition 1
Proof. Based on Eq. (5) and Eq. (28), PS can be altered by Eq. (29) below.
POR. -IR
PS, 1 - PIR,
(29)
Then,
In()R,(c.'') = POR: - -IRR
PIR
In(1 PS)
PORK
In( PIR.
In(1 POR,) - -al1-PIR) In(1-IR)
(30)
In(1 BeN P(Y = C = c))
In(1 B P(Y= = C' = =c)
1B(D P(Y / C=c))
In(Bxx))-7EE--((O0XX - P(Y #y C' cc)
In(O.(c)) -n(((cc)
Then,
SR, c') = (n((0(())))(((((())
(31)
< (,))
Then, by minimizing O,(c) - lcc',, we can minimize SR, c'). Therefore, we can get the result of Proposition By minimizing (R,(c,')) c'), it can improve the consistency of the representation results of the model.
14

---

COSDA: Counterfactual-baser Susceptibility Risk Framework for Open-Set Domain Adaptation
B.2. Proof of Theorem Given domain S/T, an invariant representation inference model G, an intervention model G", a classifier h,
SRy (c, = 0+(c) - L((c)
E
E
P' + y C c)
(x.9)~T e~ ([X=x)
E (x.1)~-T
E d' pp x=x
(Y # y C' = c')
=
E
[[x, v) E supp(S)]
R (C((((
Pd(Y + C=c)
(x.9)~T
(32)
pa * C² =c)
c'rpp'' (C
+ E (xx) (x(,)) & supp(S)
E (C|XX()
PP(Y K +
PK + K K C' x
Tena Tx,, + (X,,)
B.3. Proof of Theorem 2
Given a domain S/T, an invariant representation inference model G, an intervention model G', and classifier h. For any probability distribution p over h, we define the expected joint error es/T(x, p) and the expected disagreement ds/r P) as
(x)x)=
E hampp harppp
1 (x) # 1 (b2(x)) + v)
(33)
(x.2)~
dTx (x)
E
E
E (xxu))xx
((h( & ha(x))
(34)
h1 hamphhmup
Then we can decompose the susceptibility risk (R, c') as
SRT c') 0,(c)- le(c')
E E (c))(c) + v) + (hz + u
E (x. cFX
himphrrp
E
E
E E [[/)(ce)) + y] + 1 1/2(ce) # #b
Tx e' (C
(C'
[[hi()) + h2(c)) + 21 (/ + y A h2 + v]
(35)
=
E
E
E himpharp
E
(x e- (xxx))
2
[ch # (c)) + 21 h (x) + y ^ (x) + mv
E of
himpharp
(dTx (c) drx (c')) + ec((c) - cr((c)
We refer to the technicals in (Germain et al., 2016) by using 3 divergence, which is formalized as (T(T([
E T(x.)) vl and Hölder's Inequality, that is fl s (1) (gl dn) 2 where g = 1,g +
S(x.9) (X
15

---

COSDA: Counterfactual--ars Susceptibility Risk Framework for Open-Set Domain Adaptation
+o0,p p- + in this paper. First, we define ((x,))-(((xxx) supp(S)), then using Hölder's Inequality, we have
cT(c)=
E (x.,))~Txx
E
E
((h1(c) # l + +b)
o- (C|x
hamppppae hamp
T(x,1)
E ((b1(c) # v) (b2()))))) # #9)
E
(x,9)m08
8(x, y)
(C hrmpp hamp
(36)
+ ((xx))= (( supp(S))
E
E ((h((c) + (b2 *
lim (T(())()) rer(s(c),
7-330
er(c') S lim (()) + q-50a
(37)
Rewrite (c) es))(c()) as Te (XYY) Y). Then we have
SR7 (c, < 2 (dT
+ lim ( -s()cc)
(38)
9+000
+ (X)
Then we can get the result of Theorem 2.
B.4. Proof of Corollary
First, we introduce the PAC-Bayesian theorem (Catoni, 2007), which gives the usual bound the empirical risk.
Lemma 2. For domain S S/T, any set of voters H. any prior over H. any risk R H + [0, 1], any real number c > 0. with probability at least over the choice of {(x, (:)) T, we have for all on H:
E R(p,x,))
(x.))-//Thmp
KL(plly) In
(39)
R(p,x,, houp
c-
X
Following the same setting of lemma 2, have: with prior 7c, there exists a probability of at least 1 5 over Dj ((x))) Tx.
(p. 2KL(p]]Tc) + In 14 X c es(p.c) < 1- eD, (p, 2KI.(plhc) + 1n n4
Vp on H.,7x (p.c)
1-
(40)
C
with prior Jo', there exists probability of least 1 5 over D, -(xx,,;;)}= p ~ S,
do, (2,c) + 2KT(pplicr)) + In
Vp on Hi,Tx (p,c') 5 c
c
T-
x c
(41)
cs(p,c) 5 1- CD. (p,')++ 2KL(pI) - In
ng c
Then, we obtain the following generalization bound defined with respect to the empirical estimates of the target disagreement and the source joint error: with probability at least over D. ((x,,))) v:) Tx and Dr = {(x)) Tx, let
16

---

COSDA: Counterfactual-baser Susceptibility Risk Framework for Open-Set Domain Adaptation
8' 30 (T] and d' T-e-a op H.
SRT (c,c)) - d (d).(c) dD.((c)) + ((e),)))(( 2KL((p117c)+ + 2
+ (X, + (
m+ x -+- mmxxb))) mxxb)
x b))
mh xc + my x)6) (2KL(e]T0)) + in 2 //2
(42)
(da,(c) - -dD((')) + - -D, (c))))) + (X, (x, Y)
+2 d'
+ m. xb) (KI(PITT)) KL(TC(
my
Therefore, we can narrow the error between SRT (c) and SRp, (c) by minimizing (KL(pl)ce + KL( Then with a non-informative prior 7 == NNu,, ) the produced Gaussian N ( o²), we have
min Pe.0a
KL (N (Me: I1 (Ky. o +00000
lim
o² + (No - mn,)
min He.Pe
lim
log
+
(43)
Je
20
log 0z
01 ))
min
lim
min (- log σe).
+00
Finally, we can minimize SRy (c) by adding Eq. 14, which is the result of Corollary
B.5. Proof Proposition 2
According to the definition of the KT. divergence and the Mutual Information T(:+), we can rewrite Pr(Y +|/C E et/s) Pr(Y k C) as:
(L 1 P C
=
P(Y K |
P(Y = C,
=0
P(Y = C)
(44)
p(Y k. C)
- = log
=(Y = k C)
p(Y = | C)
Based on I(Y e C) 0, we have
[(Y;Clc)= C) I(Y; Clc.)
(45)
Based on the transmissibilityy of T(:)), T(Y; Clex) (le,) can be achieved by:
max I(C, eC; C,e.)
(46)
Finally, given the universal data generation causal model M, M C,E + X, the causal representation model G, G: X - C, we reach
& MgN/(GGLM(C..)))))MCC......
(47)
= maxI(G((x):(xx)))
Then we can get the result of Proposition
17

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COSDA: Counterfactual-baeee Susceptibility Risk Framework for Open-Set Domain Adaptation
C. Related Works & Our Innovations
In this section, we review the progress of OSDA prediction tasks, including:
First, adversarial learning-based algorithms. OSBP (Saito et al.. 2018) first introduces the concept of domain adversarial learning into OSDA. Unlike UDA, OSBP sets a fixed threshold t for separating unknown class samples and employs gradient reversal to achieve min-max adversarial optimization between the feature extractor and classifier. PGL (Luo et al., 2020) proposed Progressive Graph Learning framework based on OSBP, which integrates graph neural networks trained in context to mitigate potential conditional shifts. Recently, ANNA (Li et al., 2023) considered the unknown class information embedded in the background features of known class samples, then introduced causal unbiased learning and domain alignment on top of OSBP.
Second, score-based algorithms. Separate to Adapt (STA) (Liu al., 2019) generates weights to reject target samples belonging to unknown classes while balancing their importance in feature distribution alignment. Inspired by STA's approach, (Shermin et al., 2020) introduced weighting module based on the similarity between target samples and source domain classes to find an appropriate threshold for each sample. ROS (Bucci et al., 2020) utilizes rotational invariance to improve source domain models and proposes entropy- and confidence-based regularization scores to distinguish unknown class samples. UAN (You et al., 2019) proposed a transferability criterion to quantify sample-level transferability, aiming to discover the common label set and the label sets private to each domain. GATE (Chen et al., 2022) introduced a generic incremental classifier that adaptively learns the "unknown" threshold by minimizing open-set set entropy.
Third. pscudo-label-basee alignment strategies. OSLPP (Wang et al., 2024) calculates class means and uses them to assign pseudo-labels to target domain samples, while target samples that are "far from" all known class means are recognized as unknown classes. This approach suffers from two key limitations: first, the ambiguous definition of "far from"; second, its inability to identify unknown-class samples that are similar yet distinct from known classes. DCC proposes Domain Consensus Clustering for universal domain adaptation, using semantical and sample-level consensus to effectively separate and distinguish common classes from private ones. OVANet proposes a universal domain adaptation method that learns an open-set threshold from source data via one-vs-all classifiers and adapts to the target domain by minimizing class entropy. UADAL addresses open-set domain adaptation with unknown-
adversarial learning, aligning known classes while segregating unknowns in feature space. Recently, GLC (Qu et al., 2023) generated positive prototypes using the Top-K K most reliable samples for each class and then applied a clustering algorithm to the remaining samples to create specific negative prototypes. The class of a sample is determined by comparing its distance to both positive and negative prototypes. The computational complexity of this method is proportional to the number of known classes, which reduces learning efficiency on large datasets. Inspired by GLC, we propose a simpler and more efficient approach to pseudo-label generation, called the Virtual Multi-unknown--e catteoressatsgoiies Prototype (VMP) pseudo-labeling strategy. The difference is that we exclude all known-class positive samples and cluster only the remaining negative samples (i.e., those not belonging to any known class). Besides, unlike one-vs-all strategies requiring C' clustering operations per epoch (C = the number of known classes), COSDA achieves comparable performance with only one clustering per epoch.
Recent advances in Open Set Domain Adaptation (OSDA) have primarily focused on three key research directions: (I) enhancing source domain knowledge acquisition, (2) establishing effective boundaries for unknown class detection, and (3) aligning known class distributions across domains. Our proposed COSDA framework makes significant contributions to all three areas. For source model learning, we introduce a novel causal susceptibility risk that guides the model to capture essential causal features, with theoretical analysis providing learning upper bounds for the OSDA setting. For unknown class separation, we propose the Virtual Multi-Clas Class Prototype (VMCP) method, which generates multiple virtual unknown class prototypes through K-means clustering on global target samples while filtering potential known class prototypes, enabling robust pseudo-label assignment via similarity matching. For cross-domain alignment, we develop a class-level contrastive learning approach that leverages pseudo-labels to effectively align feature representations of known categories between source and target domains.
D. Details for Experiments.
D.I. Benchmark Dataset Settings.
Extensive experiments are conducted on five benchmarks following the standard setting (Qu et al., 2023; Bucci et al., 2020): 1) Office-Home (Venkateswara et al., 2017), dataset across four distinct domains: Art (Ar), Clipart (CI), Product (Pr), and Real World (Rw) with the first 25 categories as the known, while the subsequent 40 classes as the unknown; 2)
18

---

COSDA: Counterfactual-basee Susceptibility Risk Framework for Open-Set Domain Adaptation
Office-31 (Wang al., 2019), another dataset spanning three domains: Amazon (A), Dsir (D), and Webcam (W), with the first 10 classes the known and the last 11 classes as the unknown; 3) Image-CLEF (Li al., 2023), database with four domains and 12 shared common classes. The first 6 classes are utilized as the known, and the rest the unknown; 4) VisDA (Li et al., 2021), synthetic-to-real (S2R) dataset with 12 classes, with first 6 classes as the known and the rest classes as the unknown; 5) DomainNet (Wen & Brbic, 2024) is the largest dataset, including 345 classes and six domains. Following the previous work (Wen & Brbic, 2024), we use three domains: Painting (P), Real (R), and Sketch (S).
Dataset
#domains
#K
#U
#images
Office-Home
25
40
15,500
Office-31
10
11
4,652
Image- CLEF
4
6
6
600
VisDA
6
6
207,78 785
DomainNet
173
172
341,472
Table 5. Dataset details for open-set domain adaptation.
D.2. Baselines
Baselines. The baselines include i) adversarial-leaming methods, i.e., OSBP (Saito et al., 2018), PGL (Luo et al., 2020), ANNA (Li al., 2023). ii) score-based methods, i.e., STA (Liu al., 2019), ROS (Bucci et al., 2020), UAN (You et al., 2019), GATE (Chen al., 2022), iii) pseudo-lahel-basse alignment methods, i.e., DADO (Fang al., 2020), DCC (Li et al., 2021), OVANet (Saito, 2021). OSLPP (Wang al., 2024), GLC (Qu et al., 2023), UPUK (Wan et al., 2024), USDAP (Shao et al., 2024).
D.3. Evaluation Metrics
Following the main OSDA stream (Bucci et al., 2020; Qu et al., 2023; Saito et al., 2018; Li et al., 2023), we utilize four widely used measures, i.e., accuracy of the unknown class (U ()) normalized accuracy for the known classes only (OS*), normalized accuracy for all classes(OS), and harmonic mean accuracy (HOS).
UNK
NK+1
E (aa))D((+)
K+1
T(h(x) y),
(48)
K
OS*
E (z.g))D
I(h(x)= = v).
(49)
K
N
k=1
K+1
1
1
OS
E (a.))~2k
I(h(z) v).
(50)
K +
N
k=1
2 x OS x UNK
HOS
(51)
OS UNK
with Dj being the set of target samples in the i-th class, and h() the classifier. HOS is regarded as the most equitable evaluation criterion. strikes balance between assessing the performance of the methods on both known and unknown class samples.
D.4. Additional Benchmark Experiments Results
Table 6 shows the comparison results of Office-Home.
D.5. Details for Synthetic Numerical Experiment
In this section, we conduct two synthetic experiments to evaluate the effectiveness of Susceptibility risk. Synthetic Numerical Experiment
19

---

COSDA: Counterfactual--aace Susceptibility Risk Framework for Open-Set Domain Adaptation
Table 6. Comparison results (%) of Office-Home. (Best bold and second best underline)
Average UNK
Ar-CI UNK
Ar-Pr UNK
Ar-Rw UNK
Cl+AAr UNK
CI-Pr
OS*
HOS
OS
HOS
OS*
HOS
OS*
HOS
OS*
HOS
OS
UNK
HOS
OSBP (Saiko al., 2018)
64.1
66.3
64,7
50,2
61.1
55.1
71.8
59.8
65.2
79.3
67.5
72.9
39.4
70.3
64.3
67.0
62.7
64.7
STAsum (1.iu al, 2019)
63.4
62.6
61.9
50.8
63.4
56.3
68.7
59.7
63.7
81.1
50.5
62.1
53.0
63.9
57.9
63.5
62,5
STAmax (Lin et 2019)
61.8
63.3
61.6
46.0
72.3
55.8
68.0
48.4
54.0
78.6
60.4
68.3
51.4
65.0
57.4
61.8
59.1
60.4
UAN et 2019)
25.2
0.0
62.4
0.0
$1.1
0.0
88.2
0.2
70.5
PGL (Luo
76.1
25.0
35.2
63.3
19.1
29.3
78.9
32.1
15.6
87.7
10.9
55.8
85.9
5,3
10.0
73.9
24.5
36.8
(Bucci
2020)
72.4
66.2
50.6
75.8
77.2
65.5
65.2
DAOD (Pang et al.., 2020)
69.6
50.2
57.6
72.6
51.8
60.5
55.3
57.9
56.6
78.2
62.6
09.3
59.1
61.7
60.4
70.8
52.6
60.4
DCC (Li al., 2021)
61.7
56.1
67.5
66.7
49.6
66.5
OVANet (Salto, 2021)
64.0
58.6
66.3
69.9
62.0
65.2
GATE (Chea et al., 2022)
69.0
63.8
70.5
75.8
66.4
67.9
ANNA el., 2023)
76.7
20.7
61.4
79.9
79.7
73.1
73.6
68.6
GLC (Qu et al., 2023)
69.8
65.3
74.2
79.0
60.4
71.6
OSL (Wang al. 20144)
63.8
71.7
67.0
55.9
61.0
72.5
73.1
69.4
74.3
79.0
60.9
23.3
66.9
UPUK (Wan ol., 2024)
61.6
79.7
69.2
49.0
64.8
55.8
68.1
88.0
76.7
71.5
86.6
78.4
61.3
72.6
66.4
66.5
81.6
73.1
USDAP (Shao al., 2024)
69.6
66.7
25.3
76.2
60.7
70,0
GLC++ (Qu et al., 2021)
70.2
65.4
73.8
78.0
61.5
71.9
Ours
69.4
74.4
71.7
70.0
71.0
70.5
73,9
76.0
74.9
80.3
79.5
79.9
57.9
74.0
65.0
68.8
76.0
22.2
Method
OS
CI -Rw UNK
HOS
OS*
UNK
-Ar
HOS
OS*
UNK
:C1
HOS
OS*
UNK
-Rw
HOS
OS*
UNK
HOS
OS*
UNK
-CI
HOS
OS
UNK
HOS
OSDP
70.6
59.1
63.2
44.5
53.2
76.2
73.9
66.1
67.3
48.0
63.0
54.5
68.6
72.3
STAsum
69.8
63.2
66.3
55.4
73.7
63.1
44.7
71.5
55.0
78.1
63.3
69.7
67.9
62.3
65.0
51.4
57.9
54.2
77.9
58.0
66.4
STAmax
66.7
66.8
72.4
61.9
44.2
67.1
76.2
64.33
67.5
66.7
54.5
55.4
64.5
DAN
80.6
0.1
0.2
73.7
0.0
0.0
59.1
0.0
0.0
$4.0
D.1
0.2
27.5
0.1
0.2
66.2
0.0
0.0
85.0
0.1
0.1
PGL
70.2
33.8
45.6
73.7
34.7
47.2
59.2
38.4
46.6
$4.8
27.6
41.6
81.5
11.4
68.8
0.0
0.0
84.8
38.0
52.5
72.2
68.6
57.3
60.6
46.5
56.3
70.8
78.4
67.0
70.8
51.5
73.0
60.4
72.0
80.0
75.7
DADO
27.8
57.0
65.8
21.3
50.5
59,1
58.4
42.8
49.4
81.8
50.6
62.5
66.7
43.3
52.5
60.0
36.6
45.5
84,1
34.7
49.1
55,8
53.0
71.9
OVANe1
68.6
59.8
$3.4
69.3
68.7
$9.6
66.7
GATE
71.7
67.3
61.5
61.8
75.1
ANNA
66.9
80.2
73.0
63.0
70.3
66.5
54.6
74.8
63.1
74.3
78.9
76.6
66.1
27.3
71.3
59.7
23.1
65.2
76.4
81.0
28.2
GLC
74.7
63.7
63.2
75.8
67.1
64.3
77.8
OSLPP
67.2
73,9
70.4
51.6
76.2
63.6
53.1
67.1
59.3
77.0
71.2
74.0
60.8
75.0
67.2
54.4
61.3
59.0
78.4
70.8
74.4
UPU
71.6
84.8
77.6
55.9
85.6
67.6
45.4
70.2
55.1
73.9
K3.9
78.6
56.7
84.1
67.8
49.3
74.6
59.4
69.5
80.0
74.4
USDAP
72.6
64.5
64.6
76.5
78.0
GLC++
74.7
64.2
65.3
76.0
67.7
66.0
77.8
75.8
76.1
67.8
58.5
73.3
64.1
79.1
The effectiveness of susceptibility risk is demonstrated by examining whether can learn the essential causal relationships. To this end, in the first synthetic experiment, we designed synthetic data generator based on Fig. and created a sample set (X, Y). where X is generated from three causal factors C and a spurious association factor S. The generation process of X as follows:
nosse
nosse
8
v /
psr
S
C
Y
Figure 8. Causal graph for Synthetic Data Generation: Y .. LSS
Opsc = Y @ B(Apsc) + +,3 1),
Omean = Mcan( (Cppct)
(52)
5 Xper Cinaa * 1. + (0,
X = MLP((1Cpsc)...
In Eq. (52), to test whether susceptibility risk can focus more essential causal information, we use parameter Apsc to distinguish the importance of causal factors. When Aprc is closer to 0 or 1, the causal association is stronger to Y. Conversely, the closer Apsc is to 0.5, the weaker the causal association is. 3 represents the noise intensity in the data. We set Apsc= = (0.15.00 0.25, 0.35) and 8 = {0.1, 0.4, 0.7, 1.1). Besides, Aper denotes the spurious degree. When Apar gets higher, the spurious correlation is stronger in data X. We set = 64 and Aper = {0.1, 0.4, 0.7}. Then we develop a non-linear function to generate X from [Co.15; Co.25; Co.3s, $). We use distance correlation to evaluate the correlation between the
20

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COSDA: Couttefacctull-baeer Susceptibility Risk Framework for Open-Set Domain Adaptation
learned representation and these factors. A higher distance correlation indicates better representation of factors. We provided an ablation study demonstrate the efficiency of susceptibility risk by comparing it with vanilla empirical risk.
1.0
1.0
0.8
Distance Coneeation
Distance Correlation
0.6
0.6
0,4
0.4
B=11
-0.1
0.2
$=0,7
=04
B=04
-0.7
$=01
0.0
Age
-0.15 A
=025 A=x
-0.35
Sparious
0.0
=0.15
Ape =0.25
7/pe
=0.35
Spurious
Factors (a)
Factors (b)
Figure (a) Results of different spurious degree, and (b) Results of Suscepetibility risk yellow and Vanilla risk oorange
In Fig. 9a), we varied the level of spuriousness and computed the distance correlation between the learned representations and four factors. It can be observed that susceptibility risk achieved a higher distance correlation with critical causal factors, while the distance correlation with spurious factors showed only a slight increase as spuriousness increased. This demonstrates that our evaluator consistently focuses on critical causal factors under varying spurious levels. In Fig. 9(b), we generated data with different levels of perturbation by varying 3 and compared the performance of the Susceptibility risk evaluator with that of standard empirical risk evaluator. For critical causal factors (Aysc 0.15), method achieved higher distance correlation than the standard risk. For factors with lower causal relevance (Apsc 0.25, Apac 0.35), our method comparatively avoided overemphasis. Furthermore, for spurious factors, our method yielded lower distance correlation compared to the standard risk. These results verified that by incorporating susceptibility risk evaluation, models can reduce the learning of spurious correlations and maintain a focus on critical causal factors.
Action Recognition Appliance Disassembly under OSDA. evaluate the practical applicability of the proposed method, we selected appliance disassembly action recogmition concrete problem. Disassembly actions are complex, with similar backgrounds in images, and involve significant number of unknown actions and unknown parts, which severely degrade the performance of traditional supervised learning models. The open-set domain adaptation setup used in this paper aligns with the challenges faced in action recognition during appliance disassembly at the test stage. Thus, we constructed a custom Image dataset for Appliance Disassembly Action Recognition, Image-ADAR, for this task and compared the performance of COSDA with several baseline methods.
The dataset was collected in disassembly factory, where each collection environment represents distinct domain, labeled domains and C. After data processing, each domain consists of classes, including five shared classes and two unknown classes. The source domain includes only the five shared classes, while the target domain encompasses all categories. The objects being disassembled are air conditioners, with the shared classes being disassembling the outer shell, disassembling the evaporator, disassembling the foam, and disassembling the circuit board. The two unknown classes are action unknown (leaving the workbench) and object unknown (refrigerator). Each class contains between 150 and 450 image samples. line with standard experimental settings, the OS*, UNK, and HOS classification metrics were used, and the experimental parameters were consistent with the Office-// configuration. The results are presented Tab. 8.
6: Eeeftigaatoo
leaing workbench
disssumble cirutt
disssemble Torn
disesorblle
disasernle coter
diseseeblee outer shill
Figure 10. Examples of cach class in Image-ADAR, where label 5-6 are unknown categorics, and label 0-4 are shared categories.
21

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COSDA: Counteffactual-baee Susceptibility Risk Framework for Open-Set Domain Adaptation
Table 7. Dataset details for Image-ADAR.
Dataset
#domain name
#K
#U
Simages
A
2
1,573
1,951 5
Image-ADAR
B
C
S
1,823
Table Comparison results (%) of Image-ADAR, (Best bold and second best in underline)
B-A
Average
Methol
08
UNK
HOS
08*
UNK
HOS
05*
UNK
HOS
08
UNK
H08
0S*
UNK
HOS
05*
UNK
HOS
08*
UNK
HOS
OSBP (Satoo 2018)
56.1
79.8
65.9
749
73.5
62.5
67.4
52.4
37.6
43.8
44.2
14.2
21.5
29.9
34.7
55.1
51.5
51.2
ANNA et al., 2023)
53.4
27.3
09.2
74.4
66.1
70.0
82.3
77.0
79.6
54.8
34,9
12.6
48.6
16.0
26.1
24.5
60.3
34.9
58.0
55.3
53.5
Ours
66.9
74.5
70.5
73.
89.2
80.7
65.4
63.8
33.3
57.7
12.3
71.2
56.5
63,0
90.1
63.5
56.0
59.6
67.8
62.7
We compared our method with the classical baseline, OSBP, and the state-of-the-arr OSDA method, ANNA. The results show that method achieved the best performance of OS*, UNK, and HOS. Notably, COSDA achieves significant improvements over the baselines the C + A task, with 20.6% increase in OS*, 40.5% increase in UNK, and a 38.9% increase in HOS, demonstrating the effectiveness of our proposed method.
D.6. Qualitative Results
Trade-off Analysis. To investigate how the parameters in Eq. (25) affect the performance of COSDA, define A {0.1, 0.2, 0.5, 0.8, 1.0} and λezo = {0.1, 0.2, 0.5, 0.8, 1.0}. For each dataset, we select the final sub-task for parameter sensitivity analysis. As shown in Fig. 5, COSDA fluctuates between 93.8 and 94.8 on the P-I (Image-CLEF) task. On the Rw-Pr (Office-Homil Home) task, COSDA shows performance range of 77.8 to 78.8. This indicates that the proposed algorithm demonstrates strong parameter stability across both large and small datasets.
Loss Convergence Analysis. Fig. 11 depicts the loss convergence trends on the test of the dslr amazon (Office-31) and Art Product (Office-omee) tasks. Overall, the model achieves sufficient fitting within iterations without overfitting. Specifically, in both tasks, the sharp decline in L, reflects significant improvement in target domain classification accuracy driven by pseudo-labeling. Meanwhile, L., representing source domain classification accuracy, exhibits slight downward trend in the dslr + amazon task but remains relatively stable in the Art > Product task. Finally, Lexon which represents feature alignment, shows a gradual downward trend throughout the training process.
20
L
30.
250
Los Value
13
Valur
1,0
10
0.5
00
30
100 Itetation
150
200
800
Desttion
Figure II. Loss convergence on dslr - amazon (left) and Art + Product (right)
22


Reviews:
[{"review_id": "LbkMLfOC90", "reviewer": "Reviewer_6vAQ", "summary": "This paper introduces COSDA, a novel causal-based Open-Set Domain Adaptation (OSDA) framework. It proposes Susceptibility Risk, a theoretical approach to measuring and mitigating the risk associated with domain shifts and unknown category recognition. Then, three core components are developed: Susceptibility Risk Estimater (SRE), Contrastive Feature Alignment (CFA), and Virtual Multi-unknown-categories Prototype (VMP), all of which contribute to better feature alignment and improved classification of unknown categories. Extensive experiments on benchmark datasets (Office-Home, Office-31, and Image-CLEF) demonstrate that COSDA outperforms state-of-the-art methods, achieving significant improvements in accuracy and robustness.\n\n## update after rebuttal", "questions": "", "limitations": "", "rating": 4, "confidence": null, "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": "**Dear Reviewer 6vAQ,**\n\nThank you for your decision and constructive feedback. We have stuied the comments carefully and made through revisions. We hope that our responses have helped to clarify the concerns.\n> **Experimental Designs Or Analyses & Q1**. whether the method can perform well on harder data (like DomainNet [1]) remains unknown ;  All the conclusions and insights can change when using different backbones. Why ResNet-50 remains the preferred choice?\n\n**A1**. We sincerely appreciate your insightful suggestions and questions. Initially, we adopted ResNet50 as the backbone to maintain consistency with prior work in this domain. However, as you rightly pointed out, evaluating the model with more advanced backbones and larger-scale datasets would better demonstrate its robustness. Following this suggestion, we implemented addtional experiments on VisDA[3] and DomainNet[1][2] and discovered that **our method demonstrates good performance on both CNN-based and CLIP-based architectures**.\n\n*Table 1. Comparison results on DomainNet and VisDA with CLIP backbone **(All baseline results are obtained from Reference [2]).***\n|Method|Domain|Net|(173/172)|VisDA|(6/6)||\n|-|-|-|-|-|-|-|\n||OS*|UNK|HOS|OS*|UNK|HOS|\n|DCC[3]|50.2|45.1|47.5|75.3|46.2|57.3|\n|UNIOT[1]|59.2|45.1|51.2|75.7|49.4|59.8|\n|CROW[2]|70.3|50.9|59.0|77.0|62.8|69.2|\n|**COSDA-CLIP**|**72.0**|**76.2**|**73.9**|**85.2**|**72.6**|**78.4**|\n\n**Implementation Details**.  Considering both time constraints and GPU memory demands (particularly for the larger models), we utilized six 40GB NVIDIA A100 GPUs to execute the new experiments. DomainNet and VisDA use the same hyperparameter settings as smaller-scale datasets, specifically $\\lambda_s=0.2$, $\\lambda_{exo}=1$. But the learning rate has been reduced,  specifically $lr = 5e-4$.  \n\n**Key Findings from CLIP Backbone Experiments:**\n1. Substantial HOS Improvements:\n    - On DomainNet, COSDA-CLIP achieves  **73.9% HOS, outperforming CROW by 14.9%**.\n    - On VisDA, COSDA-CLIP reaches  **78.4% HOS, outperforming CROW by 9.2%** .\n2. Dual Strengths in OS\\*  and UNK: With CLIP, COSDA particularly further enhances known-class classification and unknown-class detection (UNK).\n\n*Table 2. Performance of COSDA on DomainNet with ResNet50*\n||ResNet50|||\n|-|-|-|-|\n||OS\\*|UNK|HOS|\n|**Avg.**|54.9|65.2|58.6|\n\nWe also note that with ResNet50, COSDA surpasses DCC [3] and UNIOT [1], confirming its robustness across backbones.  **The suggested references will be well cited in our updated version.**\n\n> **Q2**. The step of building the centroids of all known and unknown classes shares the same idea as in [2] and [3]. Please discuss the main difference between method level and motivation level.\n\n**A2**. We sincerely appreciate your insightful questions. In our work, the **VMP** module serves as a functional component to ensure **CFA**, rather than acting as a standalone clustering solution. I carefully read the papers you provided, and the difference lies in the fact that we **exclude all known-class positive samples and cluster only the remaining negative samples** (i.e., those not belonging to any known class), unlike [2][3], which cluster _all target_ samples. Due to the reduction in the number of samples and clusters, VMP has saved on the computational cost. Besides, unlike one-vs-all strategies requiring C clustering operations per epoch (C = the number of known classes), COSDA achieves comparable performance with only one clustering per epoch. This design reduces complexity from O(CN) to O(N). Additionally, we acknowledge that advanced clustering could further optimize this step and will explore this in future work.\n\n> **Q3**. Could you clarify the motivation behind designing SRE, CFA, and VMP, their specific roles in causal inference, and how they interconnect within the overall methodology?\n\n**A3**. We appreciate your questions regarding the methodological framework. SRE quantifies causal feature representation ability via susceptibility analysis. Direct SRE estimation in the target domain is infeasible due to label scarcity. To resolve this problem, we first decompose target-domain expected risk into open-set and closed-set, then bridge source/target risks using domain-invariant representations, and finally derive generalization bounds to narrow the gap between empirical and expected susceptibility risks (Theorems 1-2 & Corollary 1). To satisfy the exogeneity assumption for causal identifiability, we propose CFA, which encourages independence across causal features belonging to different categories via information bottleneck (Proposition 2) and then introduces VMP pseudo-label strategy (Eq. 17-19). Additionally, our code is open-sourced to show how SRE, CFA, and VMP are integrated end-to-end.\n\nWe sincerely appreciate your insightful comments once again. Please let us know if you need any further information or if there are additional points you would like to discuss with us.\n\nBest regards,\n\nAuthors of #10234", "claims_and_evidence": "The claims are well supported by the evidence.", "methods_and_evaluation_criteria": "The method and evaluation criteria make sense for the problem.", "theoretical_claims": "There is no obvious issue in all the definitions, lemmas, propositions, theorems, and corollaries.", "experimental_designs_or_analyses": "In general, the soundness of experimental designs and analyses is strong. However, since the experiments were conducted on Image-CLEF, Office-31, and Office-Home datasets, whether the method can perform well on harder data (like DomainNet [1] QuickDraw) remains unknown.\n\n[1] Moment matching for multi-source domain adaptation, ICCV 2019", "relation_to_broader_scientific_literature": "This work views the OSDA setting from the causal inference perspective and bridges the gap between causal-inspired theoretical frameworks and OSDA.", "essential_references_not_discussed": "-", "other_strengths_and_weaknesses": "-", "other_comments_or_suggestions": "-", "questions_for_authors": "1. ImageNet-pretrained ResNet 50 is used for all the experiments. However, as discussed in [1] and [2], all the conclusions and insights can change when using a foundation model like CLIP or DINO_v2 as the backbone. Also, given that stronger pretrained backbones generally enhance image classification performance, it is unclear why ResNet-50 remains the preferred choice. Could you discuss this decision and its potential impact on the findings?\n2. The step of building the centroids of all known and unknown classes shares the same idea as in [2] and [3]. Could you please discuss the main difference between method level and motivation level? \n3. The motivation for using causality is strong and clear. However, the motivation behind the overall method design is difficult to follow.. The framework consists of multiple components (SRE, CFA, and VMP), but their individual necessity and how they collectively contribute to the causal inference remain unclear. Could you clarify the motivation behind designing these three components, their specific roles in causal inference, and how they interconnect within the overall methodology?\n\n[1] Universal domain adaptation from foundation models: A baseline study\n\n[2] Cross-domain Open-world Discovery, ICML 2024\n\n[3] Domain consensus clustering for universal domain adaptation, CVPR 2021", "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": "", "extra_scores": {}}, {"review_id": "n6nlrmm4PR", "reviewer": "Reviewer_pQYc", "summary": "This paper addresses the Open-Set Domain Adaptation problem which is useful in real-world applications. They propose a novel Counterfactual-based susceptibility risk framework, consists of Susceptibility Risk Estimator, Contrastive Feature Alignment, and Virtual Multi-unknown-categories Prototype. Experiments on three datasets and benchmarks highlight its superior performance.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "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": "**Dear Reviewer pQYc,**\n\nWe sincerely appreciate your constructive comments on our work. We have carefully addressed each point raised and incorporated corresponding improvements. We hope our responses have adequately addressed the concerns.\n\n>**Weaknesses 1 & Weaknesses 3**.  More ablations on ViT backbone should be added; Lack of experiments on large-scale benchmarks such as DomainNet and VisDA.\n\n**A1**.  We fully agree with the reviewer's valuable suggestion regarding the importance of evaluating our method on large-scale datasets with diverse backbones, as this would further validate the generalization of COSDA. In response to this suggestion, we implemented additional experiments on VisDA and DomainNet [1][2][R1][R2] and used CLIP ViT-L14-336px as the backbone.\n\n**[R1]Cross-domain Open-world Discovery, ICML 2024  \n[R2] Domain consensus clustering for universal domain adaptation, CVPR 2021**\n\n**Implementation Details**. Considering both time constraints and GPU memory demands, we utilized six 40G A100 GPUs to execute the new experiments. DomainNet and VisDA use the same hyperparameter settings as smaller-scale datasets, specifically $\\lambda_s=0.2$ and $\\lambda_{exo}=1$. The learning rate is $5e-4$.\n\n*Table 1. Performance comparison (%) on DomainNet and VisDA using CLIP backbone. **(Baseline results from [R1]).***\n|Method|Domain|Net|(173/172)|VisDA|(6/6)||\n|-|-|-|-|-|-|-|\n||OS*|UNK|HOS|OS*|UNK|HOS|\n|DCC|50.2|45.1|47.5|75.3|46.2|57.3|\n|UNIOT|59.2|45.1|51.2|75.7|49.4|59.8|\n|GLC[1]|62.9|50.6|56.1|73.4|58.7|65.2|\n|CROW[R1]|70.3|50.9|59.0|77.0|62.8|69.2|\n|COSDA-CLIP|**72.0**|**76.2**|**73.9**|**85.2**|**72.6**|**78.4**|\n\n**Key Findings from CLIP Backbone Experiments:**\n1. Substantial HOS Improvements:\n    - On DomainNet, COSDA-CLIP achieves  **73.9% HOS, outperforming CROW by 14.9%**.\n    - On VisDA, COSDA-CLIP reaches  **78.4% HOS, outperforming CROW by 9.2%** .\n2. Dual Strengths in OS\\*  and UNK: With CLIP, COSDA particularly further enhances known-class classification and unknown-class detection (UNK).\n    - For DomainNet OS*, a 1.7% improvement; \n    - For DomainNet UNK, a 25.3% improvement;\n    - For VisDA OS*, an 8.2% improvement;\n    - For VisDA UNK, a 9.8% improvement.\n\n*Table 2. Performance comparison on VisDA (VGG19). **(Baseline results from [R2]).***\n|Metric|OSBP|STA|DCC[R2]|COSDA|\n|-|-|-|-|-|\n|OS*|62.9|66.8|68.8|**80.7**|\n|OS|59.2|63.9|68.0|**70.1**|\n\n*Table 3. Sub-Task Performance of COSDA Across Backbones on DomainNet*\n|Subtask|CLIP|||ResNet|50||\n|-|-|-|-|-|-|-|\n||OS*|UNK|HOS|OS*|UNK|HOS|\n|P-R|76.6|78.9|77.7|65.4|43.4|52.2|\n|P-S|68.8|79.1|73.6|55.1|76.9|64.2|\n|R-P|71.7|72.2|71.9|45.1|56.6|50.2|\n|R-S|70.9|77.2|73.9|42.4|49.0|45.5|\n|S-P|66.1|76.3|70.8|50.8|79.2|61.9|\n|S-R|78.1|73.2| 75.6|70.8|85.9|77.6|\n|**Avg.**|72.0|76.2|73.9|54.9|65.2|58.6|\n\n*Table 4.  Performance comparison with [1][2] on Office-Home and Office-31*\n|Method|Office-Home|Office-31|\n|-|-|-|\n|GLC[1]|69.8|89.0|\n|LEAD[2]|70.0|90.1|\n|**COSDA**|**71.7**|**92.6**|\n\nTable 2 shows leading performance on VisDA (VGG-19). Table 3 exhibited detailed results of COSDA for 6 subtasks on DomainNet with ResNet-50 and CLIP. Table 4 supplements the performance comparison between COSDA and references [1][2] on small-scale datasets. These additional experiments could further confirm the effectiveness of COSDA. **Additionally, we will well cite [1][2] you provided in the updated revisions**. \n\n> **Weaknesses 2**. The OS* of the proposed framework is worse than baselines on all datasets. For example, 0.3 on Image-CLEF, 3.2 on Office-31, and 6.7 on Office-Home.\n\n**A2**. We sincerely appreciate the reviewer's insightful observation regarding the OS* performance. We acknowledge that our method demonstrates a modest compromise in OS* scores. However, this trade-off enables significant improvements in UNK (33.2%, 43.4%, and 49.4% gains, respectively). HOS is the most crucial metric, which achieves a balance between known-class and unknown-class recognition. For HOS, COSDA outperforms the highest OS* methods by 19.3%, 28.1%, and 36.5% on three small-scale datasets. Notably, **COSDA achieves OS\\*, UNK, and HOS improvement on challenging DomainNet (Table 1)**. These results could substantiate the advantages of our approach.\n\n> **Other Comments**. There are too many loss terms in Eq (25) which is complex and may make optimization difficult. How do you balance the contribution of different terms?\n\n**A3**. Thank you for raising this important point. To balance the contributions of different loss terms in the overall objective, we introduced weight hyperparameters for loss items. These hyperparameters were optimized via a grid search strategy to ensure an appropriate trade-off for the dataset. As shown in Fig. 6, we analyzed the impact of parameters. \n\nWe sincerely appreciate your insightful comments again. Please let us know if you need any further information or if there are additional points you would like to discuss with us.\n\nBest regards,\n\nAuthors of #10234", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "The proposed method follows the traditional evaluation criteria in Open-Set domain adaptation.", "theoretical_claims": "Yes, no issues.", "experimental_designs_or_analyses": "The experimental designs are sound in general. However, the experiments on large-scale benchmark such as DomainNet and VisDA are missing.", "relation_to_broader_scientific_literature": "The proposed Counterfactual-based susceptibility risk framework could be potentially helpful to other literature.", "essential_references_not_discussed": "No", "other_strengths_and_weaknesses": "Strengths\n1. The paper addresses the Open-Set domain adaptation problem, which is a challenging and practical scenario.\n2. The paper is well written and easy to follow.\n3. The paper provides extensive experiments, showing the effectiveness and versatility of the proposed method.\n\nMajor Weaknesses\n1. The authors only use CNN backbones. More ablations on ViT backbone should be added, as it demonstrates strong generalization and adaptation performances compared with CNNs.\n2. Although it is important for Open-Set domain adaptation to have a good performance on UNK, it is also crucial to have a good OS* value. However, the OS* of the proposed framework is worse than baselines on all datasets. For example, 0.3 on Image-CLEF, 3.2 on Office-31, and 6.7 on Office-Home.\n3. Lack of experiments on large-scale benchmarks such as DomainNet and VisDA, which are commonly used in existing work [1,2].\n\n[1] Upcycling Models under Domain and Category Shift, CVPR 2023\n\n[2] LEAD: Learning Decomposition for Source-free Universal Domain Adaptation, CVPR 2024", "other_comments_or_suggestions": "There are too many loss terms in eq (25) which is complex and may make optimization difficult. How do you balance the contribution of different terms?", "questions_for_authors": "What's the performances of the proposed framework on DomainNet and VisDA?", "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": "", "extra_scores": {}}, {"review_id": "Bg2q0hcItj", "reviewer": "Reviewer_zv4D", "summary": "This paper introduces an adversarial adaptation framework called COSDA, which aims to address the challenges of unknown category recognition and domain drift in the open domain adaptation problem. The framework is based on causality theory and includes three novel components: (i) Susceptibility Risk Estimator (SRE), which is used to capture causal information and form a risk minimization framework; (ii) Contrastive Feature Alignment (CFA) module, which satisfies the external causal assumption and promotes cross-domain feature alignment based on mutual information theory proof; (iii) Virtual Multi-unknown-categories Prototype (VMP) pseudo-labeling strategy, which provides label information by measuring the similarity between samples and prototypes of known and multiple virtual unknown categories, thereby assisting open set recognition and intra-class discrimination learning. Experimental results show that the proposed method achieves state-of-the-art performance on benchmark datasets and synthetic datasets.\n\n## update after rebuttal\nThank you very much for the author's reply. I maintain my initial positive rating.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "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": "**Dear Reviewer zv4D,**\n\nThank you for your decision and constructive feedback. We have studied the comments carefully and made thorough revisions. We also greatly appreciate your insightful questions and hope that our responses have helped to clarify them.\n\n> **Weakness 1**: As reported in the main tables, in most cases the proposed methods are not good and fail to be SOTA (State of the Art). While the methods may show promise or have certain advantages in specific scenarios, they do not consistently outperform existing techniques across all metrics and benchmarks.\n\n**A1**. \nWe appreciate the reviewer's attention to our experimental evaluation. Our comprehensive assessment includes three key metrics: **OS*** (known-class accuracy), **UNK** (unknown-class detection), and **HOS (balancing** both aspects). As highlighted in our contributions, COSDA achieves consistent improvements over SOTA methods:\n- **Absolute HOS gains**: +2.9% (Office-Home), +2.2% (Office-31), +1.0% (Image-CLEF)\n- **Dominant rankings**:\n  - Image-CLEF: Achieved the highest HOS in 11 out of 12 subtasks, and the best UNK score in 9 out of 12 subtasks.\n  - Office-31: Achieved the highest HOS in 3 out of 6 subtasks, and the best UNK score in 3 out of 6 subtasks.\n\nThe method demonstrates both **generalizability** (highest average performance across all benchmarks) and **robustness** (most of the subtasks show statistically significant improvements). These results validate our design's effectiveness in handling the known-unknown class trade-off in many cases.\n\n\n> **Weakness 2**: I think this task could potentially be completed by leveraging Video-Language Models (VLMs). However, the authors did not demonstrate scenarios or cases where VLMs might fail to work effectively. It's important for a comprehensive evaluation to include both the capabilities and limitations of such models.\n\n**A2**. We sincerely appreciate this valuable suggestion.  We have conducted  additional experiments with  CLIP  ViT-L  on challenging datasets DomainNet and VisDA.\n\n*Table 1. Performance comparison (%) on DomainNet and VisDA datasets using CLIP backbone. **(All baseline results are obtained from [R1]).***\n|Method|Domain|Net|(173/172)|VisDA|(6/6)||\n|-|-|-|-|-|-|-|\n||OS*|UNK|HOS|OS*|UNK|HOS|\n|DCC|50.2|45.1|47.5|75.3|46.2|57.3|\n|UNIOT|59.2|45.1|51.2|75.7|49.4|59.8|\n|GLC|62.9|50.6|56.1|73.4|58.7|65.2|\n|CROW[R1]|70.3|50.9|59.0|77.0|62.8|69.2|\n|COSDA-CLIP|**72.0**|**76.2**|**73.9**|**85.2**|**72.6**|**78.4**|\n\n**[R1]Cross-domain Open-world Discovery, ICML 2024**\n\n**Implementation Details**.  Considering both time constraints and GPU memory demands (particularly for the larger models), we utilized six 40GB NVIDIA A100 GPUs to execute the new experiments. DomainNet and VisDA use the same hyperparameter settings as smaller-scale datasets, specifically $\\lambda_s=0.2$, $\\lambda_{exo}=1$. But the learning rate has been reduced,  specifically $lr = 5e-4$.  \n\n**Key Findings from CLIP Backbone Experiments:**\n1.  _Substantial HOS Improvements_:\n    -   On DomainNet, COSDA-CLIP achieves  **73.9% HOS, outperforming CROW by 14.9%**.\n    -   On VisDA, COSDA-CLIP reaches  **78.4% HOS, outperforming CROW by 9.2%** .\n2.  _Dual Strengths in OS\\*  and UNK_: With CLIP, COSDA particularly further enhances known-class classification and unknown-class detection (UNK).\n    - For DomainNet OS*, a 1.7% improvement; \n    - For DomainNet UNK, a 25.3% improvement;\n    - For VisDA OS*, an 8.2% improvement;\n    - For VisDA UNK, a 9.8% improvement.\n\n*Table 2. Sub-Task Performance of COSDA on DomainNet with CLIP bakcbone*\n|subtask|P-R|P-S|R-P|R-S|S-P|S-R|**Avg.**|\n|-|-|-|-|-|-|-|-|                                                   \n|OS\\*|76.6|68.8|71.7|70.9|66.1|78.1|72.0|\n|UNK|78.9|79.1|72.2|77.2|76.3|73.2|76.2|\n|HOS|77.7|73.6|71.9|73.9|70.8|75.6|73.9|\n\nTable 2 exhibited detailed results of COSDA for 6 subtasks on DomainNet with CLIP. These additional experiments could further confirm the effectiveness of COSDA. **We fully agree with the reviewer's insightful suggestion about VLMs. This represents a promising new direction worth exploring in OSDA.**\n\n> **Weakness 3 & Other Comments**: No codes are provided.\n\n**A3**. We sincerely appreciate the reviewer's emphasis on reproducibility. **As noted in our submission (Page 6, Line 321), we open-sourced the complete implementation. For greater visibility, we will relocate the code announcement to the abstract/introduction in the updated version.**\n\n**Current Implementation Overview:**\n- **Benchmark Support**: Office-Home, Office-31, Image-CLEF, DomainNet, VisDA\n- **Architecture Flexibility**:\n  - CNN backbones (ResNet, VGG)\n  - VLMs (CLIP)\n- **Training Frameworks**:\n  - Multi-GPU distributed training\n  - Single-GPU training\n\nWe sincerely appreciate your insightful comments once again. Please let us know if you need any further information or if there are additional points you would like to discuss with us.\n\nBest regards,\n\nAuthors of #10234", "claims_and_evidence": "Compared with the traditional OSDA method, the main improvement of CSDA is the introduction of causal inference technology and Susceptibility Risk Estimator (SRE), which enables the model to better handle open set problems and sources of uncertainty. In addition, CSDA also uses pseudo-labeling strategies and contrastive learning strategies for virtual multiple unknown categories to further improve the performance of the model.  This paper mainly introduces the causal inference based open domain adaptation method COSDA and conducts extensive experimental comparisons on three benchmark datasets.", "methods_and_evaluation_criteria": "This paper conducts extensive experimental comparisons on three benchmark datasets. The experimental results show that COSDA achieves good performance on all benchmark datasets, especially when dealing with unknown categories. In addition, COSDA performs well for different evaluation indicators, such as unknown-class accuracy, known-class accuracy, overall accuracy, and harmonic mean accuracy. In the Ablation study, the authors further explored the impact of different components of COSDA on the performance. Finally, by applying COSDA to practical problems, the authors demonstrated its practical value in solving complex scenarios.", "theoretical_claims": "No", "experimental_designs_or_analyses": "The experiments are reasonable.", "relation_to_broader_scientific_literature": "This work could be also finished by VLM, which is not interesitng with tranditional method.", "essential_references_not_discussed": "No", "other_strengths_and_weaknesses": "strengths:\n\n1) This paper proposes an OSDA method based on a causal model. By introducing the concept of probability sensitivity, a risk assessment framework for adversarial unknown categories is proposed, and a contrastive feature alignment and virtual multi-unknown category prototype strategy are designed to achieve open domain classification tasks. \n\n2) Authors conduct expensive experiments, which show that this method achieves significant performance improvements on three benchmark datasets.\n\n3) Paper is easy to follow. And the shown figures are interesting with enjoyable color and design. \n\nWeaknesses: \n\n1) As reported in the main tables, in most cases the proposed methods are not good and fail to be SOTA (State of the Art). This indicates that while the methods may show promise or have certain advantages in specific scenarios, they do not consistently outperform existing techniques across all metrics and benchmarks. \n\n2) I think this task could potentially be completed by leveraging Video-Language Models (VLMs). However, the authors did not demonstrate scenarios or cases where VLMs might fail to work effectively. It's important for a comprehensive evaluation to include both the capabilities and limitations of such models. \n\n3) No codes are provided, which is not too convincing. This lack of concrete examples makes it difficult to fully understand the implementation details and assess the validity of the claims being made. For a more robust evaluation, it's essential to have access to the specific code snippets or a complete codebase that demonstrates how the theoretical concepts are applied in practice. Without this, the explanation remains somewhat abstract and less actionable.", "other_comments_or_suggestions": "Please provide the code, which is important.", "questions_for_authors": "No", "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": "", "extra_scores": {}}, {"review_id": "OcLSzBowjv", "reviewer": "Reviewer_rce5", "summary": "This paper establishes a novel causal-inspired theoretical framework for Open-Set Domain Adaption by exploring the susceptibility between two visual samples. Based on the theoretical analysis, the authors propose three components: the SRE for estimating the causal relativity; the CFA module to facilitate cross-domain feature alignment; and the VMP strategy for pseudo labeling. The theoretical proof seems correct and novel, which fills up the gap of causal inference in the OSDA tasks.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "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": "**Dear Reviewer rce5,**\n\nThank you for your decision and constructive feedback. These detailed and professional comments have highly enlightened and encouraged us to make every effort to improve our work. We hope our responses could resolve the concerns.\n\n>**Claims And Evidence**.  What is the meaning of “c' is the specific implementation of C” in Definition 1.\n\n**A1**. We sincerely appreciate the opportunity to clarify this important conceptual point. We provide a simplified binary example to clarify the meaning. As shown in Fig. 7 (Appendix), for _maple leaf_ classification, let $C$ denote the presence of _palm-shaped lobes_. There the specific implementation $c\\in \\{0,1\\}$:\n- $c=1$: Sample exhibits palm-shaped lobes\n- $c=0$: Absence of this trait\n\nThen the different implementations of $C$ in the sample will influnence the probablity of the label. We hope this illustrative example has clarified the causal feature representation.\n\n> **Methods And Evaluation Criteria**. I think the authors could conduct experiments on more challenging datasets (such as DomainNet)\n\n**A2**. We sincerely appreciate the suggestion. We have expanded our experiments on both DomainNet and VisDA.\n\n*Table 1. Comparison results on DomainNet and VisDA with CLIP backbone**( Baseline results from [R1]).***\n|Method|Domain|Net|(173/172)|VisDA|(6/6)||\n|-|-|-|-|-|-|-|\n||OS*|UNK|HOS|OS*|UNK|HOS|\n|DCC[1]|50.2|45.1|47.5|75.3|46.2|57.3|\n|OVANet[2]|65.1|48.5|55.6|60.4|61.2|60.8|\n|CROW[R1]|70.3|50.9|59.0|77.0|62.8|69.2|\n|**COSDA-CLIP**|**72.0**|**76.2**|**73.9**|**85.2**|**72.6**|**78.4**|\n\n**[R1] Cross-domain Open-world Discovery, ICML 2024**  \n\n**Key Findings from Table 1:**\n1. Substantial HOS Improvements:\n    - On DomainNet, COSDA-CLIP achieves  **73.9% HOS, outperforming CROW by 14.9%**\n    - On VisDA, COSDA-CLIP reaches  **78.4% HOS, outperforming CROW by 9.2%**\n2. Dual Strengths in OS\\*  and UNK: With CLIP, COSDA particularly further enhances known-class classification and unknown-class detection (UNK).\n\n*Table 2.  Performance comparison with [1][3] on Office-Home and Office-31*\n|Method|Office-Home|Office-31|\n|-|-|-|\n|DCC[1]|64.2|86.8|\n|UADAL[3]|68.7|88.1|\n|**COSDA**|**71.7**|**92.6**|\n\nTable 2 shows leading performance of COSDA on small-scale datasets compared with [1][3]. These experiments could further confirm the effectiveness of COSDA.  **We will well cite [1][2][3] in the updated version.** \n\n>**Experimental Designs**: It is more appropriate to visualize the feature space of a more advanced method, especially ANNA (2023).\n\n**A3**. Thanks for your suggestions. We have added the requested comparison with ANNA in our feature space analysis. The visualizations can be found at https://anonymous.4open.science/r/tsne-5F2D/\n\n> **Essential References Not Discussed**: A close relative idea has been proposed in prior work DCC[1] published in CVPR 2021, which is not discussed in the related work. Several classical researches are missing, such as OVAnet [2] and UADAL [3].\n\n**A4**. We appreciate your insightful comments. **We will incorporate [1][2][3] into the updated related work.** DCC proposes Domain Consensus Clustering for universal domain adaptation, using semantical and sample-level consensus to effectively separate and distinguish common classes from private ones. OVANet proposes a universal domain adaptation method that learns an open-set threshold from source data via one-vs-all classifiers and adapts it to the target domain by minimizing class entropy. UADAL addresses open-set domain adaptation with unknown-aware adversarial learning, aligning known classes while segregating unknowns in feature space. We carefully read [1][2][3], and the difference is we exclude all known-class positive samples and cluster only the remaining negative samples (i.e., those not belonging to any known class). Besides, unlike one-vs-all strategies requiring C clustering operations per epoch (C = the number of known classes), COSDA achieves comparable performance with only one clustering per epoch.\n\n> Other Comments Or Suggestions\n\n**A5**. We sincerely appreciate your thorough review of our paper. **We will carefully correct the errors in the updated version and thoroughly review the text to prevent similar mistakes.**\n\n**LLine 133-135**: The parameter $\\epsilon$ represents the degree of intervention on the causal features. It should be large to ensure that the semantic information can be disentangled (i.e., so that it influences the probability of label $Y$).\n\n**LLine 163-164**: The command `\\LB` (which represents the label $Y$) was missing its backslash due to a typesetting error. \n\n**The anonymous code repository is unavailable**: We have updated the code in the previously provided anonymous link while also including necessary details for running it.\n\nWe sincerely appreciate your insightful comments. Please let us know if you need any further information or if there are additional points you would like to discuss with us.\n\nBest regards,\n\nAuthors of #10234", "claims_and_evidence": "What is the meaning of “c' is the specific implementation of c” in Definition 1 (LL94-95), it is a little bit confusing that I cannot relate it to any real examples. What is the connection between these variables to the source/target sample? Since this definition affects the following proofs and model design a lot, it should be more clearly defined. The authors could give a concrete example for intuitive understanding.", "methods_and_evaluation_criteria": "In the main paper, both Office31 and Image-CLEF utilized in experiments are quite simple benchmarks where the foreground objects and background in most of their samples are clearly distinguishable. I think the authors could conduct experiments on more challenging datasets (such as DomainNet), which contain more hidden causal relations that are suitable for evaluating the proposed framework.\n\nWith the above concerns, It is also suspectable for the application of this framework in practical scenarios. The proposed causal analysis seems restricted between single samples with clear foreground objects, while the open world often exists more complicated inter-object relations. Including an extended discussion for these situations will be better.", "theoretical_claims": "The proofs in this paper seem correct without explicit logistic error.", "experimental_designs_or_analyses": "The overall results in the experiment sections are comprehensive. Despite the main results, the authors also conduct a lot of analysis to verify the effectiveness of incorporating susceptibility risk.\n\nIn Figure 5, OSBP is a relatively old method (in 2018), whose performance is not outstanding in recent OSDA approaches. To a better understanding of the proposed framework, it is more appropriate to visualize the feature space of a more advanced method, especially ANNA (2023), which also explores the benefit of causality in OSDA.", "relation_to_broader_scientific_literature": "The proposed framework theoretically demonstrates the potential of causal inference in OSDA, which may inspire the following research to develop more robust and interpretable recognition systems that align with human thought in the open world.", "essential_references_not_discussed": "The second key contribution is a pseudo-labeling strategy using k-means for clustering in the target domain. A close relative idea has been proposed in prior work DCC[1] published in CVPR 2021, which is not discussed in the related work.  \nSince OSDA/UniDA has been studied for nearly 7 years, the discussion for previous works is not comprehensive. Several classical researches are missing, such as OVAnet [2] and UADAL [3]. \n\n[1] Li G, Kang G, Zhu Y, et al. Domain consensus clustering for universal domain adaptation[C]//Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2021: 9757-9766.\n[2] Saito K, Saenko K. Ovanet: One-vs-all network for universal domain adaptation[C]//Proceedings of the ieee/cvf international conference on computer vision. 2021: 9000-9009.\n[3] Jang J H, Na B, Shin D H, et al. Unknown-aware domain adversarial learning for open-set domain adaptation[J]. Advances in Neural Information Processing Systems, 2022, 35: 16755-16767.", "other_strengths_and_weaknesses": "Refer to the above comments.", "other_comments_or_suggestions": "LLine 133-135, \\epsilon in Equation 3 is not defined.\n\nLLine 163-164, what does the abbreviation LB mean, couldn’t find it anywhere in the rest of this paper.\n\nThe reference to the anonymous code repository is unavailable.", "questions_for_authors": "Please refer to the above comments.", "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": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: Reviewers appreciated the paper including both the theoretic and methodological aspects. While reviewers noted a few weaknesses, the authors' rebuttal addressed the main concerns.

Please make sure to address the comments from the reviewers in the final version to improve the paper.
Decision: Accept (poster)