Fairness-Aware Multi-view Evidential Learning with Adaptive Prior
Authors: Haishun Chen
Cai Xu
Jinlong Yu
Yilin Zhang
Ziyu Guan
Wei Zhao
Fangyuan Zhao
Xin Yang
Venue: ICLR 2026 Poster (2026)
Keywords: multi-view evidential learning
uncertainty estimation
Primary area: other topics in machine learning (i.e., none of the above)
TL;DR: We propose a FAML framework that mitigates biased evidence allocation across classes by introducing a adaptive prior and fairness constraints, achieving more reliable and fair uncertainty estimation.

Abstract: Multi-view evidential learning harnesses diverse data sources to improve prediction performance and provide reliable uncertainty estimates. Recent advances have primarily focused on optimizing evidence fusion strategies, assuming that the evidence extracted from each view is naturally reliable for downstream integration. However, our empirical analysis reveals that samples tend to be assigned biased evidence to support data-rich classes, thereby rendering unfair uncertainty estimations. This motivates us to delve into a new Biased Evidential Multi-view Learning (BEML) problem. To this end, we propose Fairness-Aware Multi-view Evidential Learning (FAML) method to rectify biased evidence learning. Specifically, FAML introduces the training-trajectory-based adaptive prior into the construction of Dirichlet parameters, flexibly calibrating the initial support evidence assigned to each class during training. Furthermore, we incorporate a fairness constraint as a regularization term to alleviate bias in the evidence. In the multi-view fusion stage, we propose an opinion alignment mechanism to mitigate view-specific bias across views, thereby encouraging the integration of consistent and mutually supportive evidence. Theoretical analysis shows that FAML effectively achieves less biased evidence allocation. Extensive experiments on real-world multi-view datasets demonstrate the superiority of our FAML, in terms of prediction performance and uncertainty estimation.

Published as a conference paper at ICLR 2026
FAIRNESS-AWARY MULTI-VIEW EVIDENTIAL LEARN- ING WITH ADAPTIVE PRIOR
Haishun Chen', Cai Xu', Jinlong Yu', Yilin Zhang',
Ziyu Guan', Wei Zhao ' Fangyuan Zhao", Xin Yang' 1 School of Computer Science and Technology. Xidian University, China
School of Computer Science and Technology, Xi' an Jiaotong University, China
/chenhaishun, 24031212287, ylzhang.3, (cxuê, zyguanê, ywzhao@mail. Jxi di an edu.cr cn 2fy14552363356sttt xjtu. edu. cn
sinyang)@stun xidian. edu.
ABSTRACT
Multi-view evidential learning harnesses diverse data sources to improve predic- tion performance and provide reliable uncertainty estimates. Recent advances have primarily focused on optimizing evidence fusion strategies, assuming that the evidence extracted from each view is naturally reliable for downstream inte- gration. However, empirical analysis reveals that samples tend to be assigned biased evidence to support data-rich classes, thereby rendering unfair uncertainty estimations. This motivates us to delve into new Biased Evidential Multi-view Learning (BEML) problem. To this end, we propose Fairness-Awaid Multi-view Evidential Learning (FAML) method to rectify biased evidence learning. Specif- ically, FAML introduces the thajinggtrajectory-boe -based adaptive prior into the con- struction of Dirichlet parameters, flexibly calibrating the initial support evidence assigned to each class during training. Furthermore, we incorporate fairness constraint as a regularization term to alleviate bias in the evidence. In the multi- view fusion stage, we propose an opinion aligmment mechanism to mitigate view- specific bias across views, thereby encouraging the integration of consistent and mutually supportive evidence. Theoretical analysis shows that FAML effectively achieves less biased evidence allocation. Extensive experiments on real-world multi-view datasets demonstrate the superiority of our FAML, in terms of predic- tion performance and uncertainty estimation.
INTRODUCTION
Multi-view learning leverages complementary information from multiple views improve model performance, providing significant advantages to real-world applications (Hu et al. 2022 2023). For example, autonomous driving systems integrate data from multiple sensors accurately perceive the driving environment (Cheng et al., 2024). However, in these high-stakes applications, is essential for models to reliably represent the uncertainty associated with their predictions (Duan al. 2024).
To address this practical limitation, a series multi-view evidential learning (MVEL) methods based on Evidential Deep Learning (EDLL)(Senso al., 2018) have been proposed to provide clas- sification predictions alongside the corresponding uncertainty. In the prevailing MVEL paradigm, evidence is collected separately from each view accordance with Subjective Logic (SL) (Jøsang) 2016) and then aggregated to parameterize Dirichlet distribution initialized with a non-informative uniform prior. Following this line of thought, many subsequent studies focus on refining the evidence-level fusion of multiple views to better handle real-world challenges such as inter-view conflict (Xu et al. 2024a Lu et al., 2025) and low-quality views (Xu et al. 2024b Liu et al. 2025c).
Although these methods demonstrate promising performance, most existing studies implicitly as- sume that the evidence extracted from each view inherently impartial and reliable for downstream fusion. However, this assumption is often violated in real- weal-world tasks, where data distributions are
"Corresponding author.

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Published as a conference paper at ICLR 2026
Hel
0.5
3.0
00
Isvidence Space
Predictive Uncertainty
Evidence Space
Predictive Uncertainty
(a) Evidential bias view
(b) Evidential bias in view
Figure I: Visualization for the classification study and associated uncertainty the BRCA dataset. To evaluate the predictive uncertainty across the feature manifold, we employ a dense sampling strategy to generate the test set. For both views, the left subfigures delineate the decision regions (shaded areas) overlaid with training instances (in points). The right subfigures depict the corre- sponding predictive uncertainty with a darker color indicating that the prediction is more uncertain.
often imbalanced due to inherent biases in the collection process((henn et al. 2025). As result, the probability of assigning more evidence is significantly higher for data-rich classes than for data-poor ones. More intuitively, as shown in Figure [ an empirical analysis on the imbalanced real- world multi-view dataset Breast Invasive Carcinoma (BRCA) (Shea al. (020)) highlights the unfairness the allocation evidence. We observe that for samples from the data-poor class (Her2), the sup- porting evidence is often largely assigned to the Normal class in the first view and to the Basal class in the second view. The view-specific biased evidence learning process leads Her2 samples to collect strong supporting evidence for data-rich classes, making them prone being confidently misclassi- fied. In contrast, correctly classified Her2 samples typically receive insufficient supporting evidence, which leads the model to assign low confidence these correct predictions. This phenomenon poses a new Biased Evidential Multi-view Learning (BEML) problem, where the allocation of supporting evidence is inherently unfair, resulting in unreliable and biased predictive uncertainty.
To address the aforementioned problems, we propose a Aairees-AAware Multi-view Evidential Learning (FAML) method address the BEML problem. Distinct from previous methods that primarily focus on how to aggregate evidence obtained from each view, FAML reformulates the evidential multi-view learning problem from the perspective of fair learning. As shown Figure to eliminate evidential bias across different classes, we introduce the mainiig-trajectoryy-r into the construction of Dirichlet parameters, adaptively calibrating the prior support assigned to each class during training, thereby promoting balanced evidence allocation. With this adaptive de- sign, the prior directly reflects class-wise performance, which naturally leads to compensatory relationship: the worse class performs, the larger the adaptive prior becomes. As the training pro- ceeds, the adaptive prior would progressively converge to a fixed value used in standard Evidential Deep Learning. In addition, we also calculate the fairness degree according the variance of class- wise evidence as an explicit constraint to regularize the evidence learning process. Considering that bias exhibits a view-specific pattern, we design an opinion alignment mechanism that minimizes the discrepancy of opinions between any pair of views, which ensures that different views align not only on what their predictions but also on how confident they are their predictions.
prior
The main contributions of this work are summarized as follows:
We reveal a neglected but widespread issue in multi-view evidential learning, where the evidence learning process often exhibits implicit unfairness practice.
From the perspective of fairness, we propose deal with the issue of biased evidential multi-view learning that arises from class imbalance.
crriiinggrraeccor---ere adaptive prior to
We theoretically prove our adaptive prior increase the evidence margin for minority classes, and thereby guarantee improved generalization error bound by a factor of ((L/VEABB))
Extensive experiments on six real-world multi-view datasets demonstrate that FAMI. con- sistently outperforms existing methods, achieving fair and reliable uncertainty estimation.
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Training: Training-Irajectory Prior
Prodictimm Training
Opinion Aligument
Dirichlet Paramsters
a²
Update Prior
View speetlic Evideniial DNNs
Bio
Piz
Pi
Prediction 3 21
View I
Bizsed Evidence
by
Training Trajectury
Predictions
like
Dirchlet Pammeters
f(()
a
Aggregated Opinioo
today.
View v*x
Update
Pitz
Pix
Pit)
Y1 75 75
Imbulanced Trining
Evidance
Tesining Epoch: 1.2.
unconsitty
Figure 2: Illustration of FAML. It first employ view-specific evidential neural networks construct opinions from each view. To mitigate evidential bias, the training-trajectory-ban is introduced into the construction of Dirichlet parameters, flexibly calibrating the initial support evidence assigned to each class during training. Afterthat, an opinion alignment mechanism is then applied to mitigate view-specific bias across views. Finally, all view-specific opinions are integrated to reach a reliable and trustworthy prediction.
adaptive prior
2 RELATED WORK
2.1 EVIDENCE THRORY.
As an arising ingle-forward-pass uncertainty estimation method, evidential deep learning (EDL) has attracted increasing research attention in recent years. Grounded in the subjective logic theory, EDL models predictive outputs as evidence for a Dirichlet distribution, offering reliable uncertainty estimation in various downstream tasks (Gao et al. 2024 Xia al. 2024). The effectiveness of EDL critically depends on the evidence collection process, with recent studies exploring improve- ments such evidence allocation refinement (Li al. 2024), sample reweighting (Pandey & Yu 2023), and advanced evidence functions et al.] 2023 Yu et al. 2024) to enhance uncertainty quantification. However, most recent works still rely on a fixed uniform prior for the Dirichlet distri- bution(Chen et al. (2024), which may undermine the reliability in uncertainty estimation in practice. To address this gap, we introduce a training-trajectovy trajectory- based adaptive prior, explicitly designed to mitigate evidence bias and enhance uncertainty reliability.
2.2 MULTI-VIEW EVIDENTIAL LEARNING.
To enhance the performance and reliability of models by integrating data from multiple views, multi- view evidential lcarning has attracted significant attention. Pionecring works like Trusted Multi- view Classification (Han et al. 2022b Liu et al. 2022) employ the Dempster-Shafer theory (Shafer 1992) to aggregate evidence from different views. Building on this research, a significant body of subsequent work has focused making the fusion process more robust real-world challenges. For example, some methods (Zhou et al. 2023; Xu et al., (2224)) focus on explicitly handling con- flicting opinions between different views achieve more reliable decision. Others (Liu et al. 2024 2025a b) are designed to dynamically assign adaptive weights to each view, effectively re- ducing the influence of low-quality views during the fusion process. More recently, improve transparency and reliance at both the evidence and the decision levels, TMCEK (Liang et al.) (0255) introduce expert knowledge to identify critical evidences relevant to decision- making, enhancing the interpretability and robustness of multi-view learning. SAEML (Xu et al. (025) explicitly nor- malizes the contribution of evidence from different views to ensure cross-view comparability, thus improving the reliance of multi-view fusion process. Despite their success, all of these methods fo- cus on enhancing the consistency and comparability of evidence across views, while the fairness in the allocation of evidence in each view is entirely neglected, which is of great significance in safety- critical domains like medical diagnosis and autonomous driving. In contrast, our method improves fairness through adaptive prior mechanism, thereby reducing the risks in final decision-making.
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2.3 FAIRNESS IN MACHINE LEARNING.
Fairness in machine learning Zhang et al. 2025 Zhou et al. (026) often concerns whether a model performs consistently across different subpopulations of data, which usually characterized by sensitive attributes such as gender, race, or age. Moving beyond sensitive-attribute faimesss, there small but growing line of work focusing on imbalanced-labet subpopulations, where quantity- imbalance between classes becomes the major source of unfairness. To alleviate such quantity induced unfairness, some approaches resort to data pre-proeessing aiming to create a balanced train- ing set through resampling (Kim et al.) (023) or synthetic data generation (Marchesi et al.) [2255]
UMIX (Han et al., 2022a) is one of the most representative works in this line, which generates train- ing samples by performing
uncertainty -waaee mixup, thereby improving model generalization
and fairness across groups. Besides, other works (Xinying Chen Hooker 2023; Yu et al. 2025)
focus on facilitating fairness notion into objective function remove discrimination during the training process. GroupDRO (Sagawa et al., (020) trains the model to minimize the worst-case loss over pre-defined groups, thus effectively mitigating discrimination in alternated manner. In trast to them, FAMI, adaptively adjusts priors based on training trajectories without subpopulation information, making a general evidential learning framework an intrinsic and flexible manner.
METHOD
3.1 PROBLEM FORMULATION
In the context of multi-view learning, each instance is characterized by multiple views. To clarify, consider dataset D [12%)== Jn with labels y/ E 21.2.... .K} where zy Rd denotes the feature vector for the e-th view of the n-th instance. Multi-view evidential learning aims integrate information from different views at the evidence level, and then aggregates the evidence to parameterize a Dirichlet distribution over class predictions, thereby enhancing both classification performance and reliability. However, in parctice, the learning process often suffers from quantity- induced bias, leading to a biased evidence allocation. To enforce fairness in multi-view evidential learning, the expected evidence assigned to the ground-truth class for each view should be class- invariant, which is formulated as:
((r,y=))D [e](x)] = (( (x)), Vk, E (1,2,..... K}
The goal of BEML eliminate evidence bias in the learning process, and achieve fair evidence allocation and reliable uncertainty estimation.
3.2
FAIRNESS-AWARE MULTI-VIEW EVIDENCTIAL LEARNING
3.2.
VIEW-SPECIFIC EVIDENCE LEARNING.
EDL extends Subjective Logic (SL.) to deep neural networks, providing the model with the ability quantify uncertainty in its predictions. Specifically, for the specific view of an instance (= D we employ Evidential DNNs to obtain view-specific evidence e = [ei,..., the evidence is then used to parameterize the Dirichlet distribution, where the k-th category Dirichlet distribution parameter ag can be derived as:
a₂ = Cx + 1,
(2)
where the constant represents non-informative uniform Dirichlet prior, implicitly assuming that each class is equally probable in the absence of evidence. According to Subjective Logic theory, the belief masses by and the uncertainty mass u are defined as follows:
K
ek
agk
K
by
by
S
S
S
where = Ex =k 0% is defined as the Dirichlet strength. To generate the final predictions, Sub- jective Logic models each view-specific prediction as multinomial opinions
(b, u, a), and the
In this section, we omit the super- and sub-scripts for clarity
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projected probability distribution of multinomial opinions is given by:
Ogk: S
ps = by + ag
for 1,,......
(4)
Normally, the base rate [a1 02 ................................ ag. is typically conformed to uniform discrete distribution, 1/K, assuming that no class preference is adopted.
While the above formulation enables uncertainty- aware multi-view prediction, it implicitly over- looks the impact of uniform Dirichlet prior assumptions on the fairness of evidence collection. In particular, an improper prior could dominate the Dirichlet posterior, especially for samples with less supporting evidence, undermining both the reliability and fairness of the multi-view learning process. To address this issue, we propose regularization. Instead of employing a uniform Dirichlet prior in parameterizing the Dirichlet dis- tribution, our approach adjusts the prior adaptively based on the learning history of each class. The training-trajechto traj--errrotoobaeeeeeee -baeed prior for the k-th class in the training epoch (L
prior as form of adaptive
is defined as follows: 2
Bk = ....NK/(
Σ n:th
K(yn, (oln:fo((a)) fo(
(5)
11 if yn fa(œn). if yn + fo(Øn).
where K (yn, fo(2n))
(0
where N₂ is the number of samples from the k-th class, and v is the upweight factor that controls the strength of the prior. To construct the trajectory-basee prior, we train the model using empirical risk minimization and record the prediction results (xx, for each sample in the training epoch t and then adaptively adjust the prior for each class based on its prediction. this way, we update the Dirichlet concentration parameters for each class follows:
ág c + Ak.
This adaptive prior exploits the learning trajectory of each class to adaptively calibrate their contri- bution in evidence learning process, thereby enhancing faimess and mitigating the evidential bias.
To further get an intuitive sense of the level of fairness among classes, we introduce a measure named Fairness Degree, which quantifies the variance of class-wise evidence allocation each view.
Definition 1 Fairness Degree. Given the set of evidence vectors produced by Evidential DNNs across all samples, the faimess degree is defined the variance of the class-wise average evidence:
1 K
f((E)) Var((e+))<1)
Σ
(E
where Eg represents the average evidence assigned the ground-trut truth class for samples belonging to class k, and ē is the global average of these class-wise average evidences.
Intuitively, this metric captures the fairness of evidence distribution across different classes. When the Fairness Degree is low, it indicates that each class receives relatively consistent amounts of evi- dence for their ground-truth predictions, suggesting fair treatment by the model. Conversely, a high Fairness Degree reveals that some classes consistently receive much more much less evidence than others, signaling systematic bias in the evidence allocation process that could compromise the reliability of uncertainty estimation.
3.2.2 EVIDENTIAL MULTI- VIEW FUSION.
In this subsection, we focus on multi-view fusion based on view-specific opinions. Since each view provides its own prediction and associated uncertainty, is necessary to aggregate these opinions to reflect the overall uncertainty of the final decision. To obtain more comprehensive joint opinion, we taking into account the view-specific uncertainty to calculate aggregated evidence. Rather than treating each view equally, we propose confidence-based evidence aggregation method as follows:
we omit the subscript in the subsequent notation for simplicity
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Definition 2: Confidence-bused Evidence Aggregation. Given two opinions w = (b4, u= an)
and w" = (b", u² a²) over the same instance, let & eg and eg represent the evidence for the k-th category from view A, view B, and the aggregated view, we have:
(1 - u Je + (1 De
ck
2 - a u
(8)
A + c k +
c c ckk
where e = 1 - u and c = u represent the confidence of view A and view B. Follow- ing Definition 2, combine the evidence from views into common aggregated representation. According to the SL theory, we can obtain the final multi-view joint opinion, and thus get the final probability of each class and the overall uncertainty (see appendix A. for detailed derivations).
To ensure different views to provide consistent evidence, we further introduce the Dissonance De- gree of views in Definition 3, which established according opinion variance.
Definition 3: Dissonance Degree of Views. Given any view represented by the opinion w the variance of opinion for k-th class is derived from the Dirichlet PDF:
k
ak aq.
Var (ax) =
E ar +11
k== 01.
(9)
1 (1 - p%) u²
K + w
then the dissonance degree between two views A and B is computed as:
d (w w w²) Var (a Var (a²)
(10)
The Dissonance Degree measures the discrepancy in uncertainty estimation between views by com- paring their Dirichlet variances, thereby reflecting cross-view consistency at the uncertainty level. Compared with traditional divergences such Kullback-Leibler (KL) Jensen-Shannon (JS) di- vergence on the expected Dirichlet probabilities, captures second-order uncertainty rather than only first-order probability differences.
3.2.3 LOSS FUNCTION,
In this subsection, will introduce the process of training evidential neural networks to obtain the multi-view joint opinion. As previously discussed, to climinate evidence bias, we introduce the adaptive iujectory-baset prior to obtain the concentration parameters of the Dirichlet distribution. For the instance { h the supervised loss is derived from the expected cross-entropy between the true label and the Dirichlet mean, which can be induced as:
K
Σk= Pak
Gnk-1
Lace (ōen) =
Unk log Pirk
dp
B (ā.))
(11)
K
Σ Unk (1b (Sn) +b (ānn)) k=1
where v'(-) is the digamma function, B(-) ) the K-dimensional multinomial beta function. Eq. is the integral of the cross-entropy loss function on the simplex determined by &,. The above loss function ensures that the correct label of each sample generates more evidence than other classes, however, it cannot explicitly guarantee that the evidence assigned to the correct label is unbiased. To this end, we introduce an additional constraint term into the loss function, namely fairness loss:
Cfc = Var (()
Ckk
2)² == Avg((G...,,Kk)
(12)
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Published as a conference paper at ICLR 2026
where Eg denotes the average evidence assigned to class & within the current bani-b and é is the mean these class-wise averages. To mitigate iepallace-inducee bias, we employ a class- balanced learning strategy (Xia et al. 2022) defined by the following batch-wise loss:
6
Lucc
Lace (ōxn) + pe Lycs
(13)
Nm
where A4 min((10,t/T) E [0, 1J is the balancing coefficient, t is the index of the current training epoch, and T is the annealing step. By increasing the influence of fairness constraint in loss, the op- timization process avoids being dominated by biased evidence and stabilizes as training progresses.
In order to strengthen the reliability constraint among views during training, minimizing the degree of dissonance between opinions was adopted. The consistency loss for mini-batchs is given by:
Loon = ΣΣΣ d (w wg)
(14)
1=1p=1pp polo
To sum up, the overall loss function for mini-batch can be calculated
V
= Traco
+
(e) acc
+
A Loon
(15)
0=1
The model optimization is elaborated in Algorithm (please refer to the Appendix A.3)
THEORETICAL STUDIES
In this section, we aim establish the generalization guarantees of the FAML. framework, partic- ularly for minority classes. The analysis is grounded in the margin theory of statistical learning, which connects the margin distribution achieved on the training set to the model's generalization error. In the following, we first introduce the definition of Evidence Margin.
Definition 4.1 (Evidence Margin). Let ha X R denote model, parameterized by 0, that maps a sample In to a K--dimensional non-negative evidence vector en = [en1:...,. Cnk]. The evidence margin Pn (f) of xn is then defined
Pr. (0) Enk max(eng),
(16)
jzk
where ls is the ground-truth class label of F.p-
To formally establish the connection between such sample-wise margin and the model's overall generalization ability, we now introduce a foundational result from statistical learning theory. The following lemma provides general bound that relates the margin distribution achieved the train- ing set to the upper bound of the generalization error.
Lemma 4.2 (Margin Generalization Bound (Bartlett & Shawe-Taylor 1998 ). For a hypothesis
space H. given any margin p with probability least 1 0, for all h H. the true risk R(h) satisfies:
Complexity(H) N2 + C2p
In(1/8) N
R(h) < (s) + Civy
(17)
where (s) is the proportion of samples in the training set S with margin less than p. Complexity(P)) is a complexity measure of the hypothesis space, and C1, C2 are constants.
Lemma 4.2 shows that increasing the margin p tightens the generalization bound via the O(1/p) term. This allows to use the change in p bridge: by analyzing the effect of the FAML algorithm on p. we can explicitly determine its impact on the generalization error bound. Theorem 1.3 formalizes this analysis.

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Theorem 4.3. Let he - R be model trained dataset S of size N. For minority class l with imbalance ratio Ek = = N > 1, where NІ and N- are the number of samples belonging class & and other classes respectively, and under the condition that the adaptive prior Sr increases when class k performs poorly, minimizing the FAMI. L(0) yields the following theoretical guarantees for the evidence margin Pr (0) Cnk
maxj4k Cuji
Margin Increase for Minority Class. bounded below by:
The expected margin improvement for class k is
A&e -
BlApn U/ k:] R mi (Sa)
EE
Sa
where 17 is the learning rate, S& = E, Onjy anj= enj + B3, and A8g is the increase
in the adaptive prior. For En 1, the positive term dominates, ensuring a net margin increase.
Tighter Generalization Bound. The increase in margin tightens the generalization bound. The effective margin Petl satisfies:
Pett Z Pb A. E -
where po is the baseline margin and X > is scaling factor. This leads to an improved generalization error bound for the minority class by ffccoor of (1.VE..)).)
Theorem delineates how the adaptive prior enhances the evidence margin and tightens the gener- alization bound, with particular efficacy for minority classes. First, as captured by the lower bound on the expected margin improvement, the corrective mechanism scales with the class imbalance ra- tio Êk. This scaling property ensures that the model automatically allocates greater corrective effort to classes that are both under-represented and under-performing. Second, the generalization im- provement factor of 0(1/VExABk) quantifies this behavior: it shows that greater data imbalance (larger (x) coupled with stronger model self-feedback (larger A3₁) leads to greater generalization gain. This result provides a theoretical foundation for the superior performance of our method on long-tailed distributions. We provide the proof in appendix A.2
EXPERIMENT
5.1 EXPERIMENTAL SETUP
We briefly present the experimental setup here, including the experimental datasets, comparison methods and evaluation metrics.
Dataset. Following previous work (Xu et al. 2024a Liu et al. 2024), we conducted experiments on six multi-vien real-world datasets as follows: Handwritten, Animal, Scene15, YaleB, Caltech-101 and BRCA. For more detailed descriptions of the datasets, please refer to the appendix A..4
Compared Methods. We compare the proposed method with the following methods. (1) Single- view evidential learning methods contain: TLC (Trustworthy Long-tailed Classification) (Li et al., 2022) combines class-imbalance classification and uncertainty estimation in multi-expert frame- work. I-EDL( Information-bass EDL) (Deng et al.) 2023) is the SOTA evidential approach for uncertainty-awer learning the single-view setting. R-EDL (Relaxed-EDL) (Chen et al.) 2024) explores the relaxation of subjective logic assumptions to improve robustness. For single-view base- lines, we report the results from the berf-perfo view. (2) Multi-view evidential learning meth- ods contain: TMC (Trusted Multi-view Classification) (Han et al. 2022b) addresses the uncertainty estimation problem and produces reliable classification results. ETMC improves upon previous methods by adding pseudo-view that concatenates multi-view features to provide complemen- tary information. CCML (Consistent and Complementary-
trusted Multi-view Learning) (Liu) et al. 2024) explicitly decouples two types of evidence to enhance robustness to ambiguous views. (Evidnnnlttiial Conflictive Multi-view Learning) (Xu et al. 2024a) is the SOTA method that proposed fusion strategy for solving multi-vien conflictive problems.
Evaluation Metrie. Similar to eL al. 2022). we evaluate the performance of FAML with diverse metrics. Besides applying Classification Accuracy (ACC) measure the classification prediction
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accuracy in different class regions (including Head, Med, Tail regions), also adopt Expected Calibration Error (ECE) (Ncinn et al. 2015) to check the correspondence between predicted prob- abilities and empirical accuracy. Along with classification, prediction using AUROC (McClish, 1989) and FPR-95 Liang et al. (2017), where the estimated uncertainties employed to distinguish between correct and incorrect predictions.
evaluate the performance failure
Table 1: Performance comparison in terms of ACC(%) and ECE(%) on test sets, indicates the standard deviation for 5 random seeds, with the best mean scores highlighted in bold.
Dataset
Method
Head
ACC(%)
Med
Head
ECE
Med
TLC
81.9 1.1
98.0 1.5
85.0 1.9
76.5
23.3 1.3
3 2.3
26.7
1.8
22.6 1.4
I-EDL
78.9 1.7
93.0
82.0 2.5
65.9
22.2 3.3
26.8 144
24.3
32. 3.5
R-EDL
8 1.2
09
8..6
72.5
14,924
0.5
31.5
35.2
239
Hundwritten
TMC
8.4
992
8.3
69.3
28.9
0.8
31.6
23.1
234
ETMC
0.
9.0
9..2
2.3
26.4
19.6
1 1.0
2.3
CCML.
87.
BCML
7..4
9.8
80.8
6.441.
31.9
40.9
34.0
2.2
Ours
94.2 a
0.4
92.5 0.5
9.7
20.6
2.41
1.3
2.3
TLC
1.8
86.3+34
7.0
55.6
2.
37
23.6
2.
I-DDL
64.0
9166199
2.4
36.0
20
47
45.2
32.9
R-EDL
68.9 1.7
90.0=2.1
7..0
4.0
13
3..0
26.8
336
Animal
TMC
0.3
89.6
6.44
4.97
16.8004
0.64
2.7
ETMC
64.5 0.3
90.0044
4.4
4
122
0.6
18.7
17,8
CCML.
0.7
898
63.8
4..9
11.1111
4..
2
198
BCML
0.5
0.7
6.2
0.3
20.5 1.5
1.1
2.19
18.7
Ours
0.4
91.6 0,9
0.7
0.49
11.0 1.0
1.3
16.4
17.6 1.6
TLC
0.4
65.9 1.7
2.0
2.9
1
3.2
57.6
17.8 1.0
I-EDL
1.9
5.9
3..63311
3.0
5..6
5.6
21.3
29.5
R-EDL
1.5
7.4
30.8
30.8
40.44.5
31.2211
464
2
25.8
4.6
Scene15
TMC
0.3
69.1
0.7
1.2
1,5
2.
13.7
14.8
1.8
ETMC
4.4
0.
4.
34
22.7
32.6
16.9 1.0
21.1 2.5
CCML
3.9
0.79
3.76
23.1
1.52
28
17.9
1.7
BCML
37.3
65.2
25.7 +
20.9
17.
35.9
13.2
18.0
Ours
1.3
75.2 1.7
50.1
4.9
18.8 3.66
1.02
12.4
TLC
7.7
8.6 7.6
55.7
29.9
3.89
37,8
46.3 2.0
I-EDL
83.7 1.4
86.7 3.5
82.9 3.8
82.1
4.0
35.2 3.6
4..2
32.1
4.9
R-EDL
1.0
96.2 =
8.8
7.96
4.2
2.5
1.5
4..9
YaleB
30
02.9
39.9
ETMC
82.2404
0..3
17.1
729
30.6244
0..7
19.1
38.8
CCML
4.7
98.1
1.9
6.
3.5
54.3
35.7
38.9 1.4
BCML
1.1
90.5
8.1
62
30.6
1..1
29.7
45.1 A
Ours
2.9
99.5 0.2
81.9 1.0
84.3
10.9
27.2
15.2
27.5 + 1.6
TLC
0.5
9..6
72.9 1.2
$7.5
2.72
3.0
29.6
34.1 1
I-EDL
1.4
99.1
82.4
5
12,
4..9
37.4
30.5
R-EDI
2.9
95.7
2.4
45.0
24.
23.9
34.7
31.5 338
Caltech-101
TMC
73.9
95.2
4.45
2.9
2.3
25.8
33.4
31.9 144
ETMC
1.1
95.2
3.2
2.16
25
21.1
2.55
2.
CCML.
9.
32.7
BCML
7.87
9..1
6.6
56.4
36.
4.6
42.2
34.3 3.8
Ours
8.0
9.9
8
67.8 2.8
14.1 1.3
1.24
1..2
26.9
TLC
2.49
3.
6.4
46.38888
32.4
1.2
50.9 42.944.1
LEDL
73.1
8..6247
718262
68.8 13.8443
44.0
53.6134
35.0
44.
R R-EDL
76.6
89.7 1.3
6.7
62.5 7.0
1.3
24.5
3.96
49.7 4 1.6
BRCA
46.9
+
29.9
ETMC
77.1411
81.2 1.6
5.24
6.2
318
32.9
32,9
47.8
CCML
75.4
90.8 1.5
47.9
4.2
24.
34
5.2
14.1
5CML
77.1
82.0=32
4.5
5..6
40.7
3.2
48.6
32.6
53
Ours
8.49
82.7
0.7=35
5329
8.42
1..0
13.5
2.
44.3 42
5.2 EXPERIMENTAL RESULTS AND ANALYSIS
Comparison with SOTA methods. According to the results in Table [ the following conclusion can be made: (1) Performance superiority: FAML demonstrates significant advantages over various advanced evidence-based methods on six real-world datasets. Taking the results on Caltech- 101 dataset as an example, our method outperforms the second-best approach by 7.7% overall accu- racy and 10.3% in tail-region accuracy. While some methods, such ECML, occasionally outper- form FAML isolated cases, FAML demonstrates more stable and consistent performance across all class regions, especially in tail class regions.
(2) Effectiveness of Multi-Vies Fusion: Com- pared to single-view methods, the fusion of multiple views does not guarantee better performance, biased evidence aggregation may even degrade accuracy. In contrast, FAMI achieves more effec-

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Published as a conference paper at ICLR 2026
Maregh
MADABGA Meaegh
Dilennce Searigh
Moregh
7-600
Indee
(a) TMC
(b) ETMC
(c) CCML
(d) ECML
(e) Ours
Figure 3: The average evidence strength of each class testing on Handwritten dataset. The shaded
backgrounds denote different class regions based on the numbers of samples per class.
tive fusion by emphasizing informative views and aligning cross-view opinions, thereby delivering consistently superior results. (3) The results in terms of ECE reveal that method maintains sig- nificantly lower ECE across all data region, which highlight the broad applicability and practical robustness of method in uncertainty estimation. Moreover, we offer more in-depth analysis for our FAML through the elaborate model analysis in the appendix(A.d A.6
Table AUROC and FPR-95 955 of uncertainty scores for identifying incorrect predictions.
Data
Metric
TLC
I-EDL
R-EDL
TMC
ETMC
CCML
ECML
Ours
Handwritten
FPR-95(%)
AUROC(S5
2.3
6.5
6.2
8..
90.9
73.1 0.8
7844
7..
819 66.5 1.8
6..6
7.88 4.5
818 64.3 7..8
85.7 1.5
AUROC(S)
7..0
6144788
16
76.9
0.6
76.9 0.7
82.1 75.3 3.34
Animal
FPR-95(66) 4
3.1
8.96
75.7
74.4 1.2
75.3
82.1
Scene15
AUROC(SS)
2.07
5.2
67.2
70.8 = 1.0
69.4
63.7
7..2 6..7
FPR 95(5)) 4
2.66
87.7 1.3
2.5
82.2 + 2.8
80.8 + 0.8
88.4 0.7
84.5 2.4
80.4 a 2.6
AUROC(S5
8.5
6.28
3.8
70.8
85.7
88.5 1.0
87.7
90.3
YaleB
FPR 95()))))))) 4
4..0
84.6 7.3
79.9 4.3
82.2 a:
63.8 A: 3.7
66.4 1. 2.6
64.7 1. 4.6
57.1
Caltech-101
AUROC(SS)
1.5
7..1
7.43 4..6
2.3
75.5 1.2
1.5
76.1 1.4
95(%)) J
82.1
7.54
75.7
3.0
AUROC(55)
7..8
7..1
75.5 2..7
76.6
76.3
77.1
3.9
BRCA
FPR-95 PPR-95(36) J
90.9
95.1
91.3
83.7 2.2
90.2 90.2 2.8
84.7
92.5
7.26
Reliability of uncertainties. Following prior work (Filos et al. 2019): we assess the reliability of uncertainty ensure thorough evaluation. Specifically, we perform the failure prediction task and employ AUROC and FPR-95 to quantify model's 's discriminate power in distinguishing incorrect predictions using uncertainty scores. As shown in Table 2 our method consistently achieves higher AUROC and lower FPR-95 across six datasets. These observations imply the reasonability of our model in estimating uncertainty, paving the way for reliable deep learning-driven high-risk appli- cations in real-world settings. To comprehensively evaluate the uncertainty estimation, we further visualize the density distribution in terms of uncertainty in appendix [A.6] Visualization of the distribution of evidence strength. Real-world class imbalance often drives evidence to concentrate in data-rich classes while starving data-poor classes. To illustrate this phe- nomenon, Figure repoott the average evidence strength for each category on Handwritten dataset. We observe that compared methods tend to allocate much more evidence to head region classes while providing substantially less to tail region classes. In contrast, FAML achieves relatively fair distribution of evidence strength by breaking the dependency between class sample size and evidence magnitude. Consequently, FAML is guaranteed to reduce the risk of overconfident mis- classifications, thereby improving the overall reliability of predictions.
CONCLUSION
In this paper, we introduce a Fairness-aware multi-view evidential Learning method for addressing the biased evidential multi-view learning problem. FAML introduces soininggtrajectoryy based adaptive prior to construct Dirichlet distribution, which adaptively calibrates the Dirichlet param- eters to mitigate view-specific evidential bias. Furthermore, we incorporate fairness degree to constrain the view-specific evidence learning process, thus explicitly enhancing balanced evidence allocation. During the fusion stage, we incorporate an opinion alignment mechanism to guide the formation the final fused opinion. Extensive experiments on real-world datasets confirm the ef- fectiveness of FAML on prediction performance and reliable uncertainty estimation.
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ACKNOWLEDGMENTS
This work was supported in part by the National Natural Science Foundation of China under Grants 62425605, 62133012 62472340, and 62373300, in part by the Natural Science Basic Research and part by the Shaanxi Province out-
Program of Shaanxi (Program No. (92JJC-QYX--4A 2025JC-JCQN-074 and in part by the Key standing Youth Science Foundation Project under Grants Research and Development Program of Shaanxi under Grants 2024CY2-GJHX-15, 2022ZDLGY01- 10, and 2025CY-YBXM-04).
ETHICS STATEMENT
This work adheres to the ICLR Code of Ethics. In this study, no human subjects or animal ex- perimentation was involved. Caltech-10) 101 and BRCA, were sourced in compliance with relevant usage guidelines, ensuring no violation privacy. We have taken care to avoid any biases or discriminatory outcomes our research process. No personally identifiable information was used, and no experiments were ducted that could raise privacy or security concerns. We are committed to maintaining transparency and integrity throughout the research process.
datasets used, including Handwritten, Animal, S5,ne YaleB,
REPRODUCIBILITY STATEMENT
We have made every effort to ensure that the results presented in this paper are reproducible. All code and datasets have been uploaded as supplement material.
The experimental setup, including training steps, model configurations, and hardware details, is described in detail in the appendix A.5 Additionally, the multi-view dataset we used in experiments are publicly available, ensuring consistent and reproducible evaluation results. We authors believe these measures will enable other researchers to reproduce our work and further advance the field.
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A APPENDIX
In the supplemental material:
A.1: We describe the derivations of Confidence-based Evidence Aggregation.
A.2: We provide theoretical proof of effectiveness of the adaptive prior.
A.3: We describe the detailed algorithm steps of the FAML method.
A.4: We give detailed descriptions of the datasets.
A.5: We explain the details the implementation.
A.6: We present the results of additional experiment.
A.7: We describe the potential limitations of FAML and future work.
A.8: We describe the Usage of Large Language Models.
A.1 DERIVATIONS CONFIDENCE-BASEN EVIDENCE AGGREGATION
This section derives the fused belief mass and uncertainty based on the fusion evidence in Confidence-based Evidence Aggregation.
A@B
bk
A
+ Σ k= E₁ AsB
K-b₁"" (1
K
(1 B)
K.b..
+ KKb.
+ Ek=1
2- -
(1-u*) )
(1-ua)
+ bp
1 u
1
Σ k
b
(1-ud)
+ b
(1-48)
(18)
ad
a
(1-wa)
(1-u²)
b
+ b/
4d
uA
B (1-wd)²
(1 91
(1-
B. (1-u2)
b/
+ bbb
uB
4 -
1 1 u15 -
by
(1 wt)
B lg (1 wB u
+ uB 2u A
According to Eq 2 and Eq
we have:
A@B
bk A
Σ K
k= ba (1
ud) B + Σ K
b
(1- uB) u
k=
ud + BB 2u 1
(19)
- (1- u + - 2 B 4
á + 13 2 11
A w u
4 + B - AB
According to Eq. 19), when combining opinion " with the original opinion V the aggregated uncertainty mass decreases if B < A increases if B > ud, and unchanged if u B
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A.2 THEORETICAL PROOF
Theorem A.I. Let hig X' - I be model trained dataset S of size N. For minority class & with imbalance ratio Ek: = N > 1, where N' and N-k are the number of samples belonging class & and other classes respectively, and under the condition that the adaptive prior 3r increases when class performs poorly, minimizing the "AML.objectie L(0) yields the following theoretical guarantees for the evidence margin Pr. (0) Cnk maxj4k Cujz
Margin Increase for Minority Class. bounded below by:
The expected margin improvement for class k is
BlApn yn kt] 2 mb (Sa) (Ee-
A Sa
O
where is the learning rate, Sa = Ej Ōnjj anj Cnj + 8g. and AB₁ > 0 is the increase
in the adaptive prior. For &n. >> 1, the positive term dominates, ensuring a net margin increase.
Tighter Generalization Bound. The increase in margin lightens the generalization bound. The effective margin Pett satisfies:
Peff 2 (1 A ABA))
where po is the baseline margin and X > a scaling factor. This leads to an improved generalization error bound for the minority class by factor of Ô (1/ A.).
Proof. We provide detailed proof by analyzing the gradient dynamics of the FAML objective and their aggregation under class imbalance.
Part 1: Gradient Analysis of the FAML Loss
Consider training sample (In, Un k) with evidence vector e,, ho (Zn). The FAML loss for this sample is:
(n) 16
Σ àns
(((nn))
where anj enj + Br.
(20)
We first compute the gradient with respect to the correct class evidence ent:
aLn
a
K
Σ
ans
v(ank)
Denk
DEni
j=1
K
K Σ
anj
anj
v ((nk))
Denk
Denk
1=1
w/ (Sa) 1 v (aan))
= W (Sa) - (b(k))))
where So E anj.
Since (x(xx) is the Trigamma function, which is strictly positive and monotonically decreasing for > 0, and since Sa > ânk > O, we have:
Thm
1 (Sa) 15 (ānk))
< 0.
(21)
Denk
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Now consider sample (Ims Um for class & on this non-k sample) is:
1) where o k. The gradient with respect to emk (the evidence
7Lm
a
Σ 1=1
amj
((mm))
demk
Denn
K
K Σ amj
dā dm
amj
2 (dml)
Demk
= v/ (5
(āmm)) -0
= n/ (5 > O,
Part 2: Quantitative Analysis of the 3r Effect
Using the asymptotic expansion of the Trigamma function for large
('(x)
+ 0
(22)
2x
6
30
We can analyze the quantitative effects of increasing 3x.
For class & sample, the update magnitude for increasing Cnk is:
0Ln
Den
et' (āánk) - (Saa)
Denk
1
+0
+0
Öbakk
20
S4
25
5
For minority class & with & >> 1, it is empirically observed that 3g >> Cnk, we therefore approx- imate Ōn = End + 3x R 3e in the subsequent analysis. Meanwhile, since each adaptive prior 3 treat the contribution from other classes C' Ljjt Önj constant
is updated independently, when analyzing the effect of increasing 3x. Thus:
1
1
1 3
Aenk ~
+0
+0
= 0
(23)
BR
Be +
D
BA
C)
+
3
For non-class lo sample, the suppression update for Cmk is:
1
Aemk α -
+
(24)
2(5
(S
&
When 3g increases by A,k, the change in suppression magnitude is:
8( ((Amm)) 23
A&
03k
Sm
1
A3
+0
(mmyy
(S
This represents reduction in the suppression force acting class k evidence from non-k samples.
Part Aggregation under Class Imbalance
The total relief effect accumulated from all non-class & samples is:
AB
Total Relief N 77
(25)
(Sm)
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The total suppression effect from all class & samples is:
Total Suppression so Ng. 17 O 3k
(26)
Key Observation:
The evidence margin change Apn for class ht sample consists of two
negative components:
PM
Annk
( (-mx enj)) J
(27)
from k-samples
from suppression on nom samples
Both components are non-negative due to the gradient analysis in Parts and To establish a conservative lower bound, we focus the first component while acknowledging that the second component provides additional margin improvement.
The net effect per class k sample thus be bounded below as:
E[ Un k]
(Total Relief Total Suppression)
N
B
1
N k
1)
NR
O
N
A
]
77 E
(S
Using the first-order approximation ('())))))
1/5 % for the lower bound derivation, we obtain:
A.
B[Apn yn k] ž &
(28)
Sa
á
The Z notation indicates that this is a conservative lower bound due to hoth the asymptotic approxi- mation and the deliberate omission of the second non-negative margin component. For & 1 and significant A8s, the first term dominates, ensuring:
E[Apn yn
(29)
Part 4: Generalization Bound Improvement
By the margin-based generalization bound shown in lemma 4.2 for any 0, with probability at least 1 8:
R(h) Rs) + +0 (v
Complexity(7))
(30)
Np²
The effective margin Per can be characterized through the harmonic mean:
(31)
Pen
The margin improvement derived above implics:
E [
Un = k] <
(32)
pg (1 A
where Po is the baseline evidence margin before model updating, is a positive factor that absorbs the learning rate 7), the inverse the evidence scale Sá, and the conversion ratio from the margin expectation the effective margin. By combining 31 and Eq 32 we have:
Pelr Z Po (1 + A(.
(33)
Substituting into the generalization bound yields the stated improvement order Õ(1/ (11/VE..
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A.3 THE FAML FRAMEWORK ALGORITHM.
FAML runs in two stages. Stage-1 (warm-up): train each view-specific evidential network with fixed uniform prior to stabilize evidence extraction and record prediction trajectories. Stage-2 (joint training): periodically derive class-wise adaptive priors from the recorded trajectories, update the concentration parameters accordingly, and optimize class-balanced objective augmented with fairness constraint (to balance evidence allocation) and consistency regularization (to align opin- ions across views).
At inference, obtain opinions from all views and fuse them via confidence based aggregation to produce the final prediction and its uncertainty. The overall procedure summarized in Algorithm
Algorithm Pseudocode for FAML.
1: Input: Multi-view dataset: f(x", 1 1. Yn |
In=1 warm-up epochs, hyperparameter and X;
2: Initialize: Initialize the parameters 9 of FAML;
3: Output: networks parameters;
4:
Training
5: /Stage-/ / Warm-up Training of View-specific Evidential Networks
6: for warm-up epochs do
7: for 1 do
8:
c² < evidential network output:
9:
Calculate Dirichlet parameters a" by Eq.
10: Obtain view-specific loss calculated by Eq.
11:
end for
12: Obtain overall loss by summing losses calculated by all {a"]
Update the parameters 9 by gradient descent with the loss from above;
14:
end for
/Stage-2 Joint Training with Adaptive Prior
16: while not converged do
17: for = 1: do
18:
e" f- evidential network output;
19:
Save the prediction results (I, ) of the current epoch;
20:
Obtain adaptive prior 3 by Eq. 5
21:
Calculate Dirichlet parameters à' by Eq. 6
22:
Obtain view-specifie loss calculated by Eq. 12
23:
end for
24:
Calculate aggregated evidence by Eq.
25:
Obtain overall loss L by Eq. 15]
Update the parameters by gradient descent with the loss from above;
27:
end while
28: return networks parameters:
29:
Test
30: Output: the final prediction and its uncertainty estimation;
31: for 1: V do do
32: e" f- evidential network output;
33:
Calculate Dirichlet parameters a" by Eq
34: end for
35: Calculate aggregated evidence by Eq.
36: Calculate uncertainty u by Eq.
Calculate prediction p by Eq. 4
38: return the prediction and its corresponding uncertainty u;
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Published as a conference paper at ICLR 2026
A.4 DATASET DETAILS
The Handwritten Dataset, Animal Dataset, Scene15 Dataset, YaleB Dataset, Caltech-10 101 Dataset and BRCA Datasets are composed of pre-extracted vectorized features.
Handwritten (Asuncion et al. 2007): It consists of 2,000 digit images evenly distributed across ten classes (0-9), with 200 samples per class. Each sample is represented from six complementary perspectives: pixel averages (PIX) computed over 2 3 grids (240 dimensions), Fourier descriptors (FOU) of character outlines (76 dimensions), Profile cor- relations (FAC) features capturing structural patterns (216 dimensions), Zernike moments (ZER) that offer rotation invariance (47 dimensions), Karhunen-Love (KAR) coefficients for compact representation (64 dimensions). and morphological attributes describing coarse shape characteristics (6 dimensions).
Animal (Lampert et al. 2013): It consists of 10,158 images from 50 categories. For feature representation, we adopt deep features extracted by DECAF and VGG19 both with 4,096 dimensions.
Scene15 (Fei-Fei & Perona 2005 :: It contains 4,485 images drawn from fifteen scene
categories, covering both indoor and outdoor environments. Each image is characterized by three complementary feature representations: GIST descriptors (20 dimensions) that capture global spatial structure, Pyramid Histogram of Oriented Gradients (PHOG, 59 di- mensions) encoding local edge and shape information at multiple scales, and Local Binary Pattern (LBP, 40 dimensions) features reflecting texture patterns.
YaleB (Georgiiades al. 2002): It is benchmark facial recognition dataset containing 650 images from 10 subject categories. Each image described by three complementary feature views: Intensity (2,500 dimensions), Local Binary Patterns (3,304 dimensions). and Gabor features (6,750 dimensions).
(Fei-Fei et al. 2004) It contains 101 object categories, from which we select the top 20 categories for evaluation. For each image, use deep features extracted from DECAF and VGG19, both represented as 4,096-dimension vectors.
Caltech-101:
BRCA (Serra et al. 2015): This is a real-world biomedical dataset collected from TCGA for breast invasive carcinoma subtype classification based on the PAM50 scheme. It con- sists of 875 patients unevenly distributed across five subtypes: Normal (115), Basal (131), Her2 (46), LumA (436), and LumB (147). reflecting the natural class imbalance in clinical data. Each patient is described by three omies views: mRNA expression (1,000 dimen- sions), DNA methylation (1,000 dimensions), and miRNA expression (503 dimensions).
In our setting, the training data exhibits significant class imbalance, where the classes can be equally separated into head, medium(med) and tail regions based the different numbers of samples. Fol- lowing the setting in most existing works on class imbalance problem, the test set is constructed to be class-balanced. Specifically,
randomly select 20% of the samples as the testing set and use the remaining data to construct revised version of the training set by sampling a subset that follows Pareto distribution (Amold 2014). To ensure reproducibility and serve as benchmark for the community, these data partitions will be publicly released. We describe the revised datasets used in the experiments in detail and summarize the datasets Table
Specifically, the Handwritten dataset contains 404 instances across 10 categories, with category sizes ranging from 11 to 160. The Animal dataset includes 1,065 samples from 50 categories, with the largest class containing 311 instances and the smallest only 3. The Scene 15 dataset is reduced to 914 samples across 15 categories, where category sizes vary between 14 and 328. The YaleB dataset now consists of ten facial categories with per-class sizes between 3 and 52 images.The the Caltech- 101 dataset is revised to include 20 categories, where the number of instances per category ranges from 19 to 638. In contrast, the BRCA dataset is
biomedical dataset with naturally imbalanced subtype distributions, and thus we directly adopt without additional resampling. More details are illustrated in Figure
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Table 3: Statistic information of revised multi-view datasets
View
Handwritten
Animal
Scene15
YaleB
Caltech-101
BRCA
Fou(76)
DECAF(4,096)
GIST(20)
Intensity(2.500)
Gabon(48)
mRNA(1 (000))
V2
Fac(216)
VGG(4,096)
PHOG(40)
LBP(3,304)
WM(40)
DNA(1.000)
VG
Kar(64)
LBP(39)
Gabor(6,750)
CENTRIST(254)
miRNA(503)
V4
MOR(6)
HOG(L1984)
ZER(47)
GIST(512)
(IX(240)
LBP(Y28)
#Imbalance Ratio (Gx)
160:11
311.3
328:14
52:3
638:19
436:46
#Lahel
A.5 IMPLEMENTATION DETAILS
Model Architectures and Training Configurations: Our computational environment was Ubuntu 20.04, with 64 GB DDR4 RDIMM, 1x 16-core Intel Core 17-12900K CPU 3.20 GHz, and NVIDIA RTX 3090 GPU (24 GB memory). For vector-type datasets, view-specific evidence tracted using fully connected networks with ReLU activations. The model trained for 200 epochs using the Adam (Kinga al. 2015) optimizer with L2-norm regularization. More specifically, FAML training involves across two stages: First Stage Warm-up Training: To avoid the influence of inaccurate predictions the early stage, each view-specific evidential network trained using the Adam optimizer for a fixed number of empirically determined epochs, during which the prior was fixed to Second Stage Joint Training with Adaptive Prior: We update adjust the prior with predictions every five epochs to ensure training stability.
To reduce randomness from data partitioning and imbalanced dataset construction, we adopted the strategy proposed in (Shi et al. 2022), repeating all random operations five times with different seeds and reporting the mean and standard deviation of results. Two hyper-parameters were particularly critical for performance tuning. We performed a grid search to identify optimal settings for each dataset. detailed sensitivity analysis of these hyper-parameters is provided while the final hyper-parameter configurations for the six datasets are summarized in Table 4
later section,
Table 4: Detailed hyperparameters for FAML running various datasets.
Handwritten
Animal
Scene15
YaleB
Caltech-101
BRCA
Learning rate
5e-3
5e-3
5e-2
le-2
2c-3
le-2
Weight decay
1e-5
le-5
1e-5
1e-3
1e-4
1e-5
Batch size
256
256
128
256
256
256
Optimizer
Adam
Adam
Adam
Adam
Adam
Adam
Warm-up epochs
20
20
30
20
20
30
Maximum Epoch
200
200
200
200
200
200
LA Lr-patience
20
30
10
10
20
10
factor
0.5
0.5
0.5
0.5
0.5
0.5
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Caltech-101 Published as a conference paper at ICLR 2026
A.6 ADDITIONAL EXPERIMENT RESULTS
In this section, we provide additional ablation studies and experimental results to facilitate a com- prehensive understanding the FAML framework. They include:
1. Cohen's 's Kappa coefficient evaluation.
2. Comparative results of FAMI. with other methods in noisy scenarios.
3. Fairness evaluation and quantitative analysis.
4. Analysis of key components in the FAML framework.
5. Ablation study of warm-up epochs.
6. Visualization of uncertainty distribution across different class regions.
7. Hyperparameter sensitivity analysis.
Cohen's Kappa Coefficient Evaluation. Beyond conventional accuracy metrics, further ploy Cohen's Kappa Coefficient (McHugh 2012) to provide a more robust evaluation of model performance. Cohen's Kappa measures the agreement between prediction and ground-truth, while accounting for the agreement that could be expected by chance. means that our evaluation is not only driven by raw accuracy but also accounts for potential random consistency, thereby offering a more robust evaluation of classification performance. The experimental results are shown in Ta- ble[5] FAML consistently achieves the best Cohen's Kappa score on all six datasets, demonstrating superior performance even after correcting for chance agreement.
Table 5: Cohen's Kappa Coefficient( ()) on six datasets. The best results are highlighted in bold.
Dataset
Handwritten
Animal
Scene15
YaleB
Caltech-101
BRCA
TLC
85.1 1.8
64.7 2.2
34.4 0.3
5.2
72.5 2.4
65.1 3.8
I-DDL
76.5 =
6.1
20.2 0.8
3.7
7.79
4.3
R-EDL
87.6 1.0
1.7
2.3
2.2
6.64
TMC
84.2
6.64
0.4
0.6
722
64.3
ETMC
0.5
0.3
4..4
6.02
7.24
6.15
CCML
82.3
6.79
3.92
7.88
0.5
63.4
ECML
6..4
0.5
3.87
1.29
7.94
63.6
FAML (Ours)
91.7 - 0.3
75.7 0.6
0.6
7.5
82,9 0.7
74.0
Comparative results of FAML with other methods in noisy scenarios. To demonstrate FAML's robustness in handling noisy or uncertain data, we also conducted evaluations on five noisy multi- view datasets. Specifically, noise standard deviation from 0.5 to 1.0. FAML underwent five iterations of testing on each dataset with both mean values and standard deviations reported. The results shown in Table 6 From the results, we observe that all comparison methods fall short of maintaining robust performance under noisy inputs. In contrast, FAML achieves ated datasets. Notably, on on the Handwritten dataset, FAML achieved a performance that was 4.2% higher than the second best method, and on the Animal dataset, surpassed the next best by 6.9%.
applied Gaussian noise to 20% of the original views, varying the
stable and consistent performance across all evalu-
Table Comparing the performance of FAML with other advanced methods on five noisy datasets.
Dataset
Handwritten
Animal
Sc
YaleB
TLC
82.5 2.2
$2.0 + 3.0
27.8 +
70.9 4.3
70.6
IEEDL.
83.3 0.7
53.5
2.6
+
0.9
R-EDL
84.2
2..7
1.64
1.39
70.4+332
TMC
84.0
6.9
3.4
7..4+1.
71.4+
ETMC
87.6 1.5
67.7 1.
1.0
7.3
CCML
80.7
6..1
2.93
78.6
76.8 1.3
FCML.
338
65.5
2.73
74.3
73.3
FAMI. (Ours)
91.8 0.8
74.6 +
47.0 + 1.2
+
80.7 + 1.3
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Fairness Evaluation and quantitative analysis. To fully demonstrate the advantages of our method and further verify its effectiveness, we conduct experiments to provide quantitative results on fair- ness. To this end, introduce new metric named Faimess Degree to measure evidential bias across classes. As shown in [ we observe that FAMIL achieves a much lower Fairness Degree, demonstrating our method exhibits significant advantages promoting model's s fairness across all five datasets. We attribute this to the incorporation of adaptive prior in the training stage, which en- sures the model automatically allocates greater corrective effort discriminated classes, thus helps mitigate the biased evidential multi-view learning problem to some extent.
Table 7: Fairness evaluation of FAML with other advanced methods on five datasets.
Data
TLC
I-EDL.
R-EDL
TMC
ETMC
CCML
ECML.
FAMIs(Ours)
Handwritten
0.1377
0,3717
4.7281
0.7287
0.9829
0,7058
0.8407
0.1005
Animal
0.7171
0.7652
4.0228
1,0958
1,4691
0,9626
0.7934
0.4457
Scene15
1,2554
0,4330
3.3339
1.7937
2.0732
1.9479
1.7697
0.2743
YaleB 0.8278
0.1554
1.1779
0.5648
0.3850
0.2086
0.3340
0.1511
Caltech-101
0.5615
1.4387
4.0557
2.6468
1.1432
0.7479
1.1427
0.2372
Analysis of key components in the FAML framework. To thoroughly validate the effectiveness of the adaptive prior, fairness constraint, and consistency regularization, we construct a detailed abla- tion study on six datasets. The experimental results are shown in Table Specifically, to verify the effectiveness of the out any components) with the model incorporating only the adaptive prior (AP). The results shows that adding the adaptive prior yields prominent improvements across all datasets. For instance, on the BRCA dataset, accuracy increases from 74.3% to 77.5%, while ECE decreases from 28.0% to 21.5%. This provides crucial insights on the effectiveness of our proposed trajectory- based prior adjustment strategy. The fairness constraint further improve performance when combined with the adaptive prior, which is particularly pronounced in the ECE metric. We attrihute this improvement to the explicit regularization of evidence variance, thus promoting more reliable uncertainty esti- mation. In contrast, the consistency regularization exhibits varying degrees of effectiveness across datasets, being particularly beneficial for datasets with a larger number of views. possible reason is that as the number of views increases, the potential for inter-view conflict and dissonance also grows. In such scenarios, explicitly enforeing consistency becomes more critical to guide the model towards a consistent and reliable fused opinion.
adaptive prior, we compare the baseline model (with-
Table 8: Ablation study on six datasets, "V" means FAML with the corresponding component, "." means not applied. The best results are highlighted by boldface.
Component
Handwritten
Animal
Scene15
YaleB
Caltech-101
BRCA
AP
Lin
Leo
ACC t
ECE |
ACC f
ECE |
ACC
ECE
ACC 1
ECE J
ACC
ECE
ACC 1
ECE
85.7
32.9
65.1
22.9
50.3
29.8
81.4
25.6
73.8
26.3
74.3
28.0
86.3
27.7
72.9
16.9
55.1
20.4
85.1
20.9
79.1
20.3
77.5
21.5
87.3
25.2
72.3
13.1
56.2
13.4
87.1
18.1
82.3
22.4
81.1
16.2
90.8
24.7
72.6
20.2
55.6
15.7
84.3
21.9
80.9
20.2
77.3
19.2
94.2
20.6
76.3
11.0
57.2
11.2
88.3
10.9
83.6
14.1
82.9
15.0
Ablation study of warm-up epochs. To ensure stable training. we first warm up the view-specific adaptive prior. The key hyper-
evidential networks before introducing parameter of the warm-up stage the warm-up epochs. We ablate different values of this hyper- parameter and evaluate the effect of it on the performance of our method. We conduct detailed ablation study on six datasets, the comparison results are shown in Figure According to the exper- imental results, it is observed that the performance from our FAML without using warm-up phase (0 epochs) generally attain worse results. In contrast, as the warm-up epochs increases, we can find that the model performance gradually improves within 10-20 epochs, while it may degrade slightly after 20 epochs. These findings confirm that an appropriate warm-up epochs is essential for balancing initial network stabilization with subsequent training.
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90
15
70
-0
Aeosety (8)
30
DSE Phi
AccurDay
DCC PM
15
ACC
ACC
10
20
30
10
10
20
30
30
5
10
20
30
Wor up spocTo
Vprmup spochs
Warm opochs
(a) Handwritten
(b) Animal
(c) Scene
100
50
40
Accuracy 196)
Accuney
80-
80
CCE 2%0
20
ECE
ECE
ECE
ACC
ACC
ACC
60
20
50
10
50
10
20
Wem--pp aprictt
WartHup apochs
Warmap spochs
(d) YaleB
(c) Caltech-101
(f) BRCA
Figure 4: The effect of different warm-up epochs on performance.
Visualization of uncertainty distribution across different class regions. To comprehensively evaluate the uncertainty estimation, we visualize the density distribution for Animal dataset in terms of uncertainty. For comparison, we use our degraded baseline model that employs the same multi- view fusion strategy as FAML but without the fairness-aware components (adaptive prior, fairness constraint, and consistency regularization). Additionally, to ensure fair comparison, the hyperpa- rameters of this degraded baseline are kept strictly consistent with FAMIL As shown in Figure we reveal the following observations: (1) For the baseline method, the uncertainty estimates are relatively low for head classes, but increase substantially for medium and tail regions. The samples from data-rich classes tend to be assigned low uncertainty due to the biased evidence collection process, suggesting unfair distribution of supporting evidence across classes. (2) In contrast, method assigns lower and more compact uncertainty distributions across all regions, with notably reduced uncertainty for tail classes compared to the baseline. This indicates that FAMI effectively mitigates evidence allocation bias through the adaptive prior and fairness constraint, delivering trust- worthy predictions and demonstrating better fairness in uncertainty estimation across different class distributions.
Uncertiisy S
0.8
Uncertainty
0.6
9.6
0.4
0.4
0.2
0.2
Head Region Med Region
Region
Region Region
Thil Region
(a) Baseline
(b) Ours
Figure Visualization of uncertainty estimation on the Animal dataset.
Hyperparameter sensitivity analysis. To further investigate the sensitivity of our proposed FAML model to its key hyperparameters, we analyze the impact the upweight factor y, which controls the strength of the adaptive prior, and the hyperparameter À in consistency loss term, which determines the strength of consistency enforcement between views. As shown in Figure 6 for the upweight fac- tor 7, the performance exhibits clear trend of first increasing and then decreasing. This indicates that large upweight factor may induce overconfidence in learning and ultimately degrade perfor- mance. For the hyperparameter X, where À means do not consider the consistency loss
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among opinions, the optimal range is À [1,5]. 5]. Our method exhibits robust performance across wide range of parameter settings, highlighting its practical reliability and ease of deployment.
100
30
90
25
ACC (16)
80
70
10
Asre
80
5-
50
0
1.0
5.0
0.5
7
0
100
30
25
ACC (16
70
15
60
10
Asta
50
Or
40
Figure 6: Sensitivity analysis of upweight factor y and the hyperparameter À on datasets.
A.7 POTENTIAL LIMITATIONS AND FUTURE WORK
Although the proposed method achieves excellent performance, it still has some potential limita- tions. (1) Our method focuses supervised multi-view classification, which limits its applicability to scenarios where complete labeled data is available. Therefore, in future work, we will explore how maintain fairness in evidence learning without explicit class labels, potentially through clustering- based approaches or contrastive learning mechanisms. (2) Our method provides overall quantifi- cation the predictive uncertainty, but does not disentangle the sources of uncertainty. It promis- ing to enhance uncertainty quantification by decoupling alcatoric and epistemic uncertainties under data imbalance, leading to more reliable interpretations of the outcomes and better understanding of when the model's predictions can be trusted. We consider these as important future works.
A.8 THE USAGE OF LARGE LANGUAGE MODELS.
Large Language Models (LLMMs) were employed to support the writing and refinement of this manuscript. Specifically, LLM utilized to improve readability, enhance clarity, and ensure grammatical accuracy across various sections of the text. The assistance included tasks such as rephrasing sentences, checking grammar, and improving the overall flow of presentation.
Importantly, the LLM was not involved the formulation of research ideas, the design of method- ologies, or the execution of experiments. All scientific concepts, analyses, and conclusions were developed independently by the authors. The role of the LLM was limited exclusively to linguistic refinement, without any contribution the substantive scientific content.
The authors take full responsibility for the content of the manuscript, including any text generated or polished by the LLM. We have ensured that the LLM- --nerreed text adheres to ethical guidelines and does not contribute to plagiarism or scientific misconduct.
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Published as a conference paper at ICLR 2026
100
120
300
Semple Count
Zample Eount
60
920
(a) Handwritten
(b) YaleB
(c) BRCA
300
600
250
500
Sample Count
400
Sample
300
100
200
100
2
3
15
12
5
8
14
4
10
11
13
3
7
16200
13
18118111 11
12 14
Class
Index
Class
Index
(d) Scene15
(e) Caltech-101
300
Sample Count
150
18 36
7
20133 Class Index
4137
49447 42 383333330083 28300433
(f) Animal
Figure 7: Train Dataset Distribution. The different background color regions correspond to head, medium, and tail categories, which are divided based on the numbers of samples in the dataset.
26


Reviews:
[{"review_id": "yGjZRah1Ye", "reviewer": "Reviewer_yDqP", "summary": "This paper addresses the issue of unreliable uncertainty estimation in multi-view evidence learning, which stems from biased evidence collection. The authors propose a framework called Fairness-Aware Multi-view Evidential Learning. This method uses a training-trajectory-based adaptive prior to calibrate the Dirichlet parameters, aiming to mitigate the evidence bias. The approach includes theoretical guarantees and is validated through experiments on six real-world datasets to demonstrate its performance.", "questions": "1. What role did the opinion alignment play in promoting fairness? It seems irrelevant to fairness?\n\n2. The paper positions fairness as a key design goal, yet there are no reported quantitative fairness evaluation metrics to determine this. Could the authors provide explicit metrics or quantitative analysis to support the fairness claims?\n\n3. The degraded baseline model is introduced for the visualization. This baseline is described as FAML without the fairness-aware components. It is unclear if this is a re-run of an existing baseline (e.g. TMC) ? What are the hyper-parameters of the compared baseline?\n\n4. In subjective logic, formulas rely on fixed priors to compute belief mass and uncertainty. When the prior becomes adaptive, do these formulations still hold as originally defined? Are the theoretical assumptions of subjective logic still satisfied after introducing the adaptive prior?\n\n5. Could you discuss the robustness of FAML in the presence of potential noisy views. How does the adaptive prior perform in such scenarios?\n\n6. Check for all possible typos in the manuscript. e.g., \"bias exhibit view-specific pattern\" should be \"bias exhibits view-specific pattern\" in Line 20.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper has a clear motivation and effectively solves the problems of biased evidence multi-view learning.\n\n2. The paper offers a clear and well-grounded theoretical analysis that connects the adaptive prior design to margin theory, helping explain why the proposed approach could improve model's generalization.\n\n3. The comparison experiments are comprehensive, including six representative multi-view datasets.", "weaknesses": "1. This work proposes an EDL-based multi-view classification method. However, the literature review for existing EDL-based multi-view methods is insufficient. The authors should provide a more comprehensive discussion of related work in this specific domain, such as, but not limited to, [1, 2].\n\n2. The text in Figure 1 is too small, and there is no explanation of what the points, lines, and colors in the figure represent or why it is imbalanced. The blue in the legend of Figure 1 is different from that in the figure.\n\n3. The phrase \"most existing studies generally assume that view-specific evidence learning is inherently reliable\" is ambiguous, especially the use of the word \"reliable.\" What you want to convey is that the evidence learned from this view is unreliable, but it may lead readers to misunderstand that the view itself is unreliable.\n\n4. Punctuation is also part of the formulas and needs to be added.\n\n[1] Enhancing Testing-Time Robustness for Trusted Multi-View Classification in the Wild. CVPR 2025.\n\n[2] Trusted multi-view classification with expert knowledge constraints. ICML 2025.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "KHnOITz7UL", "reviewer": "Reviewer_RwdE", "summary": "The paper highlights an overlooked bias in multi-view evidential learning, where evidence allocation tends to favor data-rich classes, leading to unreliable uncertainty estimates. Instead of relying on fixed uniform priors like traditional EDL methods, it adaptively adjusts class priors based on training trajectories in a principled manner. Additionally, a fairness constraint on class-wise evidence allocation and an opinion-alignment regularization across views ensure the consistent allocation of evidence across views. Experiments on six multi-view datasets demonstrate superior region accuracy and ECE compared to baselines, with ablation studies confirming the contributions of each component.", "questions": "See Weaknesses.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. This paper is well organized, and the proposed methodology is enlightening.\n\n2. The motivation behind the paper is clear, and the theoretical analysis is complete.\n\n3. The proposed method offers novel insights, particularly in using training trajectories to adjust class priors, thereby mitigating view-specific bias throughout the multi-view fusion process\n\n4. The proposed method shows a clear performance improvement in a series of experiments.", "weaknesses": "1. In this paper, the notion of fairness seems to focus on balancing the evidence allocation across different classes, rather than addressing fairness in terms of sensitive attributes like race or gender in a broader sense.\n\n2. Is this approach intended as a general framework? Can other trusted multi-view fusion methods also adopt similar strategies to improve model performance even on balanced datasets?\n\n3. Some implementation details seem to be missing. For instance: How does the hyper-parameter $\\mu$ change during training? and How is the metric ECE calculated in your experiments.\n\nIf the authors can address my questions, I am willing to increase my score.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "iHH0ycQT6i", "reviewer": "Reviewer_bZ2G", "summary": "This paper introduces a novel and important problem: Biased Evidential Multi-view Learning (BEML). The authors demonstrate through empirical analysis that existing multi-view evidential learning methods tend to allocate more evidence to data-rich (majority) classes, leading to biased and unreliable uncertainty estimates for data-poor (minority) classes.", "questions": "As shown in weaknesses.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "To address this, the paper proposes a Fairness-Aware Multi-view Evidential Learning (FAML) framework. The method has three core components:\n\nAn Adaptive Prior based on training trajectories, which dynamically adjusts the Dirichlet prior to provide more support to classes that are under-represented or poorly performing.\n\nAn explicit Fairness Constraint, which penalizes high variance in evidence allocation across different classes, encouraging a more balanced evidence distribution.\n\nAn Opinion Alignment mechanism, which minimizes the dissonance between opinions from different views during fusion to mitigate view-specific biases.\n\nThe authors provide strong theoretical grounding for their adaptive prior, proving that it increases the evidence margin for minority classes and tightens the generalization error bound. Comprehensive experiments on six real-world datasets show that FAML significantly outperforms state-of-the-art methods in terms of accuracy (especially for tail classes), calibration error (ECE), and uncertainty reliability (AUROC, FPR-95).", "weaknesses": "While this is an excellent paper, the following minor revisions could further strengthen its clarity and impact:\n\nStrengthen the \"Related Work\" on Fairness and Subpopulation Shift: The core problem FAML solves—evidence bias due to class imbalance—is deeply connected to the broader fields of AI fairness and subpopulation shift. To better position the paper's contribution, the \"Related Work\" section should be expanded to include and discuss key works from this area. For instance, the authors should cite foundational work like GroupDRO (Sagawa et al., 2019), which formalized the goal of improving worst-group generalization in subpopulation shifts. More importantly, citing a paper like UMIX (Han et al., 2022), which explicitly links Uncertainty-Aware methods to solving Subpopulation Shift, would be highly relevant. Discussing these papers would allow the authors to clearly articulate FAML's unique contribution: while GroupDRO tackles the problem via the loss function and UMIX uses uncertainty to guide data augmentation, FAML introduces a novel approach by manipulating the evidential learning framework itself (via adaptive priors and fusion) to achieve fairness in a multi-view setting.\n\nIntuition for the Adaptive Prior (Eq. 5): The paper should more explicitly state the key intuition behind Equation 5. The current description is accurate but subtle. The authors should clearly emphasize that this formula creates an inverse relationship: the worse a class performs (i.e., the fewer samples are correctly classified, the smaller the denominator), the larger the adaptive prior (Beta_k) becomes. This \"compensatory\" mechanism is the core of the idea and should be stated plainly.\n\nExplicit Formulation of L_fc and mu schedule: In Section 3.2.3, the paper introduces the fairness loss L_fc, stating it is based on Definition 1. For absolute clarity, the paper should explicitly write out the final loss term (e.g., L_fc = Var(...)). Furthermore, the balancing coefficient mu is described as \"gradually changing from 0 to 1.\" Please specify the exact schedule used (e.g., linear, exponential) to enhance reproducibility.\n\nMotivation for Dissonance Degree (Eq. 10): The \"Dissonance Degree\" used for opinion alignment is a novel metric. The authors should add a brief sentence justifying this specific choice (sum of absolute differences in variance) over other, more traditional divergence measures (e.g., KL or JS divergence on the Dirichlet means/probabilities).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "zI5cmK8HWn", "reviewer": "Reviewer_Tpet", "summary": "This paper addresses a critical bias in multi-view evidential learning: existing methods assume reliable view-specific evidence learning, but real-world data shows samples allocate more evidence to data-rich classes, harming uncertainty estimation reliability. To solve this newly defined Biased Evidential Multi-view Learning (BEML) problem, it proposes the Fairness-Aware Multi-view Evidential Learning (FAML) framework, which integrates three key components: a training trajectory-based adaptive prior (to calibrate bias), a class-wise evidence variance fairness constraint (to balance allocation), and an opinion alignment mechanism (to reduce cross-view bias). Theoretical analysis confirms FAML enhances evidence learning fairness, while experiments on 6 real-world datasets demonstrate FAML outperforms state-of-the-art methods in balanced evidence distribution, prediction performance, and uncertainty estimation reliability. The work also contributes by highlighting this implicit unfairness, proving the adaptive prior expands minority class evidence margins (with improved generalization error bounds), and validating FAML’s superiority.", "questions": "- The paper updates the adaptive prior every 5 epochs starting from the 20th training epoch. Was there any preliminary experiment to confirm that a 5-epoch update interval is more suitable for maintaining training stability compared to other intervals (e.g., 3 or 10 epochs)?\n- When defining the fairness degree (FD) based on class-wise evidence variance, did you observe how FD changes dynamically across training epochs (e.g., whether it drops faster in early or late stages)? And does this change trend correlate with the gradual increase of λ (the balancing coefficient) in the loss function?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "-  The paper acutely captures a neglected yet prevalent issue in multi-view evidential learning: implicit unfairness in evidence allocation caused by differences in class data volume, which undermines the reliability of uncertainty estimation. This finding directly challenges the flawed assumption of existing methods that \"view-specific evidence learning is inherently reliable,\" clarifies key optimization directions for future research, and reflects a deep understanding of practical pain points in the field.\n- The proposed FAML method forms a closed-loop optimization from three dimensions, with strong targeting and novel design:\nAdaptive Prior: Dynamically adjusted based on training trajectories, effectively calibrating evidence learning bias caused by class imbalance.\nFairness Constraint: Directly promotes balanced evidence allocation across different classes through class-wise evidence variance control.\nOpinion Alignment Mechanism: Reduces view-specific bias during multi-view fusion, ensuring the integrated evidence is consistent and mutually supportive.\n- The paper features both solid theoretical foundations and sufficient experimental validation, enhancing the persuasiveness of its research conclusions. First, it proves through derivation that the adaptive prior can expand the evidence margin for minority classes and provides an improved factor for the generalization error bound, offering mathematical support for the method’s effectiveness. \n-  Extensive experiments on 6 real-world multi-view datasets not only verify FAML’s advantages in prediction performance but also demonstrate its ability to achieve fairer and more reliable uncertainty estimation, ensuring the universality of the results.", "weaknesses": "- The paper does not verify FAML’s performance under input noise (e.g., Gaussian noise on view features like GIST/HOG in Scene15), leaving unclear if its evidence fairness and uncertainty estimation hold for imperfect real-world data\n- Though tested on datasets with 2-6 views, it lacks analysis on how view count changes (e.g., reducing Caltech-101’s 6 views to 3) affect FAML’s fairness (FD) and opinion alignment effectiveness", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)