Question:
According to the paper "Think Twice Before Selection: Federated Evidential Active Learning for Medical Image Analysis with Domain Shifts," the core innovation of the proposed FedEAL-Twice method lies in its two-stage sample selection strategy, which aims to address the domain shift problem in federated learning. Which of the following options most accurately and comprehensively describes this "think twice" process and the design principles behind it?
A. "Think Twice" refers to a two-step screening process on the client. First, the client uses evidence deep learning to identify samples with high uncertainty. Then, within these uncertain samples, the client performs a second screening by calculating their feature diversity with a local labeled dataset. Finally, the sample index that combines uncertainty and local diversity is submitted to the server.
B. "Think Twice" is a hierarchical screening process across the client and server. The first "thinking" occurs on the client, using evidence deep learning to quantify the sample's uncertainty and initially screen a batch of candidate samples. The second "thinking" occurs on the server side. After aggregating candidate samples from all clients, the server doesn't accept them all. Instead, it takes a global perspective, re-evaluating and making a final selection based on their contribution to improving global model diversity and reducing redundancy. This mitigates client selection bias caused by domain shift.
C. "Thinking twice" refers to the server's two-fold consideration when distributing the global model and collecting client updates. During the first "thinking," before aggregation, the server evaluates the "evidence" of each client's uploaded update and downgrades updates from clients with significant domain shift and high uncertainty. After distributing the model to the client, the server instructs the client to prioritize and label samples that most "challenge" the current global model (i.e., samples that are most inconsistent with the global model's predictions).
D. "Thinking twice" specifically refers to the two dimensions used by the client when using evidence-based deep learning to quantify uncertainty. The first "thinking" assesses the sample's "cognitive uncertainty," i.e., the confusion caused by the model's lack of knowledge. The second "thinking" assesses its "data uncertainty," i.e., the inherent ambiguity of the data. The FedEAL-Twice method balances these two uncertainties through a weighted formula to select the samples to be labeled, and the server is only responsible for aggregating these selected samples.

Answer: B

In the context of FAL with domain shifts, we integrate both
uncertainty and diversity measures to identify the most in-
formative samples for annotation (see Fig. 2(b)). As for un-
certainty evaluation, we leverage the epistemic uncertainty
in the global model to calibrate the aleatoric uncertainty in
both global and local models. We now delve into its details.
Aleatoric uncertainty. Dirichlet-based evidential models
interpret the categorical prediction ρ as a distribution rather
than a singular point estimate, which acknowledges a range
of possible predictions. We use the expected entropy of all
possible predictions to deliver the aleatoric uncertainty [76]
to quantify the inherent complexity or ambiguity present in
local data. Given a sample x and the global model θ, the
aleatoric uncertainty of the sample x in the global model θ
is represented as:
  U_{ale}(x, θ)
=
 E_{p(ρ|x,θ)}[H[P(y|ρ)]]
=-∑_{c=1}^C E_{p(ρ_c|x,θ)}[ρ_c · log ρ_c]
=∑_{c=1}^C (α_c/S)·[ψ(S+1)-ψ(α_c+1)],

where H(·) denotes the Shannon entropy [61]. Similarly,
the aleatoric uncertainty in the local model k is Uale(x, θk).
The derivation of Eq. 3 is in Appendix B.2.
Epistemic uncertainty. In the Dirichlet distribution, the
differential entropy quantifies how dispersed the probabil-
ities are across different categories [44]. We employ the
differential entropy of the Dirichlet distribution to quantify
the epistemic uncertainty linked to domain shifts between
the global model and local data. Specifically, given a sam-
ple x and the global model θ, the epistemic uncertainty of
the sample x in the global model θ is represented as:
  U_{epi}(x, θ)
= H[p(ρ|x,θ)]
=-∫ p(ρ|x,θ)· log p(ρ|x,θ) dρ
=∑_{c=1}^C log Γ(α_c)/Γ(S) - (α_c-1)·[ψ(α_c)-ψ(S)].

The derivation of Eq. 4 is in Appendix B.2.

Uncertainty calibration.
Given a sample x, the global
model θ, and the local model θk, we calculate the aleatoric
uncertainty (Eq. 3) in both global and local models and sub-
sequently calibrate the aleatoric uncertainty by incorporat-
ing the epistemic uncertainty (Eq. 4) from the global model.
The overall calibrated uncertainty for sample x is
  U(x, θ, θ_k)=[ U_{ale}(x, θ) + U_{ale}(x, θ_k) ] · U_{epi}(x, θ).  (5)

Diversity relaxation. We adopt local constraints to ensure
diversity among selected samples, contrasting with core-set
techniques that impose global diversity constraints. As out-
lined in Alg. 1, we initially sort the unlabeled set U^{r-1}_k
by descending calibrated uncertainty U(x, θ, θk), and then ex-
tract feature embeddings with local model θk. During the it-
eration over the unlabeled set U^{r-1}_k, we compute the cosine
similarity s(xi, xj) for each candidate sample xi against
all other samples xj ∈ U^{r-1}_k \ xi and form a neighbor set
N(xi) based on the similarity threshold τ. A sample xi
is selected if its neighbor counts |N(xi)| are less than the
minimum neighbor size n or if these neighbors remain un-
labeled. Following this criterion, Bk unlabeled samples are
chosen to constitute the final set Q^r_k for annotation, effec-
tively balancing diversity and uncertainty in data selection.

Algorithm 1 Diversity Relaxation for Local Client k
Input: unlabeled set U^{r-1}_k, local model θk, annotation budget
Bk, similarity threshold τ, minimum neighbor size n
Output: query set Q^r_k
1: Sort U^{r-1}_k by descending calibrated uncertainty.
2: Initialize index i = 1 and query set Q^r_k = ∅.
3: while |Q^r_k| < Bk and i ≤ |U^{r-1}_k| do
4:   Select a candidate sample xi from U^{r-1}_k.
5:   Compute feature similarity s(xi, xj) using θk, where
     xj ∈ U^{r-1}_k \ xi.
6:   Form neighbor set N(xi), including xj with s(xi, xj) ≥ τ.
7:   if |N(xi)| < n or N(xi) ∩ Q^r_k = ∅ then
8:     Add xi to Q^r_k.
9:   end if
10:  Increment i.
11: end while
12: return Q^r_k

Think Twice Before Selection: Federated Evidential Active Learning for Medical
Image Analysis with Domain Shifts
Jiayi Chen1∗
Benteng Ma2∗
Hengfei Cui1 Yong Xia1,3†
1 School of Computer Science and Engineering, Northwestern Polytechnical University, China
2 Hong Kong University of Science and Technology, Hong Kong SAR, China
3 Research & Development Institute of Northwestern Polytechnical University in Shenzhen, China
jiayichen@mail.nwpu.edu.cn, bentengma@ust.hk, hfcui@nwpu.edu.cn, yxia@nwpu.edu.cn
Abstract
Federated learning facilitates the collaborative learning
of a global model across multiple distributed medical in-
stitutions without centralizing data. Nevertheless, the ex-
pensive cost of annotation on local clients remains an ob-
stacle to effectively utilizing local data. To mitigate this
issue, federated active learning methods suggest leverag-
ing local and global model predictions to select a rela-
tively small amount of informative local data for annota-
tion.
However, existing methods mainly focus on all lo-
cal data sampled from the same domain, making them un-
reliable in realistic medical scenarios with domain shifts
among different clients. In this paper, we make the first at-
tempt to assess the informativeness of local data derived
from diverse domains and propose a novel methodology
termed Federated Evidential Active Learning (FEAL) to
calibrate the data evaluation under domain shift. Specif-
ically, we introduce a Dirichlet prior distribution in both
local and global models to treat the prediction as a distribu-
tion over the probability simplex and capture both aleatoric
and epistemic uncertainties by using the Dirichlet-based
evidential model.
Then we employ the epistemic uncer-
tainty to calibrate the aleatoric uncertainty. Afterward, we
design a diversity relaxation strategy to reduce data re-
dundancy and maintain data diversity. Extensive experi-
ments and analysis on five real multi-center medical im-
age datasets demonstrate the superiority of FEAL over the
state-of-the-art active learning methods in federated sce-
narios with domain shifts. The code will be available at
https://github.com/JiayiChen815/FEAL.
∗Equal contribution.
†Yong Xia is the corresponding author. This
work was supported in part by Shenzhen Science and Technology Pro-
gram under Grants JCYJ20220530161616036, National Natural Science
Foundation of China under Grants 62171377 and 62271405, Ningbo Clin-
ical Research Center for Medical Imaging under Grant 2021L003 (Open
Project: 2022LYKFZD06), and Foshan HKUST Projects under Grants
FSUST21-HKUST10E and FSUST21-HKUST11E.
?
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𝐿!
?
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𝐿"
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Annotate
Distribute
Aggregate
⋯
Client K
Server
Client 1
Client 2
Train
(a) FAL scheme
0.0
2.5
5.0
7.5
10.0
12.5
Energy score
0.00
0.05
0.10
0.15
0.20
0.25
Density
Client 1
Client 2
Client 3
Client 4
(b) KDE of energy score
1
2
3
4
Client
1
2
3
4
Client
1.0000
0.0001
0.0001
0.0001
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0.0031
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0.0031
1.0000
0.0
0.2
0.4
0.6
0.8
1.0
(c) p-value
Figure 1. Illustration of federated active learning (FAL) in the
presence of domain shift. (a) FAL comprises model distribution,
local training, model aggregation, and data annotation. (b) The
KDE of energy scores depicts domain shifts across clients. (c)
The low p-values in cross-client KDE of energy scores indicate
the existence of significant domain shifts between all client pairs.
1. Introduction
Federated learning enables collaborative learning across
multiple clinical institutions (i.e., clients) to learn a uni-
fied model on the central server through model aggregation
while preserving the data privacy at each client [27, 45, 71]
(see Fig. 1 (a)). Unfortunately, such a learning pipeline re-
1
arXiv:2312.02567v2  [cs.CV]  22 Apr 2024
quires each client to prepare its own labeled data, whose
scale is constrained by the available expertise, time, and
budget for data annotation.
One possible solution to alleviate the annotation cost is
to select a part of highly informative data to annotate. Ac-
tive learning (AL) has shown great potential in guiding the
data selection process [1, 6, 25, 75], leading to the federated
AL (FAL) framework. Such a pipeline [7, 18, 46, 52, 57, 79]
allows each client to assess the informativeness of unla-
beled data using either the local model at each client or the
global model from the server, greatly alleviating the heavy
annotation costs while retaining great performance. Nev-
ertheless, when using a local model to select data, there
is a bias toward prioritizing the data that improves the lo-
cal updates while disregarding the overall generalizability
of the global model. Client models trained on diverse do-
mains may exhibit significant divergence within the param-
eter space, making the use of a global model aggregated
from these models for data selection unreliable.
Recent
advances
in
FAL,
e.g.,
LoGo
[25]
and
KAFAL [6], tend to harness the knowledge of both local and
global models to identify informative samples. Although
this strategy has been proven to be more effective than em-
ploying a single model, these methods focus mainly on the
class imbalance issue while assuming that the data at mul-
tiple clients is from the same domain. However, the do-
main shift across clients is commonly seen in real-world
applications, which is evidenced by the extremely low p-
values of the kernel density estimation (KDE) of energy
scores [40] (see Fig. 1 (b) and (c)). The existence of domain
shift renders two major challenges for FAL. (1) Overcon-
fidence; Existing FAL methods evaluate data uncertainty
based on the softmax prediction made by a deterministic
model, which is essentially a point estimate and can be mis-
calibrated easily on data with domain shifts [40, 42, 53],
resulting in unreliable uncertainty evaluation. (2) Limited
uncertainty representation. Uncertainty can be divided
into aleatoric uncertainty (or data uncertainty) and epis-
temic uncertainty (or knowledge uncertainty) [54]. The for-
mer reflects the inherent complexity of data, such as class
overlap and instance noise [68]. The latter captures the re-
stricted knowledge of a model caused by insufficient data
or domain shifts.
The softmax prediction can represent
the aleatoric uncertainty but fails to capture the epistemic
uncertainty, resulting in incomplete evaluations, which are
particularly noticeable in the presence of domain shift.
To address both challenges, we propose the Federated
Evidential Active Learning (FEAL) method. Built upon
the Dirichlet-based evidential model [58, 76], FEAL treats
the categorical prediction of a sample as following a Dirich-
let distribution, thus allowing multiple potential predictions
for a sample.
FEAL comprises two key modules, i.e.,
calibrated evidential sampling (CES) and evidential model
learning (EML). CES is a novel FAL sampling strategy that
incorporates both uncertainty and diversity measures. It uti-
lizes the expected entropy of potential predictions to quan-
tify aleatoric uncertainty and aggregates the aleatoric un-
certainty in both global and local models. Further, CES em-
ploys the differential entropy of the Dirichlet distribution to
characterize the epistemic uncertainty [62] and utilizes the
epistemic uncertainty in the global model to calibrate the
aggregated aleatoric uncertainty. To enhance data selection,
diversity relaxation is also employed with the local model
to reduce redundancy and maintain diversity among the se-
lected samples. In addition to active sampling, we introduce
evidence regularization in EML for accurate evidence rep-
resentation and data assessment. The main contributions of
this work are summarized as follows:
• We explore a rarely studied problem, FAL with domain
shifts, which aims to attain a global model with a limited
annotation budget for local clients amidst domain shifts.
• We propose the FEAL method, with a sampling strategy
CES and a local training scheme EML, to tackle the chal-
lenges in FAL with domain shifts. CES is designed to se-
lect informative samples by leveraging aleatoric and epis-
temic uncertainty with both global and local models and
retaining sample diversity. EML is developed to regular-
ize the evidence for improved data evaluation.
• We conduct extensive experiments on five real multi-
center medical image datasets, comprising two datasets
for classification and three datasets for segmentation. The
results suggest the superiority of our FEAL method over
its AL and FAL counterparts.
2. Related Work
2.1. Federated Learning with Domain Shifts
Domain shift is a long-standing challenge for feder-
ated learning.
Previous approaches can be divided into
regularization-based, aggregation-based, and personalized
ones. Regularization-based methods implemented regu-
larization on model parameters [24, 35, 63] or feature em-
beddings [16, 19, 34, 74] to address the objective inconsis-
tency induced by domain shift. Aggregation-based meth-
ods dynamically adjust aggregation weights based on data
quality [41], estimated client contribution [22], general-
ization gap between global and local models [81], layer-
wise divergence [55] or performance on proxy dataset [37].
Personalized methods aggregated domain-agnostic layers,
while customizing domain-specific layers for local clients,
including batch normalization (BN) [36], high-frequency
convolution [9] and prediction layers [71]. Additionally,
several methods enhanced data diversity [39, 82] to refine
data distribution and mitigate statistical heterogeneity [78].
These approaches strive to mitigate the impact of domain
shifts across clients in supervised scenarios with fully an-
2
notated training samples. Unfortunately, they ignore the
substantial annotation costs for each client. In contrast, we
further leverage active learning to reduce annotation costs
by selecting the most informative data and propose a label-
efficient method for federated learning with domain shifts.
2.2. AL Methods
Conventional
AL
methods
can
be
categorized
into
uncertainty-based,
diversity-based,
and
hybrid
ones.
Uncertainty-based AL methods aim to select the most
ambiguous unlabeled samples for annotation. Classical ap-
proaches such as least confidence sampling [60], margin-
based sampling [46], and entropy-based sampling [61] eval-
uate the data uncertainty based on categorical probabilities.
Yoo et al. [79] and Huang et al. [18] estimated the loss for
uncertainty assessment. Moreover, several approaches as-
sess the data uncertainty by analyzing the prediction incon-
sistency among multiple augmented samples [15], standard
and dropout inferences [13, 14], or original and disturbed
features [52]. Diversity-based AL methods aim to iden-
tify a subset of samples that captures the distribution of the
complete dataset. A variety of approaches have been pro-
posed that exploit core-set techniques [7, 57] or clustering
methods [29, 48, 69] in the latent feature space, incorporate
a diversity constraint in the optimization process [11, 77], or
model the distribution discrepancy between labeled and un-
labeled samples [31] in order to identify a diverse collection
of samples. Hybrid AL methods exploit both uncertainty
and diversity in their sampling strategies. Ash et al. [2] clus-
tered the gradient embeddings to guarantee both uncertainty
and diversity. A two-stage sampling strategy has also been
implemented [52, 70, 80]. However, these methods primar-
ily focus on data selection driven by aleatoric uncertainty,
often neglecting its sufficiency and reliability in practical
scenarios. In this work, we developed a Dirichlet-based ev-
idential model to capture both aleatoric and epistemic un-
certainties. We further leveraged the epistemic uncertainty
to calibrate uncertainty estimates, enhancing their reliability
in the context of domain shifts.
2.3. FAL Methods
FAL aims to enhance the annotation efficacy of each local
client in decentralized learning. In contrast to the central-
ized scenarios, there exist two potential query-selector mod-
els in FAL [25], including the global model and the local
model. Both Wu et al. [75] and Ahn et al. [1] exclusively
utilized a singular model for data evaluation. Specifically,
Wu et al. [75] introduced a hybrid metric that considers both
the locally predicted loss and the local feature distances be-
tween unlabeled and labeled samples.
By contrast, Ahn
et al. [1] argued that evaluating samples with the global
model contributes to the objectives of federated learning
and recommended applying sampling strategies solely with
the global model. Nevertheless, as demonstrated in [25],
the superiority of the two query-selector models depends
on the global and local heterogeneous levels, and it is nec-
essary to leverage the knowledge of both global and local
models. Kim et al. [25] proposed a hybrid metric called
LoGo, which applies k-means clustering technique [43] on
the gradient space of the local model and subsequently con-
ducts cluster-wise sampling using the global model. Cao et
al. [6] proposed a knowledge-specialized sampling strategy,
which leverages the discrepancy between the global model
and local model to assess data uncertainty. However, these
methods focus on the local data from a singular domain,
which is less realistic. Though partial approaches [6, 25]
account for heterogeneity caused by class imbalance, they
often neglect another heterogeneous property known as do-
main shifts. In this work, we propose the uncertainty cal-
ibration method to achieve reliable uncertainty evaluation
with domain shifts across multiple clients.
3. Methodology
3.1. Problem Formulation
The overview of our FEAL framework is displayed in Fig. 2
and Appendix A. Under this framework, we maintain K
local models {θk}K
k=1 on clients and a global model θ on
the central server. The k-th local client contains a labeled
set Lk and an unlabeled set Uk. FAL comprises two iterative
phases: federated model training and local data annotation.
Federated model training involves model distribution, local
training, and model aggregation. In the first round, the k-th
client randomly selects Bk unlabeled samples and annotates
them to form the initial labeled set L1
k = {(xi, yi)}Bk
i=1, and
the unlabeled set is updated to U 1
k = Uk \ L1
k. In the r-th
FAL round, the k-th client constructs the query set Qr
k =
{(xj, yj)}Bk
j=1 for annotation using the sampling strategy
and updates the labeled set to Lr
k = Lr−1
k
∪Qr
k, whereas the
unlabeled set is updated to U r
k = U r−1
k
\ Qr
k. Subsequent
federated model training proceeds with the updated labeled
set Lr
k. The FAL process is repeated for R times as required.
3.2. Dirichlet-based Evidential Model in FAL
For federated active learning, we employ a Dirichlet-based
evidential model to effectively capture aleatoric and epis-
temic uncertainties in both global and local models. In this
section, we begin by presenting the foundational formula-
tion of the Dirichlet-based evidential model.
We start with the general C-class classification task.
Given an input sample x from the k-th client, a model f
parameterized with θ projects x into a C-dimensional log-
its f(x, θ). The classical CNN utilizes the softmax operator
to transform the logits f(x, θ) into the prediction of class
probabilities ρ. However, this approach essentially provides
a single-point estimate of ρ and can be easily miscalibrated
3
(a) Federated Evidential Active Learning (FEAL)
Distribute
Aggregate
⋯
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Client 1
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Min neighbor size 𝑛= 5
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Unlabeled neighbor
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Cadidate sample 𝒙% (Ignore)
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Labeled set
Client 2
Client K
Figure 2. Illustration of the proposed FEAL method.
(a) Overview of FEAL. (b) Illustration of CES module, including uncertainty
calibration and diversity relaxation.
on local data from diverse domains. The Dirichlet-based ev-
idential model, on the other hand, views the categorical pre-
diction ρ as a random variable with a Dirichlet distribution
Dir(ρ|α). The probability density function of ρ [58, 76],
given x and θ, is formulated as:
  \sma ll
\
b
e
g
i
n

{ali
gne d}
p(
\br ho |\
b
x
 ,\
bthet
a
 ) =  \l
e
f t \{ \begin {aligned} \frac {\Gamma (\sum _{c=1}^C\alpha _c)}{\prod _{c=1}^C\Gamma (\alpha _c)}\prod _{c=1}^C\rho _c^{\alpha _c-1}&, (\brho \in \Delta ^C) \\ 0\qquad \qquad &, (\text {otherwise}) \end {aligned} \right . \end {aligned}
(1)
where α denotes the parameters of the Dirichlet distri-
bution for sample x, Γ(·) is the Gamma function, and
∆C = {ρ| PC
c=1 ρc=1 and 0<ρc<1} represents the C-
dimensional unit simplex.
The posterior probability P(y = c|x, θ) for class c,
a.k.a., the expected categorical prediction ρc, is given by:
  \ v spac e {
-
1mm }  \sm a ll P(y =c |\ b x
, \btheta )=\int p(y=c|\brho )\cdot p(\brho |\bx ,\btheta )\ \text {d}\brho =\frac {\alpha _c}{S}, \label {eq:prosterior}
(2)
where S = PC
c=1 αc represents the Dirichlet strength. The
derivation of Eq. 2 is provided in Appendix B.1.
Drawing on concepts from Dempster-Shafer theory [59]
and subjective logic [23], the parameter α is linked to the
accumulated evidence e which quantifies the degree of sup-
port for the prediction on sample x. The parameter α is
derived as α = e + 1 = A(f(x, θ)) + 1, where A(·) is
a non-negative activation function that transforms the logits
f(x, θ) into evidence e.
In our study, all local models adopt the same Dirichlet-
based evidential architecture with the global model to com-
municate between local clients and the central server.
3.3. Calibrated Evidential Sampling
In the context of FAL with domain shifts, we integrate both
uncertainty and diversity measures to identify the most in-
formative samples for annotation (see Fig. 2(b)). As for un-
certainty evaluation, we leverage the epistemic uncertainty
in the global model to calibrate the aleatoric uncertainty in
both global and local models. We now delve into its details.
Aleatoric uncertainty. Dirichlet-based evidential models
interpret the categorical prediction ρ as a distribution rather
than a singular point estimate, which acknowledges a range
of possible predictions. We use the expected entropy of all
possible predictions to deliver the aleatoric uncertainty [76]
to quantify the inherent complexity or ambiguity present in
local data. Given a sample x and the global model θ, the
aleatoric uncertainty of the sample x in the global model θ
is represented as:
  \smal l \ begin {aligned} U_{\
t e
x
t
 {a
le}}(\bx , \b t het a )

&
=
 \m
at
h b b {E } _{ p (\br h o |\bx ,\btheta )}[\mathcal {H}[P(y|\brho )]]\\ &=-\sum _{c=1}^C \mathbb {E}_{p(\rho _c|\bx ,\btheta )}[\rho _c \cdot \log \rho _c]\\ &=\sum _{c=1}^C\frac {\alpha _c}{S}\cdot [\psi (S+1)-\psi (\alpha _c+1)], \end {aligned} \label {eq:ale}
(3)
where H(·) denotes the Shannon entropy [61]. Similarly,
the aleatoric uncertainty in the local model k is Uale(x, θk).
The derivation of Eq. 3 is in Appendix B.2.
Epistemic uncertainty. In the Dirichlet distribution, the
differential entropy quantifies how dispersed the probabil-
ities are across different categories [44]. We employ the
differential entropy of the Dirichlet distribution to quantify
the epistemic uncertainty linked to domain shifts between
the global model and local data. Specifically, given a sam-
ple x and the global model θ, the epistemic uncertainty of
the sample x in the global model θ is represented as:
  \smal l \ begin {a lig
n e
d
} U_{\ te x t { epi}}( \b x
,
\
b
the
ta ) &=
\mat h cal  {H } [p(\br h o |\bx ,\btheta )]\\ &=-\int p(\brho |\bx ,\btheta )\cdot \log p(\brho |\bx ,\btheta )\ \text {d}\brho \\ &=\sum _{c=1}^C\log \frac {\Gamma (\alpha _c)}{\Gamma (S)} - (\alpha _c-1)\cdot [\psi (\alpha _c)-\psi (S)]. \end {aligned} \label {eq:epi}
(4)
The derivation of Eq. 4 is in Appendix B.2.
4
Uncertainty calibration.
Given a sample x, the global
model θ, and the local model θk, we calculate the aleatoric
uncertainty (Eq. 3) in both global and local models and sub-
sequently calibrate the aleatoric uncertainty by incorporat-
ing the epistemic uncertainty (Eq. 4) from the global model.
The overall calibrated uncertainty for sample x is
  \s ma ll U (\bx , \ bt h eta , \ bthe t a _k)=[ U_{\text {ale}}(\bx , \btheta )+U_{\text {ale}}(\bx , \btheta _k)] \cdot U_{\text {epi}}(\bx , \btheta ). \label {eq:uc}
(5)
Diversity relaxation. We adopt local constraints to ensure
diversity among selected samples, contrasting with core-set
techniques that impose global diversity constraints. As out-
lined in Alg. 1, we initially sort the unlabeled set U r−1
k
by
descending calibrated uncertainty U(x, θ, θk), and then ex-
tract feature embeddings with local model θk. During the it-
eration over the unlabeled set U r−1
k
, we compute the cosine
similarity s(xi, xj) for each candidate sample xi against
all other samples xj ∈U r−1
k
\ xi and form a neighbor set
N(xi) based on the similarity threshold τ. A sample xi
is selected if its neighbor counts |N(xi)| are less than the
minimum neighbor size n or if these neighbors remain un-
labeled. Following this criterion, Bk unlabeled samples are
chosen to constitute the final set Qr
k for annotation, effec-
tively balancing diversity and uncertainty in data selection.
Algorithm 1 Diversity Relaxation for Local Client k
Input: unlabeled set U r−1
k
, local model θk, annotation budget
Bk, similarity threshold τ, minimum neighbor size n
Output: query set Qr
k
1: Sort U r−1
k
by descending calibrated uncertainty.
2: Initialize index i = 1 and query set Qr
k = ∅.
3: while |Qr
k| < Bk and i ≤|U r−1
k
| do
4:
Select a candidate sample xi from U r−1
k
.
5:
Compute feature similarity s(xi, xj) using θk, where
xj ∈U r−1
k
\ xi.
6:
Form neighbor set N(xi), including xj withs(xi, xj)≥τ.
7:
if |N(xi)| < n or N(xi) ∩Qr
k = ∅then
8:
Add xi to Qr
k.
9:
end if
10:
Increment i.
11: end while
12: return Qr
k
3.4. Evidential Model Learning
Dirichlet-based evidential models treat the categorical pre-
diction of a sample as a distribution, enabling multiple po-
tential predictions to occur with specific probabilities. Con-
sidering all possible predictions, we adopt the Bayes risk
of cross-entropy loss [58] as the task loss for classification
tasks, formulated as follows:
  \small  \b eg i
n

{
a
lig
ned } \ mat h cal {L }_{ \t
e
x
t
 {t
as k }}(\b x  ,\btheta _k,\by ) &= \int (\sum _{c=1}^C -y_c\log {\rho _c}) \cdot p(\brho |\bx ,\btheta _k)\ \text {d}\brho \\ &=\sum _{c=1}^C y_c\cdot [\psi (S)-\psi (\alpha _c)], \end {aligned} \label {eq:cls_loss}
(6)
where ψ(·) is the digamma function and yc is the label indi-
cator for class c. Similarly, the Bayes risk of Dice loss [32]
for segmentation tasks is:
  \small  \b eg i
n
 {a l
i
g
n
ed}
 \m a thca
l {
L}_{\te
xt
{ t ask}}( \bx  ,
\ b t h
e
t
a
 _k
,\b y  ) &
= \
int  (1{
-}\ f r ac {2}{C}
\su
m
_{c=1}^{C}\frac {{\Vert \boldsymbol {y}_{c}\circ \brho _{c}\Vert }_1}{{\Vert \boldsymbol {y}_{c}^2\Vert }_1{+}{\Vert \brho _{c}^2\Vert }_1}) \cdot p(\brho |\bx ,\btheta _k)\ \text {d}\brho \\ &= 1-\frac {2}{C}\sum _{c=1}^C\frac {{\Vert \boldsymbol {y}_{c}\circ \overline {\brho }_{c}\Vert }_1}{{\Vert \boldsymbol {y}_{c}^2\Vert }_1+{\Vert \overline {\brho }_{c}^2\Vert }_1+{\Vert \frac {\overline {\brho }_{c}\circ (\boldsymbol {1}-\overline {\brho }_{c})}{\boldsymbol {S}+\boldsymbol {1}}\Vert }_1}, \end {aligned} \label {eq:seg_loss}
(7)
where ◦is the Hadamard product and the expected categor-
ical probability of x is ρc = αc
S . The derivation of Eq. 6
and Eq. 7 are in Appendix B.3.
We incorporate evidence regularization to further reduce
incorrect evidence [58] and improve correct evidence [51].
  \small \mathcal {L}_{\text {reg}}(\bx ,\btheta _k,\by ) {=} KL[Dir(\brho |\tilde {\boldsymbol {\alpha }})\Vert Dir(\brho |\boldsymbol {1})] - \frac {C}{S}{\cdot }f(\bx ,\btheta _k), g
(8)
where ˜α = y + (1 −y) ⊙α and KL(·) denotes the
Kullback-Leibler divergence [28]. Notably, we calculate
the average pixel-wise Lreg in segmentation.
The overall training objective, combining task loss Ltask
and evidence regularization Lreg, is formulated as:
  \s mal l \ mathcal {L} (\ b x  ,\btheta _k,\by ) = \mathcal {L}_{\text {task}}(\bx ,\btheta _k,\by ) + \lambda \cdot \mathcal {L}_{\text {reg}}(\bx ,\btheta _k,\by ), \label {eq:overall_loss} g
(9)
where λ is the trade-off weight. between the task loss and
the regularization term.
4. Experiments
4.1. Experimental Settings
Datasets.
We evaluated FEAL on five real multi-center
medical image datasets, comprising two classification and
three segmentation datasets. The classification datasets in-
cluded
• Fed-ISIC: A skin lesion dataset from 4 data sources [49]
containing {12413, 3954, 3363, 2259} images.
• Fed-Camelyon: A breast cancer histology dataset from 5
centers [21] comprising {59436, 34904, 85054, 129838,
146722} patches.
The segmentation datasets included
• Fed-Polyp:
A endoscopic polyp dataset from 4 cen-
ters [71] with {1000, 196, 379, 612} samples.
• Fed-Prostate:
A prostate MRI dataset from 6 data
sources [39] with {261, 384, 158, 468, 421, 175} slices.
• Fed-Fundus: A retinal fundus dataset from 4 centers [39]
with {101, 159, 400, 400} samples.
In our study, each dataset was divided using an 8:2 train-to-
test split ratio at the patient level. Details of these datasets
are provided in Appendix C.1.
Evaluation metrics. For classification, we utilized the Bal-
anced Multi-class Accuracy (BMA) for skin lesion classi-
fication [8] and measured accuracy (ACC) for breast can-
cer histology classification. In the context of segmentation,
5
1
2
3
4
5
AL round
52
54
56
58
60
62
64
66
68
BMA (%)
Full
Random
Entropy (G)
TOD (G)
Gradnorm (G)
CoreSet (G)
BADGE (G)
Ours
+ 1.98
+ 1.04
+ 2.08
+ 2.84
(a) Fed-ISIC (G)
1
2
3
4
5
AL round
52
54
56
58
60
62
64
66
68
BMA (%)
Full
Random
Entropy (L)
TOD (L)
Gradnorm (L)
CoreSet (L)
BADGE (L)
Ours
+ 2.02
+ 0.92
+ 1.48
+ 2.06
(b) Fed-ISIC (L)
1
2
3
4
5
AL round
52
54
56
58
60
62
64
66
68
BMA (%)
Full
Random
Entroopy (E)
TOD (E)
Gradnorm (E)
CoreSet (E)
BADGE (E)
LoGo
KAFAL
Ours
+ 1.95
+ 1.21
+ 1.39
+ 1.62
(c) Fed-ISIC (E)
1
2
3
4
5
AL round
93
94
95
96
97
98
ACC (%)
Full
Random
Entropy (G)
TOD (G)
Gradnorm (G)
CoreSet (G)
BADGE (G)
Ours
+ 0.88
+ 0.57
+ 0.51
+ 0.44
(d) Fed-Camelyon (G)
1
2
3
4
5
AL round
93
94
95
96
97
98
ACC (%)
Full
Random
Entropy (L)
TOD (L)
Gradnorm (L)
CoreSet (L)
BADGE (L)
Ours
+ 0.69
+ 0.51
+ 0.35
+ 0.44
(e) Fed-Camelyon (L)
1
2
3
4
5
AL round
93
94
95
96
97
98
ACC (%)
Full
Random
Entropy (E)
TOD (E)
Gradnorm (E)
CoreSet (E)
BADGE (E)
LoGo
KAFAL
Ours
+ 0.73
+ 0.46
+ 0.32
+ 0.37
(f) Fed-Camelyon (E)
Figure 3. Comparison of FAL methods in medical image classification. (a)-(c) and (d)-(f) depict the results of the Fed-ISIC and Fed-
Camelyon datasets, respectively. Performance enhancements over the second-best method in each FAL round are emphasized in red text.
we used the Dice score and the 95% Hausdorff Distance
(HD95) to assess segmentation results.
Implementation details. We conducted R = 5 rounds of
FAL involving federated model training and data annota-
tion. The annotation budget Bk is 500 for Fed-ISIC and
Fed-Camelyon, 50 for Fed-Polyp, and 20 for Fed-Prostate
and Fed-Fundus. During model training, we followed the
previous work [21, 71, 73] to utilize EfficientNet-B0 [67]
for Fed-ISIC, DenseNet-121 [17] for Fed-Camelyon, and
U-Net [39, 56] for segmentation datasets. Notably, both
EfficientNet-B0 and DenseNet-121 were pre-trained on Im-
ageNet [10]. Each experiment was conducted three times
using different random seeds, and the average results were
reported. More details are in Appendix C.1.
Comparison methods.
We compared FEAL with eight
FAL methods, including random sampling (Random),
entropy-based sampling (Entropy) [61], TOD [18], Grad-
norm [72], CoreSet [57], BADGE [2], LoGo [25], and
KAFAL [6]. The first six strategies are primarily developed
for standard active learning, whereas LoGo and KAFAL
are specifically tailored for decentralized scenarios. To in-
corporate these standard AL strategies into the FAL frame-
work, we implemented them in three distinct manners: us-
ing only the global model (referred to as G), depending
solely on the local model (L), or employing a simple en-
semble method with both models (E). It guarantees a com-
prehensive evaluation of these strategies in FAL. Details of
comparison methods are summarized in Appendix C.1.
4.2. Results
Image classification. The comparative analysis of image
classification results in Fig. 3 indicates that FEAL achieves
superior results on both Fed-ISIC and Fed-Camelyon
datasets. As depicted in Fig. 3, the performance of all meth-
ods exhibits a general trend of improvement with the incre-
mental inclusion of labeled samples. However, an exception
to this trend is observed in the Fed-ISIC dataset as shown
in Fig. 3(a). As observed, the exclusive use of Entropy,
Gradnorm, and CoreSet with a single model, whether it is a
global (see Fig. 3(a)) or local model (see Fig. 3(b)), results
in suboptimal performance, leading to a notable decrease in
effectiveness beginning from the third round. The global
model delivers unreliable uncertainty evaluations, which
may result in suboptimal data selection and adversely affect
the ability of the model to generalize effectively. Moreover,
selecting data based on evaluations from the local model can
cause overfitting to its specific client, negatively impacting
the performance. Conversely, methods like Gradnorm (E)
and TOD (E) that combine both global and local models
often outperform those relying solely on the global model,
benefiting from the additional domain-specific knowledge
of the local model. However, it is important to note that
without proper calibration of the global model, the com-
bined use of both models does not always guarantee better
performance than solely using the local model.
Remarkably, FEAL consistently outperforms state-of-
the-art FAL methods on Fed-ISIC, as shown in Fig. 3(a)-
(c). This superiority is especially noticeable in the fifth FAL
round, where FEAL achieves a substantial performance
6
Table 1. Comparison of FAL methods in medical image segmentation. Dice scores for three segmentation datasets are reported. For
Fed-Fundus, Dice scores for both optic disc and optic cup segmentation and their average are presented. G and L stand for sampling solely
with the global or local model, while E represents sampling with both models. Red and blue highlight the Top-1 and Top-2 results.
Model
Method
Fed-Polyp (%)
Fed-Prostate (%)
Fed-Fundus (%)
R2
R3
R4
R5
R2
R3
R4
R5
R2
R3
R4
R5
-
Full
78.18
88.02
94.32 / 85.70 (90.01)
-
Random
67.70 72.16 75.58 76.32
80.29 82.70 83.94 84.77
92.30 / 81.41 (86.85) 93.33 / 84.45 (88.89) 94.29 / 84.80 (89.54) 94.46 / 85.05 (89.76)
G
Entropy [61]
67.45 74.65 75.30 76.69
82.17 82.53 84.05 86.10
93.19 / 82.61 (87.90) 93.84 / 84.35 (89.10) 94.27 / 85.34 (89.80) 94.47 / 85.29 (89.88)
TOD [18]
64.99 74.61 76.24 78.26
80.75 83.48 84.31 85.82
92.70 / 82.49 (87.60) 93.95 / 85.01 (89.48) 94.27 / 85.63 (89.95) 94.71 / 85.58 (90.14)
Gradnorm [72]
69.14 74.58 75.79 78.51
82.10 83.01 84.85 86.02
93.20 / 82.01 (87.60) 94.12 / 84.71 (89.41) 94.33 / 85.38 (89.85) 94.56 / 85.43 (89.99)
CoreSet [57]
69.50 73.37 76.71 78.18
82.11 83.68 84.56 85.86
93.00 / 83.07 (88.03) 93.90 / 84.75 (89.32) 94.16 / 85.35 (89.75) 94.51 / 85.63 (90.07)
BADGE [2]
70.09 74.11 76.38 76.55
82.78 83.91 85.39 85.97
93.17 / 82.54 (87.85) 94.07 / 84.46 (89.26) 94.40 / 85.37 (89.89) 94.58 / 85.19 (89.89)
L
Entropy
67.48 73.41 75.07 78.63
81.08 82.22 84.36 85.19
93.19 / 83.22 (88.21) 93.83 / 84.49 (89.16) 94.36 / 84.97 (89.66) 94.63 / 85.68 (90.15)
TOD [18]
65.95 72.92 75.19 77.97
79.59 83.74 85.50 86.03
92.82 / 82.34 (87.58) 93.98 / 85.00 (89.49) 94.37 / 85.28 (89.83) 94.65 / 85.56 (90.10)
Gradnorm [72]
70.06 74.69 77.25 78.84
80.52 83.43 84.94 86.04
93.29 / 83.04 (88.16) 94.13 / 84.69 (89.41) 94.33 / 85.60 (89.97) 94.42 / 85.53 (89.98)
CoreSet [57]
68.92 74.06 75.59 77.75
81.49 83.49 84.65 86.19
92.80 / 83.20 (88.00) 93.87 / 84.70 (89.28) 94.28 / 85.42 (89.85) 94.47 / 85.54 (90.00)
BADGE [2]
70.28 73.96 76.21 77.63
82.07 83.54 85.30 86.06
93.06 / 82.65 (87.85) 93.95 / 84.44 (89.19) 94.34 / 85.02 (89.68) 94.54 / 85.52 (90.03)
E
Entropy [61]
67.85 75.10 76.80 77.20
80.95 83.66 84.81 85.42
93.26 / 82.77 (88.01) 94.04 / 84.69 (89.36) 94.33 / 85.31 (89.82) 94.38 / 85.10 (89.74)
TOD [18]
67.25 70.43 74.84 77.53
81.45 84.46 84.51 85.65
93.13 / 82.70 (87.92) 93.63 / 84.64 (89.14) 94.31 / 85.30 (89.81) 94.54 / 85.82 (90.18)
Gradnorm [72]
68.01 75.75 77.73 75.67
81.21 83.43 85.30 85.13
93.36 / 83.09 (88.23) 93.83 / 84.91 (89.37) 94.33 / 85.59 (89.96) 94.65 / 85.52 (90.08)
CoreSet [57]
67.77 74.28 77.69 75.87
81.30 84.52 84.75 86.50
93.24 / 82.55 (87.89) 93.63 / 84.86 (89.24) 94.20 / 85.50 (89.85) 94.62 / 85.89 (90.25)
BADGE [2]
69.12 75.45 77.37 76.24
81.31 84.34 85.92 85.55
93.37 / 82.95 (88.16) 93.99 / 85.00 (89.50) 94.50 / 85.22 (89.86) 94.62 / 85.44 (90.03)
LoGo [25]
69.07 75.76 74.63 77.24
82.35 84.56 85.53 85.97
93.14 / 83.01 (88.08) 93.93 / 84.55 (89.24) 94.18 / 85.68 (89.93) 94.61 / 85.64 (90.12)
KAFAL [6]
69.69 73.83 75.38 77.97
82.65 83.49 85.58 85.96
93.11 / 82.75 (87.93) 94.01 / 84.12 (89.06) 94.37 / 85.16 (89.77) 94.46 / 85.02 (89.74)
FEAL (Ours)
72.06 76.39 78.62 80.18
82.94 85.29 86.77 87.42
93.53 / 83.72 (88.63) 94.25 / 85.19 (89.72) 94.60 / 85.96 (90.28) 94.89 / 86.27 (90.58)
gain of 1.62% over the second-best method, CoreSet (E),
as demonstrated in Fig. 3(c). Additionally, it is noteworthy
that FEAL achieves a performance comparable to training
with the fully annotated dataset in the third round and even
exceeds the fully supervised performance by 0.84% in the
fifth round. These advancements are primarily attributable
to the effective uncertainty calibration and demonstrate the
efficacy of FEAL. It is noteworthy that the baseline meth-
ods KAFAL and LoGo, designed for FAL underperform in
real-world federated scenarios. Despite showing impressive
results in simulated federated datasets, they fail to repli-
cate this success in actual multi-center federated scenarios.
This is mainly due to the inherent domain shift characteris-
tics of multi-center medical data. As depicted in Fig. 3(d)-
(f), FEAL also achieves superior performance on the large-
scale dataset Fed-Camelyon, where each local client con-
tains tens of thousands of patches. By employing a low-
data regime, where merely about 3.43% of the total train-
ing samples are annotated in the active learning process,
FEAL attains 99.40% of fully supervised performance af-
ter five rounds of FAL. This achievement represents a sig-
nificant improvement compared to the second-best method,
KAFAL, which reaches 98.93% of the fully supervised per-
formance, demonstrating the effectiveness of uncertainty
calibration in FEAL. Additional results with different an-
notation budgets/ratios are available in Appendix C.2.
Image segmentation.
To further evaluate the effective-
ness of FEAL in segmentation tasks, we conducted experi-
ments on three real multi-center datasets: Fed-Polyp, Fed-
Prostate, and Fed-Fundus, with the results summarized in
Tab. 1. As can be seen, FEAL exhibits superior perfor-
mance on three multi-center segmentation datasets, as ev-
idenced by its higher Dice scores. Specifically, for Fed-
Polyp, FEAL yields a Dice score of 80.18% in the fifth
round, outperforming the second-best method Gradnorm
(L) by 1.34% and surpassing fully-supervised training by
2.00%.
For Fed-Prostate, FEAL demonstrates improve-
ments of 0.85% and 0.92% over the second-best method
in the fourth and fifth FAL rounds, respectively. For Fed-
Fundus, FEAL not only surpasses other methods in seg-
menting both the optic disc and optic cup but also outper-
forms fully supervised training in the fourth and fifth rounds
of FAL. Complete results including HD95 and standard de-
viation are available in Appendix C.2.
4.3. Discussion
Effect of uncertainty calibration. We conducted exper-
iments on Fed-ISIC to evaluate the effects of different un-
certainty combinations: U G
epi, U G
ale, and U L
ale. As summarized
in Tab. 2, combining aleatoric uncertainty from both global
and local models proves more effective than relying on just
one model. The best results are obtained with U G
epi, U G
ale, and
U L
ale, showcasing the effectiveness of the proposed uncer-
tainty calibration. The ablation results on Fed-Polyp are in
Appendix C.3. Moreover, we visualize the aleatoric uncer-
tainty in both models on Fed-Polyp in Fig. 4. It is noticeable
that U G
ale and U L
ale highlight different regions, underscoring
the importance of combining aleatoric uncertainty in both
models for a more comprehensive assessment.
Table 2. Ablation study of uncertainty calibration on Fed-ISIC.
UG
epi
UG
ale
UL
ale
Round 2
Round 3
Round 4
Round 5
-
✓
-
60.61±1.57
66.60±0.33
67.09±1.02
66.57±1.21
-
-
✓
62.20±3.56
66.84±1.99
66.13±1.52
67.45±0.69
-
✓
✓
63.43±1.11
67.18±0.55
66.58±1.02
66.70±0.28
✓
-
-
61.97±1.25
65.87±0.59
67.09±1.24
66.41±1.10
✓
✓
-
61.95±2.12
66.08±0.40
67.19±1.02
66.85±0.84
✓
-
✓
61.07±1.24
65.17±1.58
67.16±0.73
65.92±1.95
✓
✓
✓
65.18±0.41
67.77±1.31
68.41±1.01
68.46±0.37
7
Input
Ground truth
𝑈!"#
$
𝑈!"#
%
𝑈!"#
$
+ 𝑈!"#
%
Figure 4. Visualization of aleatoric uncertainty on Fed-Polyp. U G
ale
and U L
ale denote the aleatoric uncertainty in the global and local
models, respectively.
Effect of diversity relaxation. We analyzed the impact of
hyperparameters, i.e. minimum neighbor size n and sim-
ilarity threshold τ, on Fed-ISIC. As depicted in Fig. 5(a),
eliminating diversity relaxation (‘w/o relaxation’) results in
a notable reduction in BMA in the fifth round, and the best
performance is achieved with n=5 and τ=0.85. The abla-
tion results on Fed-Polyp are reported in Appendix C.3.
1
2
3
4
5
AL round
52.5
55.0
57.5
60.0
62.5
65.0
67.5
BMA (%)
w/o relaxation
3 neighbors
5 neighbors (Ours)
7 neighbors
9 neighbors
(a) Minimum neighbor size n
1
2
3
4
5
AL round
52.5
55.0
57.5
60.0
62.5
65.0
67.5
BMA (%)
=0.75
=0.80
=0.85 (Ours)
=0.90
(b) Similarity threshold τ
Figure 5. Ablation study of diversity relaxation on Fed-ISIC.
Effect of evidential model training. We performed exper-
iments to compare the evidential loss (L in Eq. 9) against
cross-entropy loss (CE) on Fed-ISIC and against dice loss
(Dice) on Fed-Polyp. The results are detailed in Tab. 3. As
can be seen, training with evidential loss results in an aver-
age performance gain of 1.03% on Fed-ISIC and 1.16% on
Fed-Polyp, respectively. This improvement can be primar-
ily attributed to evidence regularization, demonstrating the
efficacy of evidential model training. The ablation results
on the other three datasets are available in Appendix C.3.
Table 3. Ablation study of loss function.
Dataset
Loss
Round 2
Round 3
Round 4
Round 5
Fed-ISIC
CE
64.28±1.64
66.69±0.95
67.32±1.16
67.40±0.22
L
65.18±0.41
67.77±1.31
68.41±1.01
68.46±0.37
Fed-Polyp
Dice
70.14±0.10
75.77±0.67
77.23±0.21
79.48±0.62
L
72.06±0.72
76.39±0.66
78.62±1.44
80.18±0.10
Effect
of
trade-off
weight
λ.
We
further
de-
termined
the
optimal
setting
for
the
hyperparame-
ter λ on Fed-ISIC, choosing from the candidate set
{1e−3, 5e−3, 1e−2, 5e−2, 1e−1}, the results are detailed
in Tab. 4. As can be seen, the best performance is achieved
when λ = 1e−2. The ablation results on Fed-Polyp are
reported in Appendix C.3.
Analysis of Dirichlet simplex.
We analyze the Dirich-
let simplex on a subset of Fed-ISIC encompassing three
Table 4. Ablation study of trade-off weight λ on Fed-ISIC.
λ
Round 2
Round 3
Round 4
Round 5
1e−3
63.49±3.00
64.57±2.70
66.25±1.17
65.45±1.06
5e−3
63.10±2.07
65.79±2.57
66.00±2.09
66.48±0.86
1e−2
65.18±0.41
67.77±1.31
68.41±1.01
68.46±0.37
5e−2
62.12±0.99
67.21±1.42
66.92±0.70
66.90±0.93
1e−1
63.53±2.03
66.21±0.35
66.03±2.34
67.78±1.17
classes. As illustrated in Fig. 6, when selecting samples
with FEAL, the Dirichlet distribution becomes more con-
centrated at the simplex’s corner for unlabeled samples, in-
dicating reduced epistemic uncertainty in the global model.
This trend verifies the effectiveness of CES in addressing
domain shifts. Additionally, starting with an identical set
of labeled samples, we tracked the selection of samples in
the second FAL round utilizing various FAL methods. The
Dirichlet simplexes of different methods are visualized in
Fig. 7. As can be seen, the Dirichlet distribution of sam-
ples selected by FEAL showcases a broader spread across
the simplex, indicating that FEAL effectively models the
global model’s knowledge of local data and prioritizes se-
lecting samples characterized by high epistemic uncertainty.
More details and results are available in Appendix C.3.
𝑈!"#(𝒙, 𝜽) = −4.03
MEL
BCC
BKL
Round 1
𝑈!"#(𝒙, 𝜽) = −4.42
MEL
BCC
BKL
Round 2
𝑈!"#(𝒙, 𝜽) = −5.03
MEL
BCC
BKL
Round 3
MEL
BCC
BKL
𝑈!"#(𝒙, 𝜽) = −5.55
Round 4
MEL
BCC
BKL
𝑈!"#(𝒙, 𝜽) = −6.22
Round 5
Figure 6. Visualization of the Dirichlet simplex for unlabeled sam-
ples across five FAL rounds using FEAL.
MEL
BCC
BKL
Entropy
MEL
BCC
BKL
CoreSet
MEL
BCC
BKL
LoGo
MEL
BCC
BKL
KAFAL
MEL
BCC
BKL
Ours
Figure 7. Visualization of the Dirichlet simplex for samples se-
lected in the second FAL round using various sampling strategies.
5. Conclusion and Social Impact
To address the challenge of unreliable data assessment us-
ing the global model under domain shifts, we proposed a
method FEAL, which places a Dirichlet prior over categori-
cal probabilities to treat the prediction as a distribution over
the probability simplex and leverages both aleatoric uncer-
tainty and epistemic uncertainty to calibrate the uncertainty
evaluation, enhancing the reliability of data assessment and
incorporating diversity relaxation to maintain sample diver-
sity. Extensive results verify the effectiveness. This work
holds the potential to advance healthcare by preserving data
privacy and facilitating collaborative research, ultimately
leading to more accessible and effective patient care.
8
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11
Think Twice Before Selection: Federated Evidential Active Learning for Medical
Image Analysis with Domain Shifts
Supplementary Material
In the supplementary material, we provide the workflow
of FEAL in Sec. A, formula derivations in Sec. B, detailed
descriptions of experimental settings, results, and discus-
sions in Sec. C, additional experiments conducted on OCTA
datasets in Sec. D, and discussions comparing with other
methods in Sec. E.
A. Workflow of FEAL
The detailed workflow of FEAL is summarized in Alg. 2.
Algorithm 2 Workflow of FEAL
Input: global model θ, local models {θk}K
k=1, unlabeled sets
{Uk}K
k=1, annotation budget {Bk}K
k=1, active learning rounds
R, aggregation weights {αk}K
k=1, communication rounds T
Output: trained global model θ∗
/* 1st AL round */
1: for k = 1 to K do
2:
Randomly annotate Bk samples from the unlabeled pool
Uk to construct the initial labeled pool L1
k = {(xi, yi}Bk
i=1.
3:
Update the unlabeled pool U 1
k = Uk \ L1
k.
4:
{αk}K
k=1 ←
{|L1
k|}K
k=1
PK
k=1 |L1
k|
5: end for
6: θ∗←θ
7: for t = 1 to T do
8:
for k = 1 to K do
9:
θ1
k ←θ∗
10:
θ1
k ←LocalTraining(θ1
k, L1
k)
11:
end for
12:
θ∗←FedAvg({θ1
k}K
k=1, {αk}K
k=1)
13: end for
/* 2nd ∼R-th AL round */
14: for r = 2 to R do
15:
for k = 1 to K do
16:
Qr
k = FEAL(θ∗, θr−1
k
, U r−1
k
) ▷Local data annotation
17:
Lr
k = Lr−1
k
∪Qr
k
18:
U r
k = U r−1
k
\ Qr
k
19:
{αk}K
k=1 ←
{|Lr
k|}K
k=1
PK
k=1 |Lr
k|
20:
end for
21:
for t = 1 to T do
22:
for k = 1 to K do
23:
θr
k ←θ∗
▷Model distribution
24:
θr
k ←LocalTraining(θr
k, Lr
k)
▷Local training
25:
end for
26:
θ∗←FedAvg({θr
k}K
k=1, {αk}K
k=1})▷Model aggregation
27:
end for
28: end for
29: return θ∗
The sampling strategy employed by FEAL and the ag-
gregation method utilized in FedAvg are detailed in Alg. 3
and Alg. 4, respectively.
Algorithm 3 Sampling strategy of FEAL
Input: global model θ∗, local model θr−1
k
, unlabeled set U r−1
k
,
annotation budget Bk
Output: query set Qr
k
/* Uncertainty calibration */
1: for all x ∈U r−1
k
do
2:
Compute Uale(x, θr−1
k
) and Uale(x, θ∗) using Eq. 3.
3:
Compute Uepi(x, θ∗) using Eq. 4.
4:
Compute U(x, θ∗, θr−1
k
) by Eq. 5.
5: end for
/* Diversity relaxation */
6: Determine the query set Qr
k according to Alg. 1.
7: return Qr
k
Algorithm 4 Aggregation method of FedAvg
Input: local models {θr
k}K
k=1, aggregation weights {αk}K
k=1
Output: global model θ∗
1: θ∗←PK
k=1 αk · θr
k
2: return θ∗
B. Derivations
B.1. Dirichlet-based Evidential Model in FAL
In Dirichlet-based evidential models, given a sample x and
a model θ, the categorical prediction ρ follows a Dirichlet
distribution, denoted as p(ρ|x, θ) ∼Dir(ρ|α). The prob-
ability density function of ρ [58, 76], conditioned on the
sample x and the model θ, is formulated as:
  \sma ll
\
b
e
g
i
n

{ali
gne d}
p(
\br ho |\
b
x
 ,\
bthet
a
 ) =  \l
e
f t \{ \begin {aligned} \frac {\Gamma (\sum _{c=1}^C\alpha _c)}{\prod _{c=1}^C\Gamma (\alpha _c)}\prod _{c=1}^C\brho _c^{\alpha _c-1}&, (\brho \in \Delta ^C) \\ 0\qquad \qquad &, (\text {otherwise}) \end {aligned} \right . \end {aligned} \label {eq:rho}
(10)
where α = {α1, α2, · · · , αC} denotes the parameters of
the Dirichlet distribution for sample x, Γ(·) is the Gamma
function, and ∆C = {ρ| PC
c=1 ρc = 1 and 0 < ρc < 1} is
the C-dimensional unit simplex.
As stated in [47], the marginal distributions of the
Dirichlet distribution follow Beta distributions.
Conse-
quently, given p(ρ|x, θ) ∼Dir(ρ|α), we can express
p(ρc|x, θ) ∼Beta(ρc|αc, S −αc), where S = PC
c=1 αc
represents the Dirichlet strength. The probability density
1
function of ρc, given the sample x and the model θ, is for-
mulated as:
  \smal l p
(
\rho _ c |\bx ,\b
t
he t a )=\frac {1}{\mathcal {B}(\alpha _c,S-\alpha _c)}\rho _c^{\alpha _c-1}(1-\rho _c)^{S-\alpha _c-1}, \label {eq:rho_c}
(11)
where B(·, ·) is the Beta function and B(αc, S −αc) =
Γ(αc)·Γ(S−αc)
Γ(αc+S−αc) = Γ(αc)·Γ(S−αc)
Γ(S)
.
Combining Eq. 10 and Eq. 11, the posterior probability
for class c, given the sample x and the model θ, can be
obtained as:
  \ s mall  \ b
e
gin  {ali g ned} P (y =c
|
\
bx  ,\bthe ta  )
&
=
\i n t p(y=c |\ brh
o  )\c d ot  p (\b
rho | \ b x ,
\ bth
e ta  )\ \text
{d}\ b rh o  \\ &=\
i nt \ r ho  _ c\c
dot p ( \ brh
o  |\b x  , \ bthe
ta ) \ \ text
{ d}
\ brho \\ &=\int \rho _c\cdot p(\rho _c|\bx ,\btheta )\ \text {d}\rho _c\\ &=\frac {\mathcal {B}(\alpha _c+1,S-\alpha _c)}{\mathcal {B}(\alpha _c,S-\alpha _c)}\int \frac {\rho _c^{\alpha _c}(1-\rho _c)^{S-\alpha _c-1}}{\mathcal {B}(\alpha _c+1,S-\alpha _c)}\ \text {d}\rho _c\\ & = \frac {\mathcal {B}(\alpha _c+1,S-\alpha _c)}{\mathcal {B}(\alpha _c,S-\alpha _c)}\\ & = \frac {\Gamma (\alpha _c+1)\cdot \Gamma (S)}{\Gamma (S+1)\cdot \Gamma (\alpha _c)}\\ & = \frac {\alpha _c}{S}. \end {aligned}
(12)
The Dirichlet distribution parameter α is closely linked
to the evidence e which reflects the support for the model
prediction on the given sample x [58]. The parameter α is
formulated as:
  \ s m a ll \bo lds y mbol {\alpha }=\boldsymbol {e}+1=\mathcal {A}(f(\bx ,\btheta ))+1,
(13)
where f(x, θ) denotes the output logits of model θ for
sample x and A(·) is a non-negative activation function
to transform the logits f(x, θ) into evidence e. There are
several common activation functions A(·) [51], including:
ReLU(·) = max(0, ·), SoftPlus(·) = log(1 + exp(·)),
and exp(·). In our study, ReLU(·) was employed as the
non-negative activation function.
B.2. Calibrated Evidential Sampling
Aleatoric uncertainty.
Given a sample x and the global
model θ, the expected entropy of all possible predictions is
utilized to depict the aleatoric uncertainty, quantifying the
inherent complexity or ambiguity present in sample x. The
aleatoric uncertainty of the sample x in the global model θ
is formulated as:
  \smal l \ begin {aligned} U_{\
t e
x
t
 {a
le}}(\bx ,\b t het a )
 &
=

\ma
thbb {E}_{p(\ b rho  |\
b x

,
\bt
h
eta )}[ \ mat
h ca l  {H}[P(y|
\brho  )]]\
\ &
= -
\
s
um
_{c=1}^ C \ma
thbb {E}_{
p
(\brho | \bx
 ,\ b theta )}[
\rho _c  \cdo
t \
l o
g

\rh
o _c ] \\  &=-\
sum  _{ c =1}^C \mathbb {E}_{p(\rho _c|\b x ,
\
b
t
het
a
) } [\rh o  _ c  \cd o t \log \rho _c]\\ &=-\sum _{c=1}^C\int \log (\rho _c)\cdot \frac {\rho _c^{\alpha _c}(1-\rho _c)^{S-\alpha _c-1}}{\mathcal {B}(\alpha _c,S{-}\alpha _c)}\ \text {d}\rho _c\\ &=-\sum _{c=1}^C\frac {\mathcal {B}(\alpha _c{+}1,S{-}\alpha _c)}{\mathcal {B}(\alpha _c,S{-}\alpha _c)}\int \log (\rho _c)\cdot \frac {\rho _c^{\alpha _c}(1-\rho _c)^{S-\alpha _c-1}}{\mathcal {B}(\alpha _c{+}1,S{-}\alpha _c)}\ \text {d}\rho _c\\ &=-\sum _{c=1}^C\frac {\Gamma (\alpha _c+1)\cdot \Gamma (S)}{\Gamma (S+1)\cdot \Gamma (\alpha _c)}\mathbb {E}_{\rho _c\sim Beta(\rho _c|\alpha _c+1,S-\alpha _c)}[\log \rho _c]\\ &=\sum _{c=1}^C\frac {\alpha _c}{S}\cdot [\psi (S+1)-\psi (\alpha _c+1)], \end {aligned} \label {eq:ale_suppl}
(14)
where H(·) denotes the Shannon entropy [61] and ψ(·) rep-
resents the digamma function. The aleatoric uncertainty of
the sample x in the local model θk can also be calculated
as Uale(x, θk) according to Eq. 14.
Epistemic uncertainty.
The differential entropy of a
Dirichlet distribution is employed to quantify the inherent
randomness in categorical distributions [44]. This metric is
beneficial in depicting epistemic uncertainty, which arises
due to the global model’s lack of knowledge, often caused
by domain shifts. Given a sample x and the global model
θ, the epistemic uncertainty is defined as:
  \smal l \ begin {a lig
n e
d
} U_{\ te xt {epi}} (\ bx

,
\
bth
eta  )&=\
math c al { H} [ p(\brh o  |\bx ,\btheta )]\\ &=-\int p(\brho |\bx ,\btheta )\log p(\brho |\bx ,\btheta )\ \text {d}\brho \\ &=\sum _{c=1}^C\log \frac {\Gamma (\alpha _c)}{\Gamma (S)} - (\alpha _c-1)\cdot [\psi (\alpha _c)-\psi (S)]. \end {aligned}
(15)
B.3. Evidential Model Training
Task loss for classification.
Dirichlet-based evidential
models treat the prediction of a sample as a distribution,
allowing for multiple potential predictions to occur with
specific probabilities. Taking into account all potential pre-
dictions for a sample, we employ the Bayes risk of cross-
entropy loss [58] as the task loss for classification. Given
an input pair (x, y), the task loss for classification is de-
2
rived as follows:
  \small  \b eg i n {aligned} \math cal  {L
}
_
{
\
t
ext
 {t ask}}(\b x  ,\bth eta  _
k ,
\
b
old
sy
m
bol {y} )  &= \ma thb b {
E }
_
{
p(\
br h o |\bx ,\btheta _k)}[\ma thc
a
l

{L}
_{ C E}(\b x  ,\btheta _k,\boldsymbol {y})]\\ &=\int [\sum _{c=1}^C-y_c\log (\rho _c)]\cdot p(\brho |\bx ,\btheta _k) \ \text {d}\brho \\ &=-\sum _{c=1}^C y_c\int \log (\rho _c)\cdot p(\rho _c|\bx ,\btheta _k)\ \text {d}\rho _c\\ &=-\sum _{c=1}^C y_c\cdot \mathbb {E}_{\rho _c\sim Beta(\rho _c|\alpha _c,S-\alpha _c)}[\log \rho _c]\\ &=\sum _{c=1}^Cy_c\cdot [\psi (S)-\psi (\alpha _c)]. \end {aligned}
(16)
Task loss for segmentation.
We leverage the Bayes risk
of Dice loss as the task loss for segmentation following [32].
Given an input pair (x, y), the task loss for segmentation is
denoted as follows:
  \small  \b eg i n {aligned} \mathca l { L}_
{ \text {task} } (
\
b
x
 ,\
bth e ta _
k,\
boldsym
bol

{ y})&=\mathbb  {
E
}
_
{p(
\b
rho  |\ b x ,
\b
theta _k ) }[\ma
t
h c a l

{
L
}_{
Di
ce} (\b x  ,\bth
et
a _k,\bo l dsymbol
{y})]\\ &=\mathbb {E}_{p(\brho |\bx ,\btheta _k)}[1-\frac {2}{C}\sum _{c=1}^{C}\frac {{\Vert \boldsymbol {y}_{c}\circ \brho _{c}\Vert }_1}{{\Vert \boldsymbol {y}_{c}^2\Vert }_1{+}{\Vert \brho _{c}^2\Vert }_1}]\\ &=\mathbb {E}_{p(\brho |\bx ,\btheta _k)}[1-\frac {2}{C}\sum _{c=1}^C\frac {\sum _{m=1}^M y_{mc}\cdot \rho _{mc}}{\sum _{m=1}^M (y_{mc}^2+\rho _{mc}^2)}]\\ &=1-\frac {2}{C}\sum _{c=1}^C\frac {\sum _{m=1}^My_{mc}\cdot \mathbb {E}[\rho _{mc}]}{\sum _{m=1}^M(y_{mc}^2+\mathbb {E}[\rho _{mc}^2])}, \end {aligned} \label {eq:dice}
(17)
where ◦is the Hadamard product and the image x is com-
prised of M pixels. ymc and ρmc represent the label indi-
cator and categorical probability of pixel xm w.r.t. class c,
respectively. By using the following equation:
  \s
mal l  \mathb b  {E}[\rho _{mc}^2] = \mathbb {E}[\rho _{mc}]^2 + \text {Var}(\rho _{mc}),
(18)
Eq. 17 can be updated to:
  \small  \b eg i n  {
a
l
i
gne
d}
 \m ath c al
{L
}_{\text  {t
as k }}(\bx ,\b
thet
a
 _ k ,
\
b
o
lds
ymb o l {y
})&
=1- \ fra
c { 2 } {C}\sum _
{c=
1}
^C\frac {\sum _{m=1}^M y_{mc}\cdot \overline {\rho }_{mc}}{\sum _{m=1}^M[y_{mc}^2+\overline {\rho }_{mc}^2+\frac {\overline {\rho }_{mc}(1-\overline {\rho }_{mc})}{S_m+1}]}\\ &= 1-\frac {2}{C}\sum _{c=1}^C\frac {{\Vert \boldsymbol {y}_{c}\circ \overline {\brho }_{c}\Vert }_1}{{\Vert \boldsymbol {y}_{c}^2\Vert }_1+{\Vert \overline {\brho }_{c}^2\Vert }_1+{\Vert \frac {\overline {\brho }_{c}\circ (\boldsymbol {1}-\overline {\brho }_{c})}{\boldsymbol {S}+\boldsymbol {1}}\Vert }_1}. \end {aligned}
(19)
C. Experiments
C.1. Experimental Settings
Datasets.
We verified the effectiveness of FEAL across
five real-world medical image datasets, two for classifica-
tion and three for segmentation. Detailed information, in-
cluding the data source, the number of samples, and the
resolution of each sample, is summarized in Tab. 5. Illus-
trative samples from each data source within the five multi-
center medical image datasets are showcased in Fig. 8. Note
Dataset
Data source
# Train
# Test
Resolution
Fed-ISIC
Client 1: BCN [49]
9,930
2,483
224×224
Client 2: HAM vidir molemax [49]
3,163
791
Client 3: HAM vidir modern [49]
2,691
672
Client 4: HAM rosendahl [49]
1,807
452
Fed-Camelyon
Client 1: Camelyon17 [3]
47,548
11,888
96×96
Client 2: Camelyon17 [3]
27,923
6,981
Client 3: Camelyon17 [3]
68,043
17,011
Client 4: Camelyon17 [3]
103,870 25,968
Client 5: Camelyon17 [3]
117,377 29,345
Fed-Polyp
Client 1: Kvasir [20]
800
200
384×384
Client 2: ETIS [64]
157
39
Client 3: ColonDB [66]
304
75
Client 4: ClinicDB [4]
490
122
Fed-Prostate
Client 1: BIDMC [38]
225
36
384×384
Client 2: BMC [5]
306
78
Client 3: HK [38]
134
24
Client 4: I2CVB [30]
387
81
Client 5: RUNMC [5]
337
84
Client 6: UCL [38]
152
23
Fed-Fundus
Client 1: Drishti-GS [65]
81
20
384×384
Client 2: RIM-ONE-r3 [12]
128
31
Client 3: REFUGE [50]
320
80
Client 4: REFUGE [50]
320
80
Table 5. Details of multi-center datasets utilized in our study.
Client 1
Client 2
Client 3
Client 4
(e) Fed-Fundus
Client 1
Client 2
Client 3
Client 4
(c) Fed-Polyp
Client 1
Client 2
Client 3
Client 4
Client 5
Client 6
(d) Fed-Prostate
Client 1
Client 2
Client 3
Client 4
(a) Fed-ISIC
Client 1
Client 2
Client 3
Client 4
Client 5
(b) Fed-Camelyon
Figure 8. Illustrative samples from each data source within five
multi-center medical image datasets utilized in our study.
that the Camelyon17 [3] dataset comprises five distinct data
sources with varying stains, therefore, we partitioned them
into five subsets to construct the Fed-Camelyon dataset
within the FAL framework. Similarly, the REFUGE [50]
dataset contains data from two separate sources, each
of which was treated as an individual client within the
Fed-Fundus dataset. For the three segmentation datasets,
3
we followed [71] to resize the images and ground truth
to 384×384 pixels.
In the training phase, we imple-
mented data augmentation by randomly cropping patches of
320×320 pixels. Subsequently, we evaluated the segmenta-
tion results on the entire image of 384 × 384 pixels during
the inference phase.
Evaluation metrics.
For classification tasks, we assessed
the Balanced Multi-class Accuracy (BMA) for skin lesion
classification [8] and measured accuracy (ACC) for breast
cancer histology classification.
Regarding segmentation
tasks, we used the Dice score and the 95% Hausdorff Dis-
tance (HD95) to assess segmentation results.
Implemental details.
We conducted R = 5 rounds of
FAL involving federated model training and data annota-
tion.
Federated model training comprises local training
and model communication. During local training, we fol-
lowed the previous work [21, 71, 73] to utilize EfficientNet-
B0 [67] for the Fed-ISIC dataset, DenseNet-121 [17] for the
Fed-Camelyon dataset, and U-Net [39, 56] for segmentation
datasets. Notably, both EfficientNet-B0 and DenseNet-121
were pre-trained on ImageNet [10]. In FEAL, we employed
the ReLU(·) activation as the non-negative activation func-
tion A(·) for both global and local models. We trained lo-
cal models using the Adam optimizer [26] with a learning
rate of 5e−4. The weight decay was set to 5e−4 for the
Fed-ISIC dataset and 1e−5 for the other four datasets. In
terms of communication, we employed the FedAvg algo-
rithm [27], with all clients participating in each communi-
cation round. We conducted T = 100 rounds of commu-
nication to attain a robust global model. Regarding data
annotation, we followed the previous work [6, 25] to a uni-
form annotation budget Bk across all local clients k. Specif-
ically, annotation budget Bk is allocated based on the size of
each dataset. The annotation budget Bk was set to 500 for
both Fed-ISIC and Fed-Camelyon datasets, 50 for the Fed-
Polyp dataset, and 20 for both Fed-Prostate and Fed-Fundus
datasets. Furthermore, to account for the different sizes of
datasets among local clients, we established a maximum an-
notation ratio of 85%. It means that the clients whose num-
ber of labeled samples achieves the threshold ceased further
data annotation. All the experiments were conducted three
times using different random seeds, and the average results
were reported.
Comparison methods.
We compared FEAL with eight
state-of-the-art FAL approaches, including random sam-
pling (Random), entropy-based sampling (Entropy) [61],
TOD [18], Gradnorm [72], CoreSet [57], BADGE [2],
LoGo [25], and KAFAL [6].
The first six methods are
designed for standard active learning, whereas LoGo and
KAFAL are specifically tailored for federated scenarios.
For a comprehensive comparison, we implemented the first
six sampling strategies in three distinct manners: (1) uti-
lizing the global model for data evaluation (denoted as G),
(2) employing the local model for data evaluation (L), and
(3) integrating an ensemble technique that harnesses both
global and local models for evaluation (E). The details of
comparison methods and ensemble techniques are summa-
rized as follows.
• Random: Randomly select Bk unlabeled samples for lo-
cal client k in each FAL round.
• Entropy: Entropy is an uncertainty-based sampling strat-
egy, which prioritizes the top-Bk unlabeled samples with
the highest entropy scores in model predictions. Beyond
just utilizing the global or local model for data evaluation,
we also implemented a simple ensemble strategy that ag-
gregates the entropy scores in both models.
• TOD: TOD is an uncertainty-based sampling strategy,
which leverages the temporal output discrepancy to quan-
tify the uncertainty of unlabeled samples. It selects the
top-Bk unlabeled samples with the highest cyclic output
discrepancy (COD) scores. In our implementation, we
incorporated an additional ensemble technique [25], fine-
tuning, into TOD. Specifically, local client k downloads
the global model θr and fine-tunes it with the available
labeled samples. Subsequently, local client k employs
both the fine-tuned global model and its historical local
model θr−1
k
to compute the COD score, thereby integrat-
ing insights from both global and local models for more
effective sampling.
• Gradnorm: Gradnorm initially estimates the pseudo loss
of unlabeled samples, leveraging either pseudo labels or
entropy scores derived from model predictions. This loss
estimation is then backpropagated to determine the gradi-
ent norm across all model parameters, serving as a mea-
sure of data uncertainty to evaluate the potential value of
each unlabeled sample. In our study, we aggregated the
gradient norm from both models to achieve a fundamental
ensemble setting. This approach enabled us to leverage
the knowledge of both global and local models, thereby
facilitating a more comprehensive evaluation.
• CoreSet: CoreSet is a diversity-based sampling strategy
that identifies and selects BK unlabeled samples with fea-
ture embeddings exhibiting the greatest dissimilarity to
available labeled samples. In a basic ensemble setting,
we averaged the feature embeddings from both global and
local models for each sample and applied CoreSet on the
interpolated feature embedding.
• BADGE: BADGE is a hybrid sampling strategy that si-
multaneously considers uncertainty and diversity metrics.
It begins by extracting gradient embeddings of unlabeled
samples to ensure uncertainty.
Following this, it em-
ploys k-means clustering on these gradient embeddings
to maintain a diverse selection of samples.
4
Table 6. Comparison results (mean±std) on medical image datasets for classification. We evaluated the balanced multi-class accuracy
(BMA) for Fed-ISIC and the accuracy for Fed-Camelyon and presented the mean result and standard deviation of three random seeds. Red
and blue highlights the Top-1 and Top-2 results, respectively.
Model
Method
Fed-ISIC (%)
Fed-Camelyon (%)
R2
R3
R4
R5
R2
R3
R4
R5
-
Random
61.59±1.45
64.90±1.53
65.53±1.31
64.99±1.43
94.82±0.30
95.40±0.24
96.02±0.12
96.34±0.07
G
Entropy [61]
61.82±1.38
65.74±1.62
65.99±0.35
64.44±1.21
94.91±0.54
95.98±0.14
96.53±0.16
96.84±0.14
TOD [18]
56.63±3.05
64.13±3.50
65.32±1.10
64.54±0.76
93.48±1.23
95.47±0.54
96.41±0.31
96.81±0.16
Gradnorm [72]
63.20±0.49
65.72±1.29
65.31±2.03
64.61±0.76
94.10±0.18
94.95±0.23
95.27±0.15
95.73±0.18
CoreSet [57]
62.19±1.57
66.73±0.49
66.33±0.30
65.62±1.09
93.89±0.53
94.15±0.26
95.14±0.35
96.04±0.18
BADGE [2]
62.26±1.74
64.98±1.56
65.46±1.94
64.39±0.63
94.87±0.38
95.55±0.19
96.07±0.16
96.29±0.25
L
Entropy [61]
62.61±3.39
64.95±1.87
66.93±1.44
65.76±2.34
95.07±0.24
96.05±0.03
96.68±0.07
96.73±0.12
TOD [18]
58.52±2.89
65.11±2.04
64.88±2.00
64.81±3.11
93.79±1.18
95.29±0.47
96.46±0.34
96.83±0.11
Gradnorm [72]
62.38±1.90
64.96±3.21
65.85±2.79
64.39±1.44
94.22±0.38
94.98±0.39
95.37±0.54
95.92±0.26
CoreSet [57]
63.16±0.70
66.84±0.49
66.43±0.89
66.40±0.36
93.92±0.40
94.12±0.24
95.24±0.34
95.87±0.17
BADGE [2]
63.12±0.72
65.54±1.47
65.41±1.77
64.80±2.39
95.09±0.23
95.73±0.27
96.14±0.21
96.50±0.05
E
Entropy [61]
63.21±0.59
64.86±1.09
66.35±0.14
65.57±1.92
95.03±0.01
96.08±0.23
96.52±0.20
96.88±0.18
TOD [18]
58.10±1.95
66.56±0.36
66.26±1.22
65.51±0.75
93.17±0.87
95.27±0.07
96.07±0.09
96.50±0.12
Gradnorm [72]
63.23±1.25
66.14±1.51
67.02±1.00
66.52±0.75
94.40±0.06
94.85±0.21
95.64±0.04
95.89±0.13
CoreSet [57]
62.53±1.50
65.91±0.78
66.61±0.20
66.84±0.21
93.90±0.25
93.95±0.31
94.94±0.09
95.85±0.13
BADGE [2]
59.45±0.67
64.27±0.74
66.73±0.46
64.71±1.07
94.97±0.41
95.62±0.11
96.25±0.12
96.37±0.10
LoGo [25]
62.36±2.30
66.43±0.69
66.12±2.64
66.26±0.50
94.98±0.07
95.60±0.15
96.20±0.26
96.51±0.05
KAFAL [6]
62.34±0.3
65.36±1.15
66.26±1.22
66.24±1.31
95.06±0.17
96.08±0.07
96.76±0.11
96.92±0.04
FEAL (Ours)
65.18±0.41
67.77±1.31
68.41±1.01
68.46±0.37
95.79±0.68
96.54±0.40
97.04±0.28
97.29±0.35
• LoGo: LoGo is specifically designed to address class-
imbalance issues in federated active learning, harness-
ing insights from both global and local models. It first
performed k-means clustering with gradient embeddings
extracted from the local model. Then it applied cluster-
wise sampling to select the most uncertain sample within
each cluster, identified by the highest entropy score in the
global model.
• KAFAL: KAFAL is another sampling strategy tailored
for federated active learning with class imbalance. It em-
ploys a knowledge-specialized KL divergence, calculated
between the global and local models, to quantify the in-
formativeness of unlabeled samples for both models. For
fair comparisons in our study, we implemented KAFAL
by exclusively using the supervised loss component.
C.2. Results
Image classification.
Tab. 6 summarizes the quantitative
results of image classification.
From the second to the
fifth FAL rounds, FEAL demonstrates superior performance
over the second-best method, achieving margins of 1.95%,
0.92%, 1.39%, and 1.62% on the Fed-ISIC dataset, respec-
tively. Furthermore, on the Fed-Camelyon dataset, FEAL
maintains a consistent performance advantage, surpassing
the second-best method by margins of 0.69%, 0.46%, 0.3%,
and 0.37% in these rounds. Additional results with differ-
ent annotation budgets/ratios on the Fed-ISIC dataset are
presented in Sec. C.3.
Image segmentaion.
The mean results and standard de-
viations of Dice and HD95 metrics for the Fed-Polyp, Fed-
Prostate, and Fed-Fundus datasets are illustrated in Fig. 9,
Fig. 10, and Fig. 11, respectively. Extensive results in Fig. 9
- Fig. 11 indicate that FEAL yields superior performance on
three multi-center segmentation datasets, as evidenced by
its higher Dice scores and lower HD95 metrics. Notably,
FEAL outperforms the second-best method by the margin
of 1.78%, 0.63%, 0.89%, and 1.34% from the second to the
fifth rounds on the Fed-Polyp dataset.
C.3. Discussions
Effect of uncertainty calibration.
In addition to the ab-
lation study conducted on the Fed-ISIC dataset for classifi-
cation, we expanded our analysis to include the Fed-Polyp
dataset, specifically examining the impact of uncertainty
calibration in segmentation tasks. The results, including the
average Dice score and the corresponding standard devia-
tion, are summarized in Tab. 7. Here, U G
epi, U G
ale, and U L
ale
represent the epistemic uncertainty in the global model, the
aleatoric uncertainty in the global model, and the aleatoric
uncertainty in the local model, respectively.
As can be
seen, the optimal performance is attained when incorpo-
rating U G
epi, U G
ale, and U L
ale, demonstrating the effectiveness
of the proposed uncertainty calibration method. Further-
more, we visualize the aleatoric uncertainty in both global
and local models on the Fed-Polyp dataset in Fig 12. As
depicted in Fig 12, U G
ale and U L
ale highlight different regions
of a sample, underscoring the significance of integrating the
5
1
2
3
4
5
AL round
55
60
65
70
75
80
Dice (%)
Full
Random
Entropy (G)
TOD (G)
Gradnorm (G)
CoreSet (G)
BADGE (G)
Ours
(a) Dice of Fed-Polyp (G)
1
2
3
4
5
AL round
55
60
65
70
75
80
Dice (%)
Full
Random
Entropy (L)
TOD (L)
Gradnorm (L)
CoreSet (L)
BADGE (L)
Ours
(b) Dice of Fed-Polyp (L)
1
2
3
4
5
AL round
55
60
65
70
75
80
Dice (%)
Full
Random
Entropy (E)
TOD (E)
Gradnorm (E)
CoreSet (E)
BADGE (E)
LoGo
KAFAL
Ours
(c) Dice of Fed-Polyp (E)
1
2
3
4
5
AL round
40
50
60
70
80
HD95
Full
Random
Entropy (G)
TOD (G)
Gradnorm (G)
CoreSet (G)
BADGE (G)
Ours
(d) HD95 of Fed-Polyp (G)
1
2
3
4
5
AL round
40
50
60
70
80
HD95
Full
Random
Entropy (G)
TOD (G)
Gradnorm (G)
CoreSet (G)
BADGE (G)
Ours
(e) HD95 of Fed-Polyp (L)
1
2
3
4
5
AL round
40
50
60
70
80
HD95
Full
Random
Entropy (E)
TOD (E)
Gradnorm (E)
CoreSet (E)
BADGE (E)
LoGo
KAFAL
Ours
(f) HD95 of Fed-Polyp (E)
Figure 9. Comparison results on the Fed-Polyp dataset.
1
2
3
4
5
AL round
74
76
78
80
82
84
86
88
Dice (%)
Full
Random
Entropy (G)
TOD (G)
Gradnorm (G)
CoreSet (G)
BADGE (G)
Ours
(a) Dice of Fed-Prostate (G)
1
2
3
4
5
AL round
74
76
78
80
82
84
86
88
Dice (%)
Full
Random
Entropy (L)
TOD (L)
Gradnorm (L)
CoreSet (L)
BADGE (L)
Ours
(b) Dice of Fed-Prostate (L)
1
2
3
4
5
AL round
74
76
78
80
82
84
86
88
Dice (%)
Full
Random
Entropy (E)
TOD (E)
Gradnorm (E)
CoreSet (E)
BADGE (E)
LoGo
KAFAL
Ours
(c) Dice of Fed-Prostate (E)
1
2
3
4
5
AL round
10
12
14
16
18
20
22
24
26
HD95
Full
Random
Entropy (G)
TOD (G)
Gradnorm (G)
CoreSet (G)
BADGE (G)
Ours
(d) HD95 of Fed-Prostate (G)
1
2
3
4
5
AL round
10
12
14
16
18
20
22
24
26
HD95
Full
Random
Entropy (L)
TOD (L)
Gradnorm (L)
CoreSet (L)
BADGE (L)
Ours
(e) HD95 of Fed-Prostate (L)
1
2
3
4
5
AL round
10
12
14
16
18
20
22
24
26
HD95
Full
Random
Entropy (E)
TOD (E)
Gradnorm (E)
CoreSet (E)
BADGE (E)
LoGo
KSAS
Ours
(f) HD95 of Fed-Prostate (E)
Figure 10. Comparison results on the Fed-Prostate dataset.
1
2
3
4
5
AL round
86
87
88
89
90
Dice (%)
Full
Random
Entropy (G)
TOD (G)
Gradnorm (G)
CoreSet (G)
BADGE (G)
Ours
(a) Dice of Fed-Fundus (G)
1
2
3
4
5
AL round
86
87
88
89
90
Dice (%)
Full
Random
Entropy (L)
TOD (L)
Gradnorm (L)
CoreSet (L)
BADGE (L)
Ours
(b) Dice of Fed-Fundus (L)
1
2
3
4
5
AL round
86
87
88
89
90
Dice (%)
Full
Random
Entropy (E)
TOD (E)
Gradnorm (E)
CoreSet (E)
BADGE (E)
LoGo
KAFAL
Ours
(c) Dice of Fed-Fundus (E)
1
2
3
4
5
AL round
10
11
12
13
14
15
16
17
HD95
Full
Random
Entropy (G)
TOD (G)
Gradnorm (G)
CoreSet (G)
BADGE (G)
Ours
(d) HD95 of Fed-Fundus (G)
1
2
3
4
5
AL round
10
11
12
13
14
15
16
17
HD95
Full
Random
Entropy (L)
TOD (L)
Gradnorm (L)
CoreSet (L)
BADGE (L)
Ours
(e) HD95 of Fed-Fundus (L)
1
2
3
4
5
AL round
10
12
14
16
HD95
Full
Random
Entropy (E)
TOD (E)
Gradnorm (E)
CoreSet (E)
BADGE (E)
LoGo
KAFAL
Ours
(f) HD95 of Fed-Fundus (E)
Figure 11. Comparison results on the Fed-Fundus dataset.
6
aleatoric uncertainty in both global and locals for a thorough
assessment.
Table 7. Ablation study of uncertainty calibration on Fed-Polyp.
UG
epi
UG
ale
UL
ale
Round 2
Round 3
Round 4
Round 5
-
✓
-
68.61±0.48
73.12±2.38
75.19±1.10
78.00±1.14
-
-
✓
69.13±1.15
75.19±1.29
77.85±1.20
78.12±1.29
-
✓
✓
66.89±3.41
74.48±1.00
76.56±1.49
76.86±0.43
✓
-
-
70.61±4.22
74.45±2.29
75.07±2.42
78.25±1.29
✓
✓
-
69.41±2.17
75.18±2.48
74.66±0.87
78.91±1.04
✓
-
✓
69.29±2.51
75.93±1.41
76.74±1.08
78.28±0.67
✓
✓
✓
72.06±0.72
76.39±0.66
78.62±0.81
80.18±0.10
Input
Ground truth
𝑈!"#
$
𝑈!"#
%
𝑈!"#
$
+ 𝑈!"#
%
Figure 12. Visualization of aleatoric uncertainty on Fed-Polyp.
U G
ale and U L
ale denote the aleatoric uncertainty in global and local
models, respectively.
Effect of diversity relaxation.
An ablation study was car-
ried out on the Fed-Polyp dataset to investigate the impact
of diversity relaxation. As illustrated in Fig. 13, the optimal
performance is attained when setting the minimum neigh-
bor size to n = 10 and the cosine similarity threshold to
τ = 0.90 on the Fed-Polyp dataset.
1
2
3
4
5
AL round
60
65
70
75
80
Dice (%)
5 neighbors
10 neighbors (Ours)
15 neighbors
20 neighbors
(a) Minimum neighbor size n.
1
2
3
4
5
AL round
60
65
70
75
80
Dice (%)
=0.80
=0.85
=0.90 (Ours)
=0.95
(b) Similarity threshold τ.
Figure 13. Ablation study of diversity relaxation on Fed-Polyp.
Effect of evidential model training.
We conducted ex-
periments to compare the evidential loss (L in Eq. 9) against
the cross-entropy loss (CE) on two classification datasets
and against dice loss (Dice) on three segmentation datasets.
As summarized in Tab. 8, the proposed evidential model
training yields an average performance gain of 1.03% on
the Fed-ISIC dataset, 0.29% on the Fed-Camelyon dataset,
1.16% on the Fed-Polyp dataset, 1.17% on the Fed-Prostate
dataset, and 0.36% on the Fed-Fundus dataset.
Table 8. Ablation study of loss function.
Dataset
Loss
Round 2
Round 3
Round 4
Round 5
Fed-ISIC
CE
64.28±1.64
66.69±0.95
67.32±1.16
67.40±0.22
L
65.18±0.41
67.77±1.31
68.41±1.01
68.46±0.37
Fed-Camelyon
CE
95.24±0.03
96.21±0.04
96.80±0.07
97.26±0.06
L
95.79±0.17
96.54±0.08
97.04±0.02
97.29±0.02
Fed-Polyp
Dice
70.14±0.10
75.77±0.67
77.23±0.21
79.48±0.62
L
72.06±0.72
76.39±0.66
78.62±1.44
80.18±0.10
Fed-Prostate
Dice
81.43±0.75
84.50±1.02
85.32±0.60
86.50±0.59
L
82.94±0.04
85.29±0.31
86.77±0.29
87.42±0.21
Fed-Fundus
Dice
88.11±0.3
89.68±0.22
89.84±0.23
90.15±0.19
L
88.63±0.3
89.72±0.39
90.28±0.13
90.58±0.02
Effect of trade-off weight λ.
We additionally conducted
experiments to determine the optimal value for the hyper-
parameter λ on the Fed-Polyp dataset, choosing from the
candidate set {1e−5, 5e−5, 1e−4, 5e−4, 1e−3}. The find-
ings, summarized in Tab. 9, reveal the optimal performance
is achieved when λ = 1e−4 for the Fed-Polyp dataset.
Table 9. Ablation study of trade-off weight λ on Fed-Polyp.
λ
Round 2
Round 3
Round 4
Round 5
1e−5
70.91±1.89
76.27±0.36
75.98±1.09
78.58±1.85
5e−5
70.27±2.64
74.68±1.59
76.82±1.00
78.26±0.76
1e−4
72.06±0.72
76.39±0.66
78.62±1.44
80.18±0.10
5e−4
70.90±1.82
75.59±2.02
77.63±0.84
79.76±1.08
1e−3
69.78±1.64
74.54±2.56
76.92±1.91
77.64±0.88
Effect of annotation budget Bk.
(1) Fixed-number. To
validate the effectiveness and robustness of FEAL, we fur-
ther analyzed the impact of annotation budget Bk on the
Fed-ISIC dataset. We conducted R = 10 rounds of FAL
with three configurations of Bk, i.e. Bk = {250, 500, 750},
for the Fed-ISIC dataset.
As depicted in Fig. 14(a)-(c),
FEAL consistently outperforms other counterparts across
all three annotation budget configurations Bk, demonstrat-
ing its effectiveness and resilience. (2) Fixed-ratio. Fur-
thermore, considering the imbalanced dataset sizes among
local clients, we also implemented the fixed-ratio strategy
to annotate 10% of the samples for each client in every
FAL round. The results depicted in Fig. 14(d) demonstrate
that FEAL surpasses other competing methods even under
the fixed-ratio setting. Remarkably, both fixed-number and
fixed-ratio strategies exhibit similar performance in later
rounds, indicating that FEAL is robust against variations in
dataset sizes across local clients.
7
1
2
3
4
5
6
7
8
9
10
AL round
40
45
50
55
60
65
70
BMA (%)
Full
Random
Entropy
TOD
Gradnorm
CoreSet
BADGE
LoGo
KAFAL
Ours
(a) Annotation budget Bk = 250
1
2
3
4
5
6
7
8
9
10
AL round
40
45
50
55
60
65
70
BMA (%)
Full
Random
Entropy
TOD
Gradnorm
CoreSet
BADGE
LoGo
KAFAL
Ours
(b) Annotation budget Bk = 500
1
2
3
4
5
6
7
8
9
10
AL round
40
45
50
55
60
65
70
BMA (%)
Full
Random
Entropy
TOD
Gradnorm
CoreSet
BADGE
LoGo
KAFAL
Ours
(c) Annotation budget Bk = 750
10
20
30
40
50
60
70
80
90
Annotation proportion (%)
45
50
55
60
65
70
BMA (%)
Full
Random
Entropy
TOD
Gradnorm
CoreSet
BADGE
LoGo
KAFAL
Ours
(d) Annotation budget Bk = Nk
10
Figure 14. Ablation study of annotation budget Bk on Fed-ISIC.
Analysis of Dirichlet simplex.
We analyzed the Dirichlet
simplex on a subset of the Fed-ISIC, specifically encom-
passing three classes: MEL, BCC, and BKL. In Fig. 15 and
Fig. 17, the unlabeled samples are predicted to belong to
MEL, BCC, and BKL from the first to the third rows, re-
spectively. Within the Dirichlet simplex, a concentrated red
region indicates low epistemic uncertainty Uepi, while a red
region near the corner suggests a low aleatoric uncertainty
Uale. As depicted in Fig. 15 and Fig. 16, when selecting
samples with FEAL, the Dirichlet distribution becomes nar-
rower and more concentrated for unlabeled local data from
the first to the fifth FAL round. This trend suggests a reduc-
tion in epistemic uncertainty within the global model, vali-
dating the effectiveness of calibrated evidential sampling in
mitigating domain shifts. Moreover, starting with an identi-
cal set of labeled samples, we tracked the selection of sam-
ples in the second FAL round utilizing multiple FAL meth-
ods. The resulting Dirichlet simplexes, corresponding to
these different methods, are depicted in Fig. 17. A criti-
cal observation from this analysis is that the Dirichlet dis-
tribution of samples selected via FEAL exhibits a notably
broader spread across the simplex. This broader spread in-
dicates that FEAL effectively models the global model’s
understanding of local data and prioritizes the selection of
samples characterized by high epistemic uncertainty.
C.4. Evaluation Time Costs
All experiments were conducted using an NVIDIA GeForce
RTX 2080Ti GPU. The average time cost for one round of
data selection across all clients is presented in Tab. 10. Note
that we reported the time cost for the ensemble settings of
Entropy, CoreSet, TOD, Gradnorm, and BADGE.
Round 1
Round 2
Round 3
Round 4
𝑈!"#(𝒙, 𝜽) = −5.03
MEL
BCC
BKL
𝑈!"#(𝒙, 𝜽) = −4.03
MEL
BCC
BKL
𝑈epi(𝒙, 𝜽) = −4.42
MEL
BCC
BKL
MEL
BCC
BKL
𝑈!"#(𝒙, 𝜽) = −5.55
MEL
BCC
BKL
𝑈epi(𝒙, 𝜽) = −6.22
Round 5
MEL
BCC
BKL
MEL
BCC
BKL
MEL
BCC
BKL
MEL
BCC
BKL
MEL
BCC
BKL
𝑈!"#(𝒙, 𝜽) = −3.81
𝑈!"#(𝒙, 𝜽) = −4.25
𝑈!"#(𝒙, 𝜽) = −4.84
𝑈!"#(𝒙, 𝜽) = −5.26
𝑈!"#(𝒙, 𝜽) = −5.48
MEL
BCC
BKL
MEL
BCC
BKL
MEL
BCC
BKL
MEL
BCC
BKL
MEL
BCC
BKL
𝑈!"#(𝒙, 𝜽) = −3.83
𝑈!"#(𝒙, 𝜽) = −4.75
𝑈!"#(𝒙, 𝜽) = −5.01
𝑈!"# 𝒙, 𝜽= −5.33
𝑈!"#(𝒙, 𝜽) = −6.02
Figure 15. Visualization of the Dirichlet simplex for unlabeled
samples across five FAL rounds using FEAL.
MEL
BCC
BKL
Round 1
MEL
BCC
BKL
Round 5
Red region ! Spread: more concentrated →lower aleatoric uncertainty (𝑈!"#)
Location: closer to corner →lower epistemic uncertainty (𝑈#$%)
Figure 16. Comparison of the Dirichlet simplex for unlabeled sam-
ples in the first and fifth FAL round using FEAL.
MEL
BCC
BKL
Entropy
MEL
BCC
BKL
CoreSet
MEL
BCC
BKL
LoGo
MEL
BCC
BKL
KAFAL
MEL
BCC
BKL
Ours
MEL
BCC
BKL
MEL
BCC
BKL
BKL
BKL
BKL
MEL
BCC
MEL
BCC
MEL
BCC
BKL
MEL
BCC
BKL
MEL
BCC
BKL
MEL
BCC
BKL
MEL
BCC
BKL
MEL
BCC
Figure 17. Visualization of the Dirichlet simplex for samples se-
lected in the second FAL round using multiple sampling strategies.
Table 10. Time cost (in seconds) for one round of data selection.
Method
Fed-ISIC
Fed-Camelyon
Fed-Polyp
Fed-Prostate
Fed-Fundus
Entropy
23.49
189.97
8.11
14.20
8.39
CoreSet
81.27
340.24
9.68
14.56
8.30
TOD
23.26
331.01
14.50
55.71
28.53
Gradnorm
1126.95
5335.42
72.49
128.49
67.42
BADGE
24.51
178.66
68.12
119.74
69.17
LoGo
96.22
378.81
86.52
80.21
43.20
KAFAL
23.27
175.95
14.54
13.35
7.45
FEAL (Ours)
21.76
191.71
14.88
13.59
13.98
8
D. Investigations on OCTA Datasets
D.1. Experimental Settings
Dataset.
We further validated the effectiveness of FEAL
on another medical image dataset OCTA-500 [33] for foveal
avascular zone (FAZ) segmentation. The OCTA-500 dataset
comprises two subsets, namely OCTA 3M and OCTA 6M,
each providing a distinct field of view (FOV). Specifically,
the field of views (FOV) for OCTA 3M is 3mm × 3mm ×
2mm, while that for OCTA 6M is 6mm × 6mm × 2mm.
In our study, we regarded each subset as an individual lo-
cal dataset within federated scenarios and then divided each
local dataset into training and test sets using an 8:2 ratio.
Note that we utilized the projection maps between the In-
ternal Limiting Membrane (ILM) layer and the Outer Plexi-
form Layer (OPL) in experiments. Details of the OCTA-500
dataset are provided in Tab. 11, while illustrative samples
from both data sources are shown in Fig. 18.
Table 11. Details of multi-center datasets utilized in our study.
Dataset
Data source
# Train
# Test
Resolution
OCTA-500
Client 1: OCTA 3M [33]
160
40
304×304
Client 2: OCTA 6M [33]
240
60
400×400
(a) Client1: OCTA_3M
(b) Client2: OCTA_6M
Figure 18. Illustrative samples from each data source within the
OCTA-500 dataset.
Evaluation metrics.
In line with the aforementioned
three image segmentation datasets, we employed the Dice
score and the 95% Hausdorff Distance (HD95) as metrics
to quantify segmentation results.
Implemental details.
We conducted R = 5 rounds of
FAL, which comprises federated model training and data
annotation. For federated model training, We adopted U-
Net [39, 56] as the backbone and employed the ReLU(·)
as the non-negative activation function A(·) for both global
and local models. We trained local models using the Adam
optimizer [26] with a learning rate of 5e−4 and a weight
decay of 1e−5. The federated learning process comprises
T = 100 rounds of communication to attain a robust global
model, with each local training session lasting for 1 epochs.
Regarding data annotation, the annotation budget Bk was
set to 20 for the OCTA-500 dataset.
D.2. Results
We compared FEAL with eight state-of-the-art FAL ap-
proaches and present the results in Fig. 19. The results in
Fig. 19 verify the effectiveness of FEAL on the OCTA-500
dataset, characterized by superior Dice scores and lower
HD95 metrics. It is noteworthy that FEAL achieves a Dice
score of 94.18% while utilizing only 24% of annotated sam-
ples, which is equivalent to 99.25% of the fully supervised
performance.
1
2
3
4
5
AL round
90
91
92
93
94
95
Dice (%)
Full
Random
Entropy (E)
TOD (E)
Gradnorm (E)
CoreSet (E)
BADGE (E)
LoGo
KAFAL
Ours
(a) Dice of OCTA-500 (E)
1
2
3
4
5
AL round
6
8
10
12
14
16
18
20
HD95
Full
Random
Entropy (E)
TOD (E)
Gradnorm (E)
CoreSet (E)
BADGE (E)
LoGo
KAFAL
Ours
(b) HD95 of OCTA-500 (E)
Figure 19. Comparison results on the OCTA-500 dataset.
E. Discussion with EDL and DUC
Discussion with EDL.
While Sensoy et al. [58] leveraged
evidential deep learning (EDL) to quantify the overall un-
certainty of training samples and alleviate model overcon-
fidence, our FEAL differs significantly in both objectives
and approaches. Specifically, we employed evidential deep
learning to decompose the overall uncertainty into aleatoric
and epistemic components, aiming to measure the uncer-
tainty of unlabeled samples and reduce annotation costs in
federated learning scenarios with domain shifts.
Discussion with DUC.
Although DUC [76] employs ev-
idential deep learning to differentiate between aleatoric un-
certainty and epistemic uncertainty, there are notable dif-
ferences in both objectives and methods compared to our
FEAL. In terms of objectives, DUC aims to enhance do-
main adaptation by annotating partial samples from the tar-
get domain, whereas FEAL focuses on reducing annotation
costs for local clients in realistic medical federated scenar-
ios. Regarding informativeness measurement, DUC evalu-
ates the data informativeness based on a model trained on
the source domain, whereas FEAL quantifies data informa-
tiveness leveraging both global and local models in feder-
ated scenarios. Furthermore, DUC is an uncertainty-based
method that overlooks the diversity of selected target sam-
ples. By contrast, FEAL identifies and annotates samples
considering both uncertainty and diversity measures.
9