Adapt via Bayesian Nonparametric Clustering: Fine-Grained Classification for Model Recycling Under Domain and Category Shift
Authors: Zeya Wang
Longwen Shang
Yang Ni
Chenglong Ye
Venue: Accepted by TMLR ()

Abstract: Recycling pretrained classification models for new domains, known as Source-Free Domain Adaptation (SFDA), has been extensively studied under the closed-set assumption that source and target domains share identical label spaces. However, this assumption does not hold when unseen classes appear in the target domain. Addressing this category shift is challenging, as unknown target classes usually arise with no prior knowledge of their identities or number, and becomes particularly difficult in the source-free setting, where access to source data is unavailable. Most existing methods treat all unknown classes as a single group during both training and evaluation, limiting their capacity to model the underlying structure within the unknown class space. In this work, we present Adapt via Bayesian Nonparametric Clustering (ABC), a novel framework designed for SFDA scenarios where unknown target classes are present. Unlike prior methods, ABC explicitly achieves fine-grained classification of unknown target classes, offering a more structured vision of the problem. Our method first identifies high-confidence target samples likely to belong to known source classes. Using these as guidance, we develop a guided Bayesian nonparametric clustering approach that learns distinct prototypes for both known and unknown classes without requiring the number of unknown classes a priori, and assigns target samples accordingly. We further introduce a training objective that refines the source model by encouraging prototype-based discriminability and local prediction consistency. Experiments show that our method achieves competitive performance on standard benchmarks while simultaneously providing effective clustering of unknown classes.

Published in Transactions on Machine Learning Research (04/2026)
Adapt via Bayesian Nonparametric Clustering: Fine-Grained Classification for Model Recycling Under Domain and Cate- gory Shift
Zeya Wang"
zeyo, wangowan@@ullg edu
Dr. Bing Zhang Department of Statistics University of Kentucky
Longwen Shang
longwensheng@@uric..m
Department of Mathematics and Statistics University of Vicloria
Yang Ni
yang. wwng..ni@toouttnn.tee. utw.asiitttess... eduu
Department of Statistics and Data Sciences The University of Texas at Austin
Chenglong Ye
chenglong,, ye @uky edu
Dr. Bing Zhang Department of Statistics University of Kenbucky
Reviewed on OpenReview: https: // openreview. net/ forum? id= J5B4yt 7C37
Abstract
Recycling pretrained classification models for new domains, known Source-Free Domain Adaptation (SFDA), has been extensively studied under the closed-set assumption that source and target domains share identical label spaces. However, this assumption does not hold when unseen classes appear in the larget domain. Addressing this calegory shift is challenging, as unknown target classes usually arise with no prior knowledge of their identities or number, and becomes particularly difficult in the source-free setting, where access to source data is unavailable. Most existing methods treat all unknown classes as single group during both training and evaluation, limiting their capacity to model the underlying structure within the unknown class space. In this work, present Adapt via Bayesian Nonparametrie Clustering (ABC), novel framework designed for SFDA scenarios where unknown target classes are present. Unlike prior methods, ABC explicitly achieves fine-grained classification of unknown target classes, offering a more structured vision of the problem. Our method first identifies high-confidence target samples likely to belong to known source classes. Using these as guidance, we develop a guided Bayesian nonparametric clustering approach that learns distinct prototypes for both known and unknown classes without requiring the number of unknown classes priori, and assigns target samples accordingly. We further introduce training objective that refines the source model by encouraging prototype- based discriminability and local prediction consistency. Experiments show that our method achieves competitive performance on standard benchmarks while simultancously providing effective clustering of unknown classes.
"Corresponding author. Address: 725 Rose Street, Lexington, KY 40536, United States. Email: zeya. kanghuky.

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Published in Transactions on Machine Learning Research (04/2026)
1 Introduction
Deep learning models usually roquire large labeled datascts, but due to costly annotation (Ganin et al., 2016), labeled data in source domain is often used to train models for uulabeled data in target domains. However, due to domain shift (Torralba & Efros 2011), these models often fail to generalize, motivating the development of Unsupervised Domain Adaptation (UDA) techniques to bridge the gap. Traditional UDA methods typically assume no category shift, meaning the label sets of the source and target domains, denoted as C, and Ce: are identical, i.e., C, = C,, a setting known as closed-set domain adaplation. With the progress of UDA, increasing attention has been paid to the more realistic category shift scenarios that relax this assumption, allowing C, 2 Ct2 and thus permit the presence of unknown target classes. While many methods have been proposed to handle different category shift settings, most still follow traditional UDA approaches that require access to source data. This requirement limits the practicality of UDA methods due to factors such as privacy concerns, bandwidth constraints in distributed systems, and the lack of access to source data, for example when it is sensitive, too large to transmit, or lost due to corruption (uuduu et al.) 2020). In such cases, is desirable to recycle the source model without access to the original source data. These challenges have motivated the development. of sourco-free domain adaptation (SFDA) methods, which perform UDA without the source data. Despite their potential, existing SFDA research has primarily focused the closed-set setting. More realistic scenarios with label mismatches, where unknown target classes may be present (as illustrated in Figure 1. remain underexplored due to their increased complexity and ambiguity, with only a few works addressing these challenges (Liang et al. 2021 Qu et al. 2023 Liang et al. 2020
While these prior works have demonstrated effective performance in classifying known classes and effectively detecting samples from unknown classes, they typically frame the problem within a standard classification setting, treating all unknown classes as a single unified "unknown" category. However, collapsing all unknown classes into one label risks overlooking the latent structure within them, potentially hindering transfer learning performance. Furthermore, with the growing interest and development in deep clustering (Min et al. 2018), where unlabeled samples are automatically grouped based on their learned embeddings, there is increasing practical value in partitioning samples from unknown classes into finer-grained clusters. This not only enhances interpretability, but also supports downstream tasks that benefit. from more gramular classification. For example, in medical imaging, it may reveal previously unobserved patient subpopulations when adapting a diagnosis model to data from a new cohort; in robotics, it could help systems distinguish novel sensory patterns in unfamiliar settings; and in security, it can facilitate identifying and separating unseen attacks anomalous bchaviors when deploying a rocognition model to new environment, enabling more effective handling of different unknown patterns.
A promising strategy is to integrate clustering into the adaptation process, enabling the model to simultaneously classify known classes and cluster unknown samples (i.e., samples from unknown classes) into distinct latent groups. This joint (ask presents additional challenges: not only is the identity of unknown classes unavailable during adaptation, but the number of unknown classes is also unknown. The number of ways to cluster n samples into k non-empty subsets is given by the Stirling number of the second kind S(n, k), whercas allowing unknown number of subsets yields the Bell number B,, Ek= S(n,k), k)), which grows much more rapidly with n. Traditional methods that tune the number of clusters K (e.g., using internal measures such as the Silhouette score [Rousseeuw] 1987) or Elbow methods (Thorndike) 1953)) often require repeatedly refitting the clustering model across a set of candidate K values, which can introduce non-negligible computational overhead and make integration into the SFDA pipeline less soraight More critically, such tuning procedures require defining a scarch space for the number of clusters K, e.g., for a grid search, which relies heavily on prior knowledge of the true K and whose range depends on the dataset scale. For instance, target-domain datasets with many classes demand much broader search ranges than those with only a few, making grid design not very practical for real-world scenarios where prior knowledge of the number of target-domain classes is usually unavailable.
In this paper, we propose a novel algorithm to Adapt via Bayesian Nonparametric Clustering (ABC), which simultancously classifies known-class samples and clusters unknown ones, while recycling a source model when unknown classes arise in the new domain. ABC first identifies target samples with high confidence of belonging to known classes. Using these detected samples as anchors, a guided Bayesian nonparametric clustering (BNC)
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Source Domain
Source-private classes
Bike
Classification Model
Bird
Domain Shift
Horse
Sore Shift
Recycling
Bi
Dog
Car
x
Classification
À
Umbrella
x
x
Shared classes
Target-private classes
Clustering
Target Domain
Figure 1: An illustration of the SFDA problem with unknown target classes (with both source- and target- private classes displayed) and the goal of our method.
model is introduced to assign the remaining samples either to existing known classes or to newly formed unknown classes, while simultancously learning prototypes for all classes, both known and unknown. We further incorporate a prototype regularizer, which aligns samples with their assigned protolypes, and a local consistency regularizer, which promotes prediction agreement within local neighborhoods, together facilitating iterative refinement of the source model for adaptation to target samples. In our model, the BNC component automatically learns the number of unknown classes, allowing their structure to emerge posteriori and eliminating the need for costly grid searches to determine K. We conduct extensive experiments and analyses, and demonstrate its effectiveness and solid performance compared to competitive baselines.
2
Related Work
UDA methods improve the generalization ability of deep neural networks across different domains and mitigate the performance degradation caused by domain shift.
Unsupervised Domain Adaptation (UDA):
Among the most widely adopted approaches are discrepancy minimization methods (ettoods(zzeng et al. 2014 Long
ct al.
2015 Sun et al. 2016 Long et al.) 2016
2017 Chen et al. 2019) and adversarial training techniques
[Ganin & Lempitsky 2015 Ganin et al. 2016 Tzeng et al. 2017 Zhang et al. 2018 Wang et al.
2020
To reduce domain shift, discrepancy minimization methods introduce a divergence measure between data
distributions across domains and minimize it, while adversarial training, inspired by generative adversarial
networks (GANs) Goodfellow et al. 2014 leverages a domain discriminator to classify samples as originating
from the source or target domain, thereby encouraging the learning of domain-invariant features (Ganin
& Lempitsky 2015 Ganin et al.
2016). More recent research has begun to address the UDA problem
under category shift. Research has examined partial al. 2018a
Wang al. 2020 Li et al.
2021
open-set<Lu et al.
2022 Panareda Busto & Gall 2017 Saito al. 2018 Jang et al. 2022 Li et al. 202
and open-partial domain adaptation sccnarios(Yon et al. 2019 Li et al. 2021). Furthermore, there is a
growing interest in developing general methods that can handle different settings (Cenn et al. 2022 Saito et al. 2020 Li et al.) 2021). Many of these approaches detect samples from unknown classes by identifying uncertain instances based on indicators derived from prediction outputs, such as entropy values (You al. 2019: Jang et al. 2022). Other approaches leverage chustering based strategies to identify shared classes.
For example, Domain Consensus Clustering [Li al. 2021 clusters samples in both source and target.
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domains and then evaluates semantic consensus among cluster centers to identify shared classes. Global and Local Clustering (Qu et al. 2023) performs one-vs-all clustering by comparing target samples to source-class prototypes and negative prototypes obtained via clustering, assigning known-class labels based on higher similarity to source prototypes. While these mothods provide flexible clustering- based frameworks that aid identifying shared classes, most still rely on standard clustering algorithms like KMeans (MacQueen et al. 1967) and require repeated refitting across candidate K values.
Source-free Domain Adaptation (SFDA): SFDA focuses on adapting model pre-trained on the source domain to target domain without requiring access to the source data. Many methods have been proposed to address this problem, often concentrating on conventional settings where no category shift is assumed between source and target domains (Liang et al. 2020 Qu et al. 2022 Yang et al.) 2021b Ding ct al. 2022 Yang et al. 2022). Some approaches utilize the source model to extract anchor features and then assign pseudo-labels based on these anchors (Ding et al. 2022.. while others adapt. the source model by promoting consistency among local neighborhood features the target domain (Yang ct al. 2022). ) Only few works have tackled SFDA under category shift conditions, where larget classes may not completely overlap with source classes (Qu et al. 2023 Kundu et al., 2020 Liang et al. 2021). Although these methods represent significant progress, they often treat all unknown classes uniformly in both modeling and evaluation, and seldom explicitly explore the clustering behavior of samples from unknown classes in the target domain.
Bayesian Nonparametric Clustering (BNC): Clustering aims to group similar observations into a fixed number of clusters. Common methods like K-Means and finite mixture models require specifying the number of clusters, K, in advance [JAIN et al. 1999; Reynolds, 2015). While internal validation approaches can help tune this parameter by evaluating internal metrics across different values of K, including in deep clustering settings (Wang & Ye 2026), they often require repeated model refitting, selection of evaluation criteria, and careful design of a search range. BNC addresses this limitation by inferring the number of clusters a8 part of the model (Hjort et al.] 2010), allowing clustering without predefining the number of clusters. BNC encompasses a flexible family of mixture models, such as Dirichlet Process Mixtures (Ferguson 1973 Antoniak 1974), Pitman Yor Process Mixtures (Pitman & Yor 1997], and Normalized Generalized Gamma Process Mixtures (Lijoi et al., 2207], which can approximate complex data distributions. Advances in scalable inference techniques, such variational inference (Blei & Jordan
2006 Ni et al. 2020b) and consensus Monte Carlo Ni et al. 2020c ab, have enabled BNC to handle large datasets, making it applicable in large-scale scenarios. Recent advances have integrated BNC with deep neural networks, enabling automatic discovery of the number of clusters when clustering high-dimensional data (ang et al.) 2021 Ronen et al. 2022). Together, these developments make BNC accessible to a wide range of large-scale and high-dimensional data settings. Compared to conventional clustering strategies in SFDA methods such as Domain Consensus Clustering and Global and Local Clustering, BNC offers clear advantage: it can directly estimate the number of unknown target-domain classes while clustering, eliminating the need for repeated model refitting or manual grid scarches over K. This allows the unknown class structure to emerge a posteriori, reduces computational overhead, facilitates seamless integration into SFDA pipelines, and makes the approach more robust to datasets where the number of unknown classes varies widely. Unlike other clustering- based approaches, which primarily use clustering to assist in identifying shared classes, our method leverages BNC to directly discover individual unknown classes, supporting more precise and fine- tha-ggr adaptation.
3 Methodology
In SFDA, neither source data X,, source labels V)., nor target labels }/ are accessible during adaptation. To address scenarios with unknown classes, consider the setting where the source and target class sets C. and C, satisfy C2 n C, * 0, and C, \ C, + 0. For clarity, we define C = C, nC as the common label space, = \ C. as the source-privale label space, and C; c C, as the targel-privale label space. We will refer to the classes within C, as known classes and those within C; as unknown classes. While prior work typically treats classes in Ci as a single category Cunk: we aim to distinguish these classes individually, denoting the sot of discovered unknown classes by Cg. Our learning objective is twofold: to classify target instances as the estimated label of C if they belong to known classes, and to assign them to discovered groups Cj if they
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Adapt via Bayesian Nonparametric Clustering (ABC)
Model Reeyeling with Fine- Grained Classification
High-confidence samples
High-confidence Known-Class Samples Detection
2 D
Guided BNC (Unknown class discovery)
Predicted labels
Uncertain samples
Go
Yt
Target samples
Source model g
dg
G
x, (Unlabeled)
Φ
Training objective
Prototypical Regularization Eyeg
H4, 4
y
ZE
Back-propagate
Local Prediction Consistency
Regularization Lioc
Target samples
Features 2,
Known-class Unknown-class Boundary (Known)
Boundary (Unknown)
Prototypes
Source model f
C1 C2
Figure 2: An overview of Adapt via Bayesian Nonparametric Clustering (ABC).
belong to unknown classes. The overall workflow of the proposed algorithm is illustrated in Figure 2 detailed steps described the following sections.
with
3.1 High-Confidence Common Class Samples
We first focus on detecting samples most likely to belong the common label C. Let the source model be denoted é = o f, where f represents the feature extractor mapping 2; X, to feature representation 2, E Ih and is the classifier that maps to source classes C. = 21, ... Ke), where K2 represents the number of source classes. Let w m. denote the weight matrix of the classifier g, where cach column w E RR corresponds to the weight vector associated with source class k. Each w can be interpreted as an anchor representing the k-th source class the feature space, and has been leveraged to initialize source cluster centers for spherical k-means clustering previous SFDA methods, where target instances are assigned source classes by maximizing cosine similarity to these centers (Ding al., 2022). The cosine &, Twg
similarity between a target feature 2, and cach source class anchor wy. defined as cos(2;, wx) I @ measures proximity to known class k. Consequently, the maximum similarity over all source classes provides an interpretable measure of the sample's affiliation with the known classes. A low maximum similarity indicates the sample may not. belong to any known class.
The source model's output often used to initialize the detection and classification of known-class samples and can provide informative indicators, denoted as K, for identifying known-class versus unknown-class the discussion above, define K;
samples (Jang al.) 2022 Qu et al.] (023). Building max cos(2,, wx) and model its marginal distribution using mixture of two Beta distributions, a choice that is both natural and effective in many prior UDA work targeting unknown classes.
p (x) #known (N E C.) Tanknownp (x y $ C.)
(1)

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where Tknown and Tunknown represent the probabilities P(y E C.) and P(y & C,); respectively. Given this Beta mixture model, we can est estimate the posterior probability P(y E C2 k), which represents the confidence that a sample belongs to the source classes. The parameters of the Beta distributions, along with Tknown and Tunknown, are estimated by fitting the Beta mixture model using the Expoctation-Mxximizatiie (EM) algorithm (Arazo et al.j 2019 Jang et al. 2022). Once the parameters are obtained, the posterior probability
Ply E C. k) is given by: C, x) Tknowap (N| y E C.) /[TkuowuPP (N y E C.) + Tunknown (r: & C.)]. The decision boundary P(y E C. ()) > P(y & C. k), which indicates that the posterior probability of belonging to the known classes exceeds that of the unknown classes, corresponds to P(y E C. R) > 0.5. Consequently, we can identify high-confidence common-class samples by applying a threshold P(u CC, <) > 8 with 0 0.5 as the default. The threshold å can be slightly adjusted around 0.5 using an auto-tuning strategy, and the details of this implementation will be discussed in Section 4.3 For samples that meet this criterion, we assign their predicted label to the class with the highest cosine similarity, computed as arg max; cos wg). We denote the identified high-comfidence samples and their estimated labels as X," and ".M", respectively. Based on D we can derive estimate of the common label set C, denoted as C. The remaining target samples, for which the source-class confidence is insufficient, are considered as uncertain samples and denoted by N, We use 2," and z to denote the embeddings extracted by the encoder corresponding to X," and X, respectively.
3.2 Guided Bayesian Nonparametric Clustering
Uncertain samples may include both instances outside the common label set (i.e., from larget-private label space) and those within that received low-confidence predictions. High-confidence common-class samples can serve anchors references to guide the clustering of uncertain samples, making the problem more aligned with weakly-supervised clustering. Furthermore, clustering samples from unknown classes requires a method that does not rely on a predefined number of clusters, as this information is usually not available. To this end, we propose a guided Bayesian nonparametric clustering (GBNC) framework that automatically discovers previously unseen classes while simultancously classifies samples into known classes.
Given the embeddings 2 = (aff...., > of uncertain samples with size ny, we consider leveraging Bayesian nonparametric clustering (BNC) technique to estimate the corresponding cluster labels yy = {2f ........ .....,,, J as it can both handle unknown class discovery and incorporate weak supervision effectively. Specifically, we build our model on the Dirichlet Process Mixture (DPM) framework, widely used Bayesian nonparametric approach known for its simplicity of implementation and extensive litcrature support. The DPM-based formulation naturally accommodates a flexible and palentially unbounded nunber of clusters, allowing the model to adjust automatically to the number of clusters as the data grows. Our method can also be extended to other Bayesian nonparametric mixture models, such as Pitman-Yor process mixtures and Normalized Generalized Gamma process mixtures, which, like the DPM, allow the number of clusters to emerge from the data. The Dirichlet Process (DP) is stochastic process that defines a distribution over distributions, meaning that each draw from it is itself probability distribution. A key property of the DP is its almost surely discrete realizations, which naturally induces clustering by allowing parameter sharing among individual data points and eliminates the need to specify the number of clusters in advance. A DPM constructed from the observed data 2 can be formulated within a Bayesian hierarchical framework,
2 ~ p(z)(m), WGG GG G~ DD Go).
p(: | m)) denotes the likelihood function, following a probability distribution parameterized by th where ne is drawn from -idiittributed prior G. The DP prior is characterized by the concentration parameter a and the base distribution Go, which specifies prior probability distribution over the parameters. The base distribution Go is typically chosen to be conjugale to the likelihood to make the inference tractable and thus simplify computation. Due to the discrete nature of G, multiple 7, associated with different observations may take the same value, naturally forming clusters. Cluster assignments arise from these shared values, meaning that v = =y when 7);- = ni- The concentration parameter a is directly related to the prior expected number of clusters, which can be set in noninformative manner, as discussed in our Section 4.3
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We denote the labels generated in Section 3.1 for the high-confidence samples S {0f ..... Dns l where is their number. These labels are assumed to be reliably assigned to known classes and are therefore treated as fixed. Accordingly, for the embedddings 2 = {x] "..;"...,,....... -ny } we can directly model their distribution given these fixed labels as 2 ~ p(2;" (1 where Tiz denotes the parameters associated with
the cluster corresponding to the predicted label v." Let (c] denote the mumber of estimated common classes, i.e, the number of unique classes in D To address the potential mismatch in cluster indices between D and V we assume that all 0f" take values from the index set (1,2...., |C]}. In our experiments, we include an additional step to align and remap the estimated labels 5 to this index range, facilitating the subsequent prototype-base based regularization. Further details on this step are provided in Appendix [B]
2 the hierarchical model can be reformulated as an infinite mixture model, as in Equation A2 also known as the stick- breck-breaking representation (with more details in Appendix A). We then integrate this representation with the distribution of M to yield:
By marginalizing out G Equation
2 IV. U k =< (nt),,))).... of ~ (egh)gg)) mhe Go
(3)
of | C,)(T)) क (T,, T2, " aaa ".),, Th Uk II uj); Un Beta(l,
where is a probability vector over clusters for k- 1,2, ..... The categorical distribution Cat((T) assigns cluster memberships to the uncertain samples with probabilities Ply = = = -kk Beta(.) denotes the beta distribution.
We model the mixture components using a multivariate Gaussian distribution, p(-Int) NT-1UR,, A&), where Aş is the inverse covariance matrix (i.c., precision matrix). While deep emboddings may deviate from idcal normality, Gaussian mixture models are flexible, can approximate a wide range distributions ions in practice, and have been widely used in deep clustering literature (Wang & Jiang [018 Wang et al. 2021 Ronen et al., 2022). We adopt conjugate Normal-Wishart prior, Go = (uels, 7Ax) W(Ag 10, S2), where is scaling lactor, b is the degrees of freedom, and Ω is the scale matrix. The overall model is therefore parameterized by {uk, (Uk,/A; A& )= and latent cluster labels {vf" ) The constructive stick-breaking representation allows us to derive a tractable joint distribution for posterior estimation. For computational efficiency, we choose Variational Bayes (VB) to approximate the posterior of these parameters. The joint probability distribution of all random variables can be factorized as follows, where boldsace symbols denote vectorized forms of the corresponding variables in Equation
"," ") p(z" Y .H, A)p((" |,A)p(YY [))(())(( A)p(A)
(4)
The goal of VB to find a variational distribution that minimizes the Kullback Leibler (KL) divergence to
the true posterior. We assume fully factorized variational family, as in Equation which allows us to apply
mean-field approximation to yield tractable updates in our VB implementation (Bishop & Nasrabadi 2006).
K--1
Ry
II
((v)) II g( A&) II ( )
(5)
where g(vx), q(u, As), and q(vl') denote the variational distributions for the corresponding variables and form the factors of the factorized variational distribution. This structure enables efficient optimization via coordinate ascent. Following the standard approach of applying a truncated stick-breaking representation in VB for DPMs (Blei & Jordan 2006), we truncate the stick-breaking process at level K such that q(UK- = 1) = 1. The value K* serves as a practical upper bound, fundamentally different from the number of clusters K in tuning- based methods which is repeatedly adjusted, and consistent results can be expected with any sufficiently large K* (o.g., 100). In our model, the variational distributions are specified as: q(v))= Beta(uy, 771. 782), q(p,, A&) N(uu (mg TgAx) W WAAlcc Dx), and q(v!") = Cat(()), where Φi = (da, ..). The variational parameters {me, Tky Ck. DRy Tai, n2)x and (dx) are updated via the VB
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algorithm. Both the full conditional and variational distributions belong to the exponential family, allowing the variational distributions for the parameters to be derived from their full conditionals (Blei & Jordan 2006). Building on this, we derive our VB algorithm. Let ng =>:= ( = k). The iterative update steps for each variational parameter in our inference procedure are presented below, with detailed derivations and hurther implementation details provided in Appendix B Finally, with the estimated Φs, each uncertain sample is assigned a predicted label of¹ arg max; Pik: forming D = {of ,..,,.................... Dnyy }.
Update steps within each iteration:
1. Compute (Aa, St):
nv
1
T
fkk [ng
Σ
Diki
Pak 2
U
1(O!" k))²"1
f + ft
St
Dik (2 mイ) (2 - -xa)
10 k) (2 - xR) -xx)
f
1=
1=1
2. Update variational parameters (7k1, 7x2):
7k1 = [mt + 1] = fg + 7k2 = Eg 1
n + a| = Σ
ng +
jzk
j>k
3. Update variational parameters (Tk, my, Ck: Dk):
The = + 2u + n my IS I ny
0ik
11 + +Σ Ry H I(D =
+ fu + K
(āx n )r
Ck 2U + n +
Di = =-==--1 + (fx )s
(2t () T)
T + n4 + nzt
4. Update variational parameters Φ; = (Bi1 $122....
k-1
log(dn) x (b(1))) 1b(7k) + 7k2) +
Σ [vb(1))) - -66751 + 752)]
5=1
+
2
Ck 2
+ log Dall
|dTT + cx(l m2) DD(= - m]]]
where v+) and vla(-) represent the digamma and multivariate digamma functions, respectively.
3.3 Optimization and Inference
Prototype-based Regularization: To enhance target sample separation, we alternate clustering updates with end-to-end training using pscudo-cluster labels generated in Scctions 3.1 and
3.2. optimized under a
clustering- based objective. Inspired by prior work on con-source-free settings eL al, 2021 ), we incorporate a prototype-based regularizer that promotes intra-cluster compactness and inter-cluster separation. Specifically, we first compute a centroid eg for each cluster k, used as its prototype, based on all target samples and their predicted labels Di+ 1 1341, where DiHf and Di!' are obtained from Sections 3.1 and 3.2 respectively. cx] represent the estimated prototypes, computed as the I.2-normalized centroids of the obtained target clusters. These prototypes are dynamically updated during each training iteration, and recomputed after each update of Dr. = {Vi, 022 .. Before applying the regularizer, we convert each predicted label of into its one-hot representation, where 0 = 1 if o = k. The prototypical regularizer for a minibatch B then defined as:
Let = [c1, ,,, [x]
L
--
Di log P(o.e)
(6)
iEB 1=1
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exp(( cx/0.1)
where, P(a)) Σx= (xp( /a.01)) and o denotes the L2- 12-normalized feature of target sample i. To gradually regulate the influence of Freg and avoid premature over-cxpansion, we adopt the ramp-up schedule from (Li et al. 2021), using dynamic weight Aveg e 3 1), where ( is the current step and L the total training steps, yiclding the term Arggrro in the training objective.
Local Prediction Consistency Regularization: To further refine the source classifier and align similar larget samples, we introduce a local consistency loss Lioce which enforces prediction consistency within local neighborhoods.
Lion Σ iEB JEN
log(s)) of
of denotes the softmax prediction of a target sample from the source classifier g, representing a probability distribution over source classes. The set M refers to the local neighborhood of target sample i, defined its top Kun nearest neighbors based cosine similarity in the feature space. To implement the nearest- neighbor computations during minibatch training, we follow prior work (Yang et al., 2021a 2022 2021b)
and maintain two memory banks: one storing all target features and the other storing their corresponding softmax predictions, both updated incrementally using minibatch data. During training, g is retrieved from the memory bank and treated as a fixed reference, so gradients are only backpropagated through gf- Similar to methods that align neighboring samples by maximizing the dot product of their predictions (e.g., Yang et al. (2022)), this regularizer maximizes the dot product between a query sample's log prediction and the predictions of its neighbors. This encourages consistency among nearby samples while reducing the tendency toward overly peaked (i.c., one-hot-like) softmax outputs over the source classes, that high-cntropy (less confident) ) predictions are aligned more softly. Since gradients are only propagated through g our objective also resembles (L minimizing the KL divergence between a fixed neighbor distribution and the query sample.
The final training objective integrates two components: the proto- typical regularizer Grog and the local prediction consistency regularizer Cioer balanced by their respective weighting coefficients Areg and Atoe- The overall loss function is formulated as: XregGreg + Aioc Ltor- With this overall objective, the workflow of ABC, comprising the iterative steps detailed in Sections 3.1 3.2 and
Training Objective and Inference:
3.3 is outlined in Algorithm [ During inference, with the final set of prototypes [c1, c2...., Ck), cach target sample is assigned the label ol the most similar protolype based cosine similarity between its L2- feature and the normalized prototypes, according to of = arg max, (2), cx).
Algorithm Adapt via Bayesian Nonparametric Clustering
1: Input: Unlabeled target samples Xe: pretrained classification model & = g f Output: Predicted labels o. ob..... prototypes {c1, ea,,c,,..,cr for epoch = -., do Identify high-confidence samples X. with pseudo-labels D
b. Identify uncertain samples X,
6: c. Estimate labels Di for X via guided Bayesian nonparametric clustering
7: d. Generate protolypes c = [.....,ck]
8: epoch < T; for iteration = 1, do Backpropagate & w.r.t. the loss and update c
10: end for
11: end for
12: Inference: Assign final labels o. .....
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Table 1: H-score (%) on Offece-Home, Office-31, and VisDA under OPDA settings. "SF" indicates source- free methods, and 'FG' refers fine-grre grainedind discovery of unknown classes. Bold blue numbers highlight top non-SF methods, and bold red numbers highlight leading SF methods (excluding the GBNC-only module).
(a) Home
Methods
SF
FG
A2C
A2P
A2R
C2A
C2P
C2R
P2A
P2C
P2R
R2A
R2C
It2
Avg
DAN
You et a
2019
X
K
51.6
51.7
54.3
61.7
57.6
61.9
50.4
47.6
61.5
62.9
52.6
65.2
$6.6
CMU
56.0
56.9
59.2
67.0
64.3
67.8
54.7
51.1
66.4
68.2
57.9
69.7
61.6
DCC
77.5
OVANet
Stenko
2021
X
62.8
75.6
78.6
70.7
68.8
75.0
71.8
58.6
80.5
76.1
64.1
78.9
71.8
GATE
CChell Cl. m1.
A022
X
K
63.8
75.9
81.4
74.0
72.1
79.8
74.7
70.3
82.7
79.1
71.5
81.7
75.6
Best Epoch (Best H-score)
SHOT-O [Liang et al.
2020
x
43.2
56.1
57.4
57.5
54.5
60.3
56.7
45.7
62.2
37.6
44.4
58.5
54.3
Quu
53.8
78.0
64.5
75.8
ABC
v
56.7
80.6
84.5
71.4
80.3
82.9
71.2
55.1
83.8
71.
56.9
79.8
72.9
20.8
21.0
20.4
20.7
213
10.
211
20.8
20.3
20.9
20.3
20.8
Final Epoch
SHOT-O [Liang et
2020
x
31.9
30.8
39.6
49.8
29.1
38.3
50.8
34.9
43.0
51.6
32.6
36.0
39.0
2.07
20.
11
20.5
20 8
41.2
11
20.3
20.
11.
10.4
20.8
GLC QQu et al. 2023
x
10.6
77.5
88.6
16.8
74.6
88.3
74.8
13.4
87.8
76.
14.5
83.5
$8.9
10.5
11.
20
11.0
235
10.6
103
10.3
10.
10
20.0
GBNC-only
52.
7
61.9
66
78.0
61.0
50.9
80.
62
53.3
77.5
66.8
ABC
54.5
82
70.3
72 9
$1.3
69
53.6
83.
69
55.1
75.5
70.4
+0.4
+23
20.8
+1.9
+3.0
+0.4
0.
+1.0
00.
+0.
42.2
+2.8
(b) Office-31 and VisDA
Office-31
82R
A2D
A2W
D2A
D2W
W2A
W2D Avg
UAN
You et
2019
X
X
34.8
59.7
58.6
60.1
70.6
60.3
71.4
63.5
CMU
PD
2020
X
32.9
68.1
67.3
71.4
79.3
72.2
80.4
73.
DOC
OVANe
S510 & Ssenko
2021
53.1
79.4
80.1
95.4
84.0
94.3
GATE CChn et al
X
56.4 X
87.7
81.6
84.2
94.8
83.4
94.1
87.6
Best Epoch (Best. H-score)
SHOT-O [Langg et al.
2020
31.5
61.5
58.6
61.5
78.8
60.8
73.6
GLC Qu al.
2023
65.4
8166
83.6
87.8
90.1
86.0
90.2
86.6
22.0
40.0
ABC
G1.7
86.4
94.8
88.8
94.9
89.
93.5
91.2
2003
20.2
11.2
10.8
20.4
20.4
20.2
Final Epoch
SHOT-O Liang et al.
2020
X
18.1
37.7
56.7
59.2
75.2
57.6
69.
62.6
=022
$1.9
#1.1
$1.6
+3.7
28.3
$0.7
GLC Qu et al. 2023
x
63.7
70.5
$1.8
79.8
65.6
75.8
$4.1
80.1
GBNC-ouly
31.
10.7
20.2
20.0
228
128
220
2..0
ABC
59.4
84.2
93.6
87.0
93.6
85.3
88.6
88.7
200
10.9
1
11.8
11.
20.3
12.1
4 Experiments
4.1 Experiment Setup
Datasets: We evaluate on three widely-used benchmark datasets: 1. Office-31 Saenko et al. 2010
comprises more than 4k images from 31 categories across three domains: Amazon A), DSLR (D), and Webcam (W). 2. Office-Homme (Venkateswara al., 2017), includes about 15,500 images categorized into 65 classes across four domains: Artistic (Ar), Clip Art (CI), Product (Pr), and Real- World (Rw); 3. VisDA- C. (Peng al. 2017 is challenging wruthetic-to-real benchmark with 12 object categories, featuring around 152k synthetic images in the source domain and 55k real-world images in the target domain. In the main experiments, we focus on the selling where neither C, nor C, is a subset of the other (C, & C, and C, Z C,), which is known as open-partial domain adaptation (OPDA) (Qu et al. 2023). We follow the class split settings used prior OPDA works (Qu et al.) (023),, using 10/ 10/10/11 shared/
classes for Office-31, 10/5/50 for Office-Home and 6/3/3 for VisDA-C. We also discuss the case where C, S C., known open-set domain adaptation (OSDA) (Qu et al.
2023 in Appendix D.5
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Evaluation Protocol: We follow the standard evaluation protocol used in prior works CChen al. 2022
Liang et al. 2021 Qu et al., 2023). reporting the harmonic mean (H-score) between the average accuracy on known classes and the accuracy on unknown-class samples, along with the average per-class accuracy (mean accuracy), treating the unknown class as a single category. Since these widely used metrics treat all unknown ground-truth classes as a single category, we additionally report Normalized Mutual Information (NMI (Vinh) ctt al. 2010); ; described in Appendix C to evaluate fine-grained classification. NMI measures the alignment between predicted and ground-truth labels across individual classes, independent of class label permutations, thereby treating each unknown class separately. For all metrics, we report the average performance of our method and the reproduced source-free baselines across three independent random experiments, together with the standard deviation for each transfer task.
We compare our method against representative non-SFDA baselines in terms of H-score, with their results reprinted from previous work (Chen et al., 2022 Qu et al., 2023). Additionally, we evaluate against two recent SFDA methods: SHOT (Liang et al. 2020 and GLC (Qu al. 2023). with results reproduced using their publicly available codebases. As both methods predict all unknown samples as single "unknown" class and do not directly produce fine-grained classifications, we apply the DPM, using the same configuration in our model, to the unknown target samples predicted by SHOT and GLC, and then combine the resulting cluster assignments with their known-class predictions to compute NMI against the ground-truth labels.
Implementation Details: For a fair comparison, we adopt the same backbone, ResNet-50 pretrained (He et al. 2016) on ImageNet. (Deng et al. 2009); in line with existing benchmark methods SHOT (Liang et al. 2020) and GLC (Qu et al. 2023 We pretrain the source model using the code provided by GLC (Qu et al. 2023), following the source model pretraining procedure recommended in SHOT (Liang et al. 2020 to apply 90/ 10 split for training and validation. Instead of a random split, we employ stratified sampling to maintain the class distribution across both training and validation sets, reducing the impact of class imbalance during source raiiing Due to space constraints, implementation details and configuration settings of our method are provided in Appendix C
4.2 Experiment Results
H-score, mean accuracy, and NMI results for all three datascts are reported in Tables Ia lb
2a and
respectively. Due to the absence of standardized epoch selection criteria in SFDA methods, results are reported for both the Best Epoch (the highest H-score) and the Final Epoch (the last training epoch) for the two SFDA baselines and ours. Best Epoch metrics ensure comparability with prior literature, while Final Epoch metrics provide a practical, label-free evaluation that better reflects real-world performance. As A and [22] on both Office-31 and Office-Home, ABC outperforms GLC under the Final Epoch setting and consistently outperforms SHOT in terms of average H-score and mcan accuracy. Notably, although GLC is one of the strongest baselines, ABC surpasses by a substantial margin in the Final Epoch setting on both datasets, achieving at least a 10% improvement in average H-score, while also attaining higher mean accuracy under both scttings. Furthermore, ABC delivers performance comparable to non-SFDA methods on sifice-Home, and achieves higher average H-score Office-31, regardless of whether results are taken from the best or final epoch. This demonstrates that ABC can achieve strong adaptation performance even without access to source data. On VisDA, while GLC slightly outperforms ABC, the gap is small, and ABC remains among the top-performing methods; both ABC and GLC significantly outperform SHOT, and surpass all compared non-SFDA methods.
2b
shown in Tables la Ib
From Tables 2a and 2b which report NMI between true and predicted labels, including unknown classes, we observe that ABC achieves the highest average NMI on Office-31 (both settings) and on Office-Home under the Final Epoch, while closely matching GLC+DPM on Office-Home under the Best Epoch. On VisDA, ABC shows slightly lower average NMI compared to GLC+DPM. Note that the compared methods group all unknown classes into a single category and do not inherently support fine-grained (FG) classification by explicitly predicting labels for individual unknown classes. The NMI results of these methods are obtained by applying the DPM module, which is central to our approach, their predicted unknown samples. Comparod to appending a separate BNC step to existing methods, our approach integrates it into a unified franework, enabling joint optimization, minimixing error propagation between clustering and adapting the source model,
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Table 2: NMI (%) on Home, Office-31, and VisDA datasets under OPDA settings.
(a) Office-Home
Methods
A2C
A2R
C2A
C2P
C2R.
P2A
P2C
P2R
R2A
R2C
R2P
Avg
Best Epoch
SHOT-O [Liang et sl.
2020 +
18.6
66.5
6133
57.6
63.3
63.1
57.4
48.0
61.0
58.0
48.8
67
58.9
DPM
40.5
10.1
20.5
10.5
20.2
10.5
-6.7
10.1
10.9
20.8
40.5
20.3
GLC Qu et al.
2023
DPM
49.3
75.3
73.9
57.7
75.6
73.8
62
47.6
73.6
63.7
48.8
74.6
64.7
403
20.3
203
204
203
402
20
10.2
203
40.8
403
20
ABC
48.3
74.0
75-1
61.0
74.5
73,4
61.8
47.8
73.4
62.9
48.0
75.4
64.6
+0.4
40.8
+0.3
40.5
+0.6
+0.5
Final Epoch
SHOT-O [Liang et
2020
46.9
62.0
60.9
56.6
61.3
59.8
57.0
46.4
60.1
57.1
47.2
62.8
56.5
DPM
+0.9
+0.1
20.8
+0.3
-0.6
+12
-05
10.6
+1.
+0.1
+0.
20.9
GLC (Qu et al. 2023
DPM
40.4
75.5
73.7
49.0
75.6
73.7
63.6
35.4
73
64.5
40.3
74.2
61.6
+0.3
+.4
40.
+0.3
+0.5
82
+0.
+11
+0.2
+0.5
-0.0
GBNC-only
49.9
73.6
73.0
49.9
68.
64.9
53.9
46
70.3
57.4
48.7
73.7
60.8
ABC
48.0
73.2
73.2
60.9
734
12.8
61
47.5
73.4
62.5
47.4
74.3
64.0
+0.
+0.8
20.7
+0.
202
20.
-
+0.1
10.1
30.4
+02
=0.4
(b) Office-31 and VisDA
Methods
VisDA
Office-31 A2W
S2R
A2D
D2A
D2W
W2A
W2D
Avg
Beat Epoch
SHOT-O [Llang et al.
2020
39.4
77.6
82.1
DPM
+0.4
+0.8
+0.4
+1.2
+0.2
+0.7
+0.2
GLC
Quu et al.
2023
DPM
47.2
79.6
82.0
67.6
83.1
66.9
81.9
76.9
20-3
10-4
134
10.9
392
ABC
Final Epoch
SHOT-O [Llang et al.
2020
43.5
79.1
$2.4
08.6
DPM
20.0
+0.2
+0.2
+0.7
+0.3
+0.8
+-0.3
GLC QQu al. 2023
DPM
48.1
81.7
83.0
69.6
83.8
70.1
82.5
78.4
GBNC-only
20.1
10.7
10.4
5..TT
3.0.0
ABC
46.9
81.0
85.
70.4
84.9
70.5
81.5
78.9
20.3
10.2
10.3
20.6
10.4
20.4
2.05
and eliminating the need for post hoc processing. We also evaluate the GBNC component in isolation (GBNC-only), which performs competitively on Office-31 and Office-Home but significantly worse on VisDA, demonstrating both its effectiveness and the added value of the full learning framework. Furthermore, evaluate ABC's performance in estimating the number of unknown clusters in Appendix D.3 focusing major clusters containing more than 1% of the data. As shown in Figure A1 the estimated number closely matches the ground truth for Office-31 and VisDA, and is underestimated for Office- Although estimating K without prior knowledge is inherently challenging, ABC provides a reasonable approximation across datasets, demonstrating its ability to achieve fine-grained classification.
While our experimental validation primarily focuses on the OPDA setting, we also provide an additional evaluation under the Open-Set Domain Adaptation (OSDA) setting in the Appendix, where the source-private class set is empty (i.e., C. Ct). As shown in Appendix D.5 ABC also performs well in this setting, suggesting that it can generalize effectively to other scenarios involving unknown classes.
4.3 Experiment Analysis
To better understand the robustness and reliability of our method, conduct comprehensive sensitivity and ablation analyses key hyperparameters. For the sensitivity analyses, average results across tasks are reported in the main paper; per-task results are in Appendix D.6 All results are based on single run. The results demonstrate that our method achieves robust performance across a wide range of hyperparameter values. In addition to the analyses presented in the main text, we include further studies in the Appendix on runtime and memory (Appendix D.2), clustering evaluation of the discovered unknown clusters samples (Appendix D.1 and t-SNE visualizations (Van der Maaten & Hinton 2008) of discovered unknown clusters (A (Appendix D.4
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Offle-48
AMRICTA TO
100 TM1
12
HOS 180
X
8
Epoch
Taska
(a) Beta mixture detector vs. OOD detectors
(a) HOS(%) vs. Epoch
Office 31
Offic Hove
12-
13
A-O
NMI (9)
12
22
(b) Sensitivity to 8
(c) Sensitivity to
Epoch
(b) (MI(%) vs. Epoch
Dffic-33
Hofo
Aowrae (051N)
HOS
Figure 4: Performance curve on VisDA for different Aloc
22-
12.8
264
0.0
8.3%
6.31
Ken
Auc
(d) Sensitivity to Kun
(e) Sensitivity to Aloc
Figure 3: Hyperparameter sensitivity and ablation study (H-score) on Office-31 and Office-Home under OPDA.
4.3.1 High-Coofidence Sample Selection
The anchor-based mechanism used in the first step to identify high-confidencee common-class samples plays a critical role in the overall method. In this section, we present an ablation study to evaluate the impact of the Beta-mixture detector on high-confidence sample selection, along with sensitivity analysis examining the effect of the decision-boundary threshold, 5.
Ablation Study of Beta-Mixture Detector: In our method, we employ a Beta mixture model (BMM) to estimate the posterior probability Ply E C, | k)), representing the likelihood that a sample belongs to the common classes. To evaluate its role high-confidence sample selection, we compare it with an alternative strategy based on out-of-distribution (OOD) detection for identifying unknown-class samples. Unlike the BMM, which explicitly models indicator values of known and unknown samples two mixture components, OOD approaches treat unknown-class samples as outliers relative to the distribution of known-class samples. We consider two widely used statistical OOD methods based on 1 1- k:
crantile-based approach and the interquartile range (IQR) method (Tukey et al. 1977)- For both, we adopt automatic threshold selection. Specifically, for the quantile method, the quantile is searched over {0.05, 0.1, 0.15,, 0.2, 0.25]: for the IQR mothod, the multiplier k varied over (0.5, 1.0, 1.5, 3.00 using onc-sided (lower-tail) criterion. In each case, the threshold that maximizes the Silhouette score is selected. We evaluate these detectors on Office-31 and Office- and compare them with BMM When the OOD detectors classify too many samples
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known-class, yielding too few outliers, we adaptively reduce K to ensure GBNC remains computationally feasible. We report the comparison between BMM and the OOD approaches at the final epoch. H-scores are shown in Figures 3a] with additional metrics in Figures A4 The results demonstrate that BMM consistently achieves superior performance in terms of H-scores, while the OOD approaches not only perform worse but also the IQR method fails on one task (marked by crosses). Regarding detection errors, two failure modes may occur when high-connfidnce labels are incorrect: (1) misassigned known-class samples, where confusion between similar source classes causes the GBNC step propagate incorrect labels and bias class estimation; and (2) unknown samples treated as known, where excessive inclusion of unknown samples as anchors prevents discovery of some unknown classes. Empirically, the second case dominates: manual inspection shows the first case is rare (accounting for =0% of incorrect labels in the majority of Office-31 tasks and <5% on average across Office-Home tasks). The poor performance of OOD alternatives therefore illustrales these failure scenarios, where inaccurate detectors misclassify many unknown samples as known. Overall, the results underscore the importance of the Bota mixture model, which explicitly models the indicator distributions of known and unknown samples rather than treating unknown samples merely as outliers.
8 for Ciigh-Confidence Sample Selection: To select high-confidence samples, we apply P(y E C, x) > 6. Setting& 8 too high results in too few selected samples, potentially omitting entire common classes, while low 8 may admit too many, increasing the risk of including misclassified unknown-class samples. The natural decision boundary, where P(y E C, k) > Ply & C, I k), suggests a default threshold of 5 = 0.5, but it need not always be fixed at this value. For Office-31 and Office-Home, we lune d per epoch within the range [0.4,0.0 0.6] (with a step size of 0.05), selecting the value that maximizes the Silhouette score (Rousseeuw 1987 based on the embedded data and the estimated labels from the GBNC. To assess scnsitivity, we also rerun our algorithm using fixed values 8 {0.4. 0.450.440000 0.5, 0.55, 0.6} and compare the results to our tuning strategy (denoted as "auto"). As shown in Figures 3b
A8 A9 and A10 performance remains relatively stable around 8 0.5, The auto-tuning strategy yields similar results to fixed settings, further mitigating sensitivity to the choice of 5 without requiring manual selection.
4.3.2 DPM Hyperparameter a
The concentration parameter a plays a key role in the DPM model, controlling its ability to infer the number of clusters. Following a common practice, we set a a with a" = 1 a noninformative prior, allowing the influence of the hyperparameters to diminish with increasing sample size. To assess sensitivity, Office-31 and Office-Home using a" E (01. 1, 100, 200, 400} (i.e., a E {10-4, 10-3, 10-2,1,11111 2, 4} for K 100), as shown in Figures 3c with additional metrics provided in Figures AS A9 and [AT0] Results demonstrate robust performance, supporting the use of a non-informative prior. While a can also be estimated via empirical Bayes or assigned a hyperprior, where the hyperparameters are either inferred from the data or exert less influence higher in the model hierarchy, the performance stability across values suggests that our choice achieves reliable performance while providing both efficiency and simplicity, making the modeling process more controllable. In general, we prefer non-informative priors in our model to let the data drive the clustering process while keeping the implementation simple and efficient.
we further report the H-score
4.3.3 Kmn for the Calculation of Lioc
For Office-31 and Office-Home we evaluate performance with different number of nearest neighbors Kyn E (5, 10, 20, 50), reporting H-scores in Figures 3d and additional metrics in Figures A8 Ag and A10 Our method demonstrates robustness to the choice of Knn, with H-scores remaining stable across tested values. Given the size of these two datasets, this range of Knn is appropriate: too few neighbors (e.g., 1 or 2) can lead to unstable estimates, especially when those neighbors are misclassified, while too many may introduce noise by incorporating samples from different classes, as noted in similar settings (Yang et al. 2022). For larger datasets like VisDA, we adopt higher Knn to account for its much larger target domain.
4.3.4 *ooc for Local Prediction Consistency Regularizer
We evaluate the impact of AJoc E {0, 0.001, 0.01, 0.1, 1}. H-scores on Office-31 and Office-Home are shown in Figures 3el with NMT and mean accuracy provided in Figures A8 A9
and A10 Results show that performance
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remains generally stable, indicating robustness to Mloe though larger values may degrade performance Office-31. For VisDA, analyze performance across training epochs (Figure λloe shows stronger impact: small Aloe values performs better compared to Alce 0, and it shows more stable, gradual convergence while larger values lead to faster convergence but compromise final performance. Across small Aloc values, metrics steadily improve over time, indicating stable and effective learning- This suggests that Loe can be particularly helpful when baseline adaptation performance is weak, typically challenging tasks, as in VisDA.
5 Conclusion
In this paper, propose Adapt via Bayesian Nonparametric Clustering (ABC) for SFDA with unknown target classes, enabling both discovery and fine-grained classífication of unknown classes. Through the development of a guided Bayesian nonparametric clustering algorithm, our approach first identifies high- confidence target samples from known classes and then uses them as anchors to effectively cluster known-class samples and discover previously unseen ones, without requiring prior knowledge of the number of unknown classes or specifying in advance. A prototype-band incorporated to further refine the source model for adaplation to the larget data. Experiments demonstrate that ABC achieves solid performance across various benchmarks and evaluation metrics. By enabling the identification and classification of unknown classes in new domains without access to source data, ABC has the potential to provide important practical values across a range of real-world applications.
regularizer and a local prodiction-consistenng term are
Acknowledgments
This work was partially supported by a start-up fund from the College of Arts and Sciences at the University of Kentucky. Computational resources were also provided by the College of Arts and Sciences at the University of Kentucky.
References
Charles E Antoniak. Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. The Annals of Statistics, pp. 1152- 1174, 1974.
Eric Arazo, Diego Ortego, Paul Albert, Noel O'Connor, and Kevin McGuinness. Unsupervised label noise modcling and loss correction. In International conference on machine learning, pp. 312-321. PMLR, 2019.
David Arthur and Sergei Vassilvitskii. k-means++: Stanford, 2006.
The advantages of careful seeding. Technical report,
Christopher M Bishop and Nasser M Nasrabadi. Pattern recognition and machine learning, volume Springer, 2006.
David M Blei and Michael Jordan. Variational inference for Dirichlet process mixtures. Boyesian Analysis, 1(1):121-143, 2006.
Silvia Bucci, Mohammad Reza Loghmani, and Tatiana Tommasi. On the effectiveness of image rotation for open set domain adaptation, 2020.
Zhangjie Cao, Mingsheng Long, Jianmin Wang, and Michael I Jordan. Partial transfer learning with selective adversarial networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 2724-2732, 2018a.
Zhangjie Cao, Lijia Ma, Mingsheng Long, and Jianmin Wang. Partial adversarial domain adaptation. In Proceedings of the European conference on computer vision (ECCV), pp. 135-150, 2018b.
Chao Chen, Zhihong Chen, Boyuan Jiang, and Xinyu Jin. Joint domain alignment and discriminative feature learning for unsupervised deep domain adaptation. Tn AAAT Conference Artificial Intelligence, 2019.
15

---

Published in Transactions on Machine Learning Research (04/2026)
Liang Chen, Yihang Lou, Jianzhong He, Tao Bai, and Minghua Deng. Geometric anchor correspondence mining with uncertainty modeling for universal domain adaptation. In Proceedings of the TEEE/CV conference on computer vision and pattern recognition, pp. 16134 16143, 2022.
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In IEEE CVPR, pp. 248 255. IEEE, 2009.
Ning Ding, Yixing Xu, Yehui Tang, Chao Xu, Yunhe Wang, and Dacheng Tao. Source-free domain adaptation via distribution ion estimation. In Proceedings of the IEEE/CVF conference on compuler vision and pollern recognition, pp. 2212-7222, 2022.
Thomas S Ferguson. A Bayesian analysis of some nonparametric problems. The Annals of Statistics, 1 209 230, 1973.
Bo Fu, Zhangjic Cao, Mingsheng Long, and Jianmin Wang. Learning to detect open classes for universal domain adaptation. In Computer Vision ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 28, 2020, Proceedings, Part XV, pp. 567-583, Berlin, Heidelberg, 2020. Springer- Verlag. ISBN 978-3-030-58555-9, doi: 10.1007/978-3 030-58555-6 34.
Yaroslav Ganin and Victor Lempitsky. Unsupervised domain adaptation by backpropagation. In JCML, pp. 1180 1189, 2015.
Yaroslav Ganin, Evgeniya Ustinova, Hana Ajakan, Pascal Germain, Hugo Larochelle, François Laviolette, Mario Marchand, and Victor Lempitsky. Domain-adversarkle training of neural networks. Journal of Machine Learning Research, 17(1):2096-2033 2016.
Tan Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In NewrIPS, pp. 2672 2680, 2014.
Aritra Guha, Nhat Ho, and XuanLong Nguyen. On posterior contraction of parameters and interpretability in bayesian mixture modeling, Bernoulli, 27(4)22159 2188, 2021.
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In IEFE Conference on Computer Vision and Paltern Recognilion, pp. 770 770-778, 2016.
Nils Lid Hjort, Chris Holmes, Peter Müller, and Stephen G Walker. Bayesian Nonparametrics. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge, 2010. doi:
10.1017/CB0078001188222
AK JAIN, MN MURTY, and PJ FLYNN. Data clustering: review. ACM Computing Surveys, 31(3), 1999.
JoonHo Jang, Byeonghu Na, Dong Hyeok Shin, Mingi Ji, Kyungwoo Song, and I1-Chul Moon. Unknown-aware domain adversarial learning for open-set domain adaptation. Advances in Neural Information Processing Systems, 55:16755-16766 2022.
Jeff Johnson, Matthijs Douze, and Hervé Jégou. Billion-scale similarity search with gpus. IEEE Transactions Big Data, 7(3):535-547, 2019.
Jogendra Nath Kundu, Naveen Venkat, R Venkatesh Babu, et al. Universal source-fres fuuree-free domain adaptation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 4544-4553, 2020.
Guangrui Li, Guoliang Kang, Yi Zhu, Yunchao Wei, and Yi Yang. Domain consensus clustering for universal domain adaptation. In Proceedings of the IEEF/CVF conference on computer vision and pottern recognition, pp. 9757-9766, 2021.
Jian Liang, Dapeng Hu, and Jiashi Feng. Do we really need access the source data? source hypothesis transfer for unsupervised domain adaptation. In International conference on machine learning, pp. 6028- 6039. PMLR, 2020.
16

---

Published in Transactions on Machine Learning Research (04/2026)
Jian Liang, Dapeng Hu, Jiashi Feng, and Ran He. Umad: Universal model adaptation under domain and category shift. arXiv preprint arXiv:21 22.8855, 2021.
Antonio Lijoi, Ramses H Mena, and Igor Prunster. Controlling the reinforcement in Bayesian non-parametric mixture models. Journal of the Royal Statistical Society: Series B, 69(4):715- -400 2007.
Zhengfa Liu, Guang Chen, Zhijun Li, Yu Kang, Sanqing Qu, and Changiun Jiang. Psdc: A prototype-basee shared-dummy classifier model for open-set domain adaptation. IEEE Tronsactions on Cybernetics, 53(11): 7353-7366, 2022.
Mingsheng Long, Yue Cao, Jianmin Wang, and Michael Jordan. Learning transferable features with deep adaptation networks. In ICML, pp. 97 105. JMLR. org, 2015.
Mingsheng Long, Han Zhu, Jianmin Wang, and Michael 1 Jordan. Unsupervised domain adaptation with residual transfer networks. In NewrIPS, pp. 136 144, 2016.
Mingsheng Long, Han Zhu, Jianmin Wang, and Michael I Jordan. Deep transfer learning with joint adaptation networks. In ICML, pp.
JMLR. org, 2017.
James MacQueen et al. Some methods for classification and analysis of multivariate obscrvations. In Proceedings of the fifth Berkeley symposium on mathematical slatislics and probability, volume 1, pp. 297-297, 1967.
Christopher D Manning. Inlroduction to information relricval. Syngress Publishing, 2008.
Jeffrey W Miller and Malthew T Harrison. A simple example of dirichlet process mixture inconsistency for the number of components. Advances in neural information processing systems, 26, 2013.
Erxue Min, Xifeng Guo, Qiang Liu, Gen Zhang, Jianjing Cui, and Jun Long. A survey of clustering with deep learning: From the perspective of network architecture. IEEE Access, 6:39501-39514 2018
Peter Müller, Riten Mitra, et al. Bayesian nonparametric inference- why and how. Boyesion Analysis, 8(2): 269-33 1009-02,-40 2013.
Yang Ni, Yuan Ji, and Peter Müller. Consensus monte carlo for random subsets using shared anchors. Journal of Computational and Graphical Statistics, pp. 1-12, 2020a.
Yang Ni, David Jones, and Zeya Wang. Consensus variational and Monte Carlo algorithms for Bayesian nonparametric clustering. In 2020 IEEE International Conference on Big Data (Big Data), pp. 204 209. IEEE, 2020b.
Yang Ni, Peter Müller, Maurice Dicsendruck, Sincad Williamson, Yitan Zhu, and Yuan Ji. Scalable Bayesian nouparametric clustering and classification. Journal of Computational and Graphicul Statistics, 29(1): 53 65, 2020c.
Pau Panareda Busto and Juergen Gall. Open set domain adaplation. In Proceedings of the IEEE internalional conference on computer vision, pp. 754-763 2017.
Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high-performance deep learning library. Advances in neural information processing systems, 32, 2019.
Fabian Pedregosa, Gaäl Varoquaux, Alexandre Gramfort, Vincent Michel, Bertrand Thirion, Olivier Grisel, Vincent Dubourg, Joris Van Meerbergen, Rémi Weiss, and et al. Scikit-learn: Machine learning in python. Journal of Machine Learning Research, 12:2825-288 2011.
Xingchao Peng, Ben Usman, Neela Kaushik, Judy Hoffman, Dequan Wang, and Kate Saenko. Visda: The visual domain adaptation challenge. arXiv preprint xrX:::1710006924, 2017.
Jim Pitman and Mare Yor. The two-parameter nator. The Annals of Probability, pp. 855-900, 1997.
distribution derived from a stable subordi-
17

---

Published in Transactions on Machine Learning Research (04/2026)
Sanqing Qu, Guang Chen, Jing Zhang, Zhijun Li, Wei He, and Dacheng Tho. Bmd: A general class-balancee multicentric dynamic prototype strategy for source-free domain adaptation. In European. conference on computer vision, pp. 165 182. Springer, 2022.
Sanqing Qu, Tianpei Zou, Florian Röhrbein, Cewu Lu, Guang Chen, Dacheng Tao, and Changjun Jiang, Upcycling models under domain and category shift. In Proceedings of the IEEE/CVF conference on computer vision and paltern recognition, pp. 20019- 20028, 2023.
Douglas Reynolds. Gaussian mixture models. Eneyclopedia of biometrics, pp. 827- 2015.
Mcitar Ronen, Shahaf E Finder, and Oren Freifeld. Deepdpm: Deep clustering with an unknown number of clusters. In Proceedings of the IEEE/CVF Conference on Compuler Vision and Pallern Recognition, pp- 9861-9870, 9870, 2022.
Peter Rousseeuw. Silhouettes: graphical aid to the interpretation and validation of cluster analysis. Journal of computational and applied mathematics, 20:53-65, 1987.
Kate Sacnko, Brian Kulis, Mario Fritz, and Trevor Darrell. Adapting visual category models to new domains. In ECCV, pp. 213 226. Springer, 2010.
Kuniaki Saito and Kate Saenko. Ovanet: One-vs-all network for universal domain adaptation. In Proceedings of the ieee/cuf international conference on computer vision, pp. 9000 9009, 2021.
Kuniaki Saito, Shohci Yamamoto, Yoshitaka Ushiku, and Tatsuya Harada. Open set domain adaptation by backpropagation. In Proceedings of the European conference on computer vision (ECCV), pp. 153-168, 2018.
Kuniaki Saito, Donghyun Kim, Stan Sclaroff, and Kate Saenko. Universal domain adaptation through self supervision. Advances in neural information processing systems, 33:16282 16292, 2020.
Jayaram Sethuraman. A constructive definition of dirichlet priors. Stolislica sinica, pp. 639 650, 1994.
Baochen Sun, Jiashi Feng, and Kate Saenko. Return of frustratingly easy domain adaptation. In AAAI Conference on Artificial Intelligence, 2016.
Robert Thorndike. Who belongs in the family? Psychometrika, 18(4):267-276, 1953.
A Torralba and AA Efros. Unbiasod look at dataset bias. IEEE CVPR, pp. 1521-1528. IEEE Computer Society, 2011.
John Wilder Tukey et Exploratory data analysis, volume Springer, 1977.
Eric Tzeng, Judy Hoffman, Ning Zhang, Kate Sacnko, and Trevor Darrell. Deep domain confusion: Maximizing for domain invariance. arXiv preprint 1rx2::411..374, 2014.
Eric Tzeng, Judy Hoffman, Kate Saenko, and Trevor Darrell. Adversarial discriminative domain adaptation. In IEEE CVPR, volume pp. 4, 2017.
Laurens Van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. Journal of machine learning research, 9(11), 2008.
Hemanth Venkateswara, Jose Eusebio, Shayok Chakraborty, and Sethuraman Panchanathan. Deep hashing network for unsupervised domain adaptation. In Proceedings of the IEEE conference on compuler vision and pattern recognition, pp. 5018 5027, 2017.
Nguyen Xuan Vinh, Julien Epps, and James Bailey. Information thcoretic measures for clusterings comparison: Variants, properties, normalization and correction for chance. Journal of Machine Learning Research, 11 (95):2837-285. 2010.
18

---

Published in Transactions on Machine Learning Research (04/2026)
Jinghua Wang and Jianmin Jiang. An unsupervised deep learning framework via integrated optimization of representation learning and gmm-based modeling. In Asian Conference on Computer Vision, pp. 249-263) Springer, 2018.
Zeya Wang and Chenglong Ye. Deep clustering evaluation: How to validate internal clustering validation mcasures. Journal of the American Statistical Association, 0(0):1-14, 2026. doi: 2592926.
Zeya Wang, Baoyu Jing, Yang Ni, Nanqing Dong, Pengtao Xie, and Eric Xing. Adversarial domain adaptation being aware of class relationships. In ECAI 2020, pp.
IOS Press, 2020.
Zeya Wang, Yang Ni, Baoyu Jing, Deqing Wang, Hao Zhang, and Eric Xing. Dnb: A joint learning framework for deep bayesian nouparametric clustering. IEEE Transactions on Neural Networks and Learning Systems, 33(12):7610-7620, 2021.
Shiqi Yang, Joost Van de Weijer, Luis Herranz, Shangling Jui, et al. Exploiting the intrinsic neighborhood structure for source-free domain adaptation. Advances in neural information processing systems, 34: 29393-29405, 2021a.
Shiqi Yang, Yaxing Wang, Joost Van De Weijer, Luis Herranz, and Shangling Jui. Generalized source-free domain adaptation. In Proceedings of the IEEE/CVF international conference on computer vision, pp. 8978 8987, 2021b.
Shiqi Yang, Shangling Jui, Joost Van De Weijer, et al. Attracting and dispersing: A simple approach for source-free domain adaptation. Advances in Neural Information Processing Systems, 35:5802 5815, 2022.
Kaichao You, Mingsheng Long, Zhangjie Cao, Jianmin Wang, and Michael I Jordan. Universal domain adaptation. In Proceedings of the IEEE/CVP conference on computer vision and pattern recognition, pp. 2720 2729, 2019.
Weichen Zhang, Wanli Ouyang, Wen Li, and Dong Xu. Collaborative and adversarial network for unsupervised domain adaptation. In TEEE CVPR, pp. 3801-30 1001-380,,400 2018.
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Appendix
Appendix
Description
Appendix
More Details about Guided Nonparametric Bayesian Clustering
Appendix
B
Approximate Posterior Inference via Variational Bayes
Appendix
Additional Experiment Setup
Appendix
D
Additional Results
A More Details about Guided Nonparametric Bayesian Clustering
Treating the embodding data 2 = {=Y ...., _ as observed data, Dirichlet Process Mixture (DPM) model for z can be naturally represented within a Bayesian hierarchical framework (same as Equation
Im (el)))) m|G G, G~ DP(a, Go).
(A1)
The probability function p(- n:) is parameterized by т,, which is drawn from a DP-distributed prior G. In our method, we adopt a Dirichlet Process Gaussian Mixture Model (DPGMM), where p(- πι) is a multivariate Gaussian, and 87 consists of the mean and covariance parameters the Gaussian. Equation Al can be equivalently formulated as an infinite mixture model in Equation A2 by marginalizing out
k ~ p(z, (nt),
1/ ~ Col(T), क = (TI,,T2,""
=s
k-1
(A2)
II (1 uz), uk ~ Beta(1, m Gu 1=1
Th
where of represents the parameters of the distribution associated with the mixture component. & and л is a probability vector specifying the mixing distribution over clusters kt = 1,2, The categorical distribution, denoted by Cat(-), assigns cluster memberships according to y! π ~ Cat(r), which equivalent to the probability expression Ply! = k) = иk. Equation A2 adopts the stick-breaking representation, where the DP prior G is explicitly expressed as an infinite mixture of point masses weighted by क (Sethuraman) 1994. Blei & Jordan] 2006). In Equation A22] the mixing proportions mi can be viewed being generated by sequentially "breaking" unit-length stick into infinitely many pieces, with each piece determined by ug from the remaining stick.
2 we treat their labels D [ol" ....,..... /d obtained during the sigh-confidence sample selection step, as fixed, giving:
For the embedding data from high-confidence samples, z = (
z p(a In
(A3)
With the alignment mentioned in Section 3.2 we combine Equation A3 with Equation A2 to obtain
(same as Equation
U 10 = k ~ p(z In)); # ~ p(= H man") 2
1 r Cal(T))
(m,,T2, ".. ...)
(A4)
T Uk II (1- Uz), un Beta(l, mi Go j=1
where p(-Im)) N...,. Ag). We place a conjugate Normal- Norhal-Wishart prior, N(PKI AAg) (Aa 12) on (mu, Ak); where T, and Ω are Bayesian hyperparameters.
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B Approximate Posterior Inference via Variational Bayes
Our model is parameterized by four sets of parameters and latent variables: {UR]E= 1=11= {pt (Aa and [v/ Jem where no denotes the size of z We employ Variational Bayes (VB) to approximate the posterior distribution. VB approximates the true posterior by minimizing the KT. divergence between a variational distribution and the posterior. To facilitate this, we apply the mean filed approximation and assume a fully factorized variational distribution (Bishop & Nasrabadi 20061,
K- a( (((u))Er1 (mx)E (A tut MEL) = II ((v)) k=1
K" II
aln A&) k=1
II alvl
(A5)
The stick-breaking process is truncated at a value K with ((vx- =) 11 construction known as the truncated stick-breaking representation. should be noted that K does not represent a pre-determined number of clusters, as in conventional clustering algorithms like K-Means. Instead, it serves as a practical upper bound on the number of clusters, and any sufficiently large value (e.g.. 100) is generally expected to yield consistent results. We present the model specifications.
for computation purpose, a
0
V/ ,h, A NWWg Agy)
28
,1, A N(ug Agp) (0." considered as fixed)
Vi
π Cat(TT)
A NCS
A W(),
A-1
T& U II j=1
-----) Mg)
Uk Beta(1, a))
(A6)
Given Equation A6 the joint distribution of all random variables, expressed in their vectorized forms, can be factorized as:
PZZ z", Y vz u, A) = pZz Y nu ()"" n. A))(" v)p(v)p(H) A))(A)
(A7)
The full conditional distributions our model belong the exponential family. Accordingly, select variational distributions also from the exponential family: g(vx) Beta(vs (eetauuxheeea 7k2), q(ux;A N(p mi, TeAx)W(AR cx, Dk), q(v") Cal(de), and apply mean-field variational inference for exponential families (Bei & Jordan 2006). Variational inference typically proceeds via coordinate ascent algorithm, updating the parameters of each variational distribution sequentially. Under the mean-field framework, the variational parameters for each distribution are updated by computing the expected natural parameters of the corresponding full conditional, evaluated with respect to the current variational distributions. For completeness, we provide below the detailed update steps for our model.
Variational distributions:
a(Mu, NR) = N(u ma, T cx, Dx)
((vx) = Beta(Ux 7k1, 712)
q/0! = k)) 0i
[k)
(A8)
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Update variational parameters (Tk, my, Ck: Dk):
To simplify the notations, we let ni n 1( = -k), Ag. = =E[[nu] = Ein1 oue and fn = Ein 1(t = =k).
Also, we set
2k
Te = =
Σ 1=1
Ti = =k)=
(A9)
1=1
ay I( k) (2f mx) (2. zn)
5
I( = (z!" zx) (2/ =z)"
(A10)
71
FT +
1
For the likelihood of the parameters associated with cluster k, given the embedding data 2f' and 2.",, we have
II N24
Pk. (R)
10 II
N(, H Ab) RR)
E=1
1
exp
I 1 = 1){ - -m)) T Aa(2)
ms)) - log A
2 1=1
(A11)
THP = ((= - mF) Ae(= - ma) - log [Ax1]
X exp
2 F=1
14 + f
tr(S nkk + f (3k- px Ax ma) + n + nz log |Axl]
exp
2
2
Lot d denote the dimensionality of the embedding data. We can casily show that the full conditional distribution of each uk:, Ag-
TR
TH
p(pk, As 1-) x
II
[2 I Pk. AA) A kk)
II
(2 I ME, Ac) =k N(Ux (. 6,
6=1
i=1
n% + og
12k + t 2 tr(SAAx)
21k + n
X exp
(Zk- [xx)
T AnlEe - -mb) +
log [Aa|
2
2
2 TPM - 5) Au(Hle -() + 1 log |Ax
X exp
1 1r(22 AAe) + b b-d-1 logg Mcl 2
X exp
2
1 [mmx + n (Ex mm)) Aal - m4)) + -T(1xx - TT AR - 5)
X cxp
1 2
1 [ (nR + f H + b d)) log (eal)
tr(((1e
+ # S + ---1)/a)) +
(A12)
[(T (-21(-
TG + (nz + n )a1 ST T *
T5 + (nax + f )20
x exp
ni + n (m
T + n4 + f
T + ne + np
(n + n )T
(Zx- - 5) T (z - <)
7 + ny + .t
1 tr((12- + (nx + n )at)Aa + (nx + H +b log /Ael
2
2
(T + no + (14 T + (nx + +n 2 )T A + + (n+ + f ) T n2 + f
x exp
7 + ny + +f
1
(nz + fo )T
マ/ ur((12) + +n= + n S5x +
(5x - ()x - -)) AAa)
+ nx + f
11
1
2 (nx + ag + b - d) log |Aal
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Thus the natural parameters are
(ng + fn )r
71 vec(S2- (nx f/6 )s
(3k ()x c)T +
(A13)
+ nh + f
(TC + (ng - -n (TT + (nz + )xx)
(A14)
+ 71 + A
1/2 = Tς + (n, + )x = Σ I(y! =k)= + Σ I = k) + T5,
(A15)
G3 = + 11 + ;
(A16)
74 n fikk + d
(A17)
Solve Tk
(T + fuz + fg
Thk
f4 f
H
(A18)
Solve mg
R0
mm = Egl
IV = k)2 v +
I = k))2," + T
nv
ng
TkilkK = T
2ik2
U
1 k))
7C + Σ 1=1
Dak
+ Σ 2 # T( k))
-m,-
(A19)
fu
+ f
Solve
C d Eg m
2 d)
Ck = b + fuy + n
-4 14 + x + b
(A20)
Solve Dr
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(ne + )
D + Fkmmm Egg (2 + (nx + )+x
(2k (2x 5)
(A21)
T + Tok + n
(T( + (nx + ) (TC + (nt + + )xx)
+
+ n& + f
ny
DE 1 + Tamam
Egg [2 >
I(y! =b) (2) -zx) (2 zn) T
(A22)
RH
10 1:) (2/ =x) (2l" Wk
+ (n+ )= + =
Dr 1 + mm = E.g [22
I(U = x))
Σ TO,!0 = = (=!1)²)
i=1
1=1
TV = (T) 22k
I = k))
+ n + n ) + +
ny
RM
Dr + Tpmam
Fig [2
T(y! =
Σ
T(
+ +
1=1
ny
DE = 2-
Σ
1
1)
Σ I(0
( +T55 -K-mAm
(A23)
If we further set:
RU
TH
U + Σ 1 k)
(A24)
Sak 2
f.k + f
i=1
St
Dik
U 2/) (2f - -
Σ T H = (2
- -z)
(A25)
nu + f
1=1
We can rearrange Equation
A23 to have:
+ (fux + +n )T
DE 12 + (fex + sS
(at () - -C)
(A26)
T + hu + ni
Update variational parameters (7k1, 7w2): Given Ωe = Eg[rx] = Ene dik.
7k1 Enira +1] f4 + 1
(A27)
7k2 Eg Σ nÿ +a] = Σ n +
(A28)
Update variational parameters Φ; (d11, 012 ...2.....
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log(Os)) x Egllog Th + log loogogN( (2 lik Ax]]
k-1
log(1 Uz) + 1 log |axl - 1
x log uk +
2 -((2" - pxx) A -mx)]
2
k-1
x (7(11) )- 1//1111 + Yk2) + Σ
(1(712)) 1/(1 + [32)]
1=1
Ck [
+ log D&ll |dTx ca(2! -mx) Dx - -ma)l
(A29)
2
where ()) and vba(-) represent the digamma and multivariate digamma functions, respectively.
Given these update steps for the variational paramcters, we employ a coordinate descont algorithm to iteratively refine them until a convergence criterion is met, such as the convergence of the Evidence Lower Bound (ELBO), which is typically used as the objective in standard Dirichlet Process Mixture (DPM) models (Blei & Jordan 2006). For initialization, we assign clusters using & variant of the KMeans algorithm, adapted to our setting (standard KMeans is commonly used in the variational Bayes (VB) procedure for DPMs). In this variant, we incorporate the labels of high-confidence samples during updates of the source-class cluster centers and modify the KMcans++ initialization (Arthur & Vassilvitskii, 2006) to consider class-center information from these samples at the start of KMeans. Finally, using the estimated values of dx, the predicted labels for the uncertain samples, DD "o.......yy J. are determined by g.' = arg max Osk-
In our method section, we assume all estimated labels of" take values from the index set 21. [ (for clarity, we use one-based indices in the method description, while in practice zero-based indices are used). This allows unknown clusters be represented by indices larger than |C] (1č) in zero-based indexing), enabling prototype based regularization to use one-hot encodings of cluster labels. Inference is then performed by assigning samples to the nearest prototypes in c = [C1, . ck] with consocutive indices. In our experiments, all datasets use zero- based class indices, and transfer tasks are designed so that unknown classes are assigned indices greater than or equal to the number of source classes, |C.l (following the conventions of prior work). For example, in Office-31 with a 10/10/11 split (shared/ wwwprrce-piivaeettateree prrittte classes), shared classes get indices 9, source-private classes get 10 19, and unknown target classes get indices 2 20. After the GBNC step, add |c,| only to the labels of samples whose class is not among those represented by the high-confidence samples Doft ensuring clear separation between known and unknown classes for subsequent implementation. We then reindex all estimated labels to consecutive zero-based indices {0, 1,,....... } using a monotonic mapping that preserves ordering. This produces both the reindexed label array and a reverse mapping from new indices to original labels, which we use during inference to identify unknown-class samples and recover original cluster indices for known classes.
C Additional Experiment Setup
Normalized Mutual Information (NMI) Vinh et al., 2010). NMI is standard metric for evaluating the agreement between two label assignments, invariant to permutations of the class labels. Given label assignments Da and Vh, NMI can be computed by scaling the mutual information between Va and V%b by the arithmetic mean of their respective entropies:
2 I().;))) NMI()I: = H())) + H()))'
(A30)
where ((5.) represents the mutual information between two random variables and H(-) represents the entropy of a random variable. NMI takes values between 0, suggesting no mutual information, and 1, indicating perfect alignment, with higher values reflecting better correspondence between the two label assignments. In our evaluation, we compute N NMI))))) comparing ground-truth labels y with predicted cluster labels ÿ across all samples. To evaluate NMT for the compared methods in our experiments, which requires estimated
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labels for unknown-class samples, apply the DPM component, using the same model configurations in our approach, to the unknown target samples predicted by SHOT and GLC, then combine the resulting cluster assignments with their known-class predictions to compute NMI against the ground-truth labels.
Additional Settings: During target model adaptation, we use the SGD optimizer with a momentum of 0.9 and weight decay of 0.001, , following the conventional inverse learning rate decay schedule defined as T 11+1100mmm(1 where To the initial learning rate. тoo is set to 10-2 for the classifier on Office-31, Tig
10-4 for Offico-Home, and 10-3 for VisDA, with a scaling factor of 0.1 appliod to the extractor and bottleneck layers. The batch size is fixed at 64 for all benchmark datasets. The weight for λtoe is set to 0.01. The number of nearest neighbors, Knns is set to 5 for both Office-31 and Office-Honne account for its considerably larger data scale. We run Algorithm D for 10 epochs across all three datasets. For high-confidence sample selection, we use the default threshold value 5 = 0.5 for the VisDA dataset. For the other two smaller datasets, we tune 8 over the range [0.4, 0.6] in increments of 0.05, selecting the value that maximizes the Silhouette score (Rousseeww] 1987p computed on the embedded data and the estimated labels produced by the GBNC. This choice is supported by the sensitivity analysis in Section 4.3] The hyperparameters in the DP base distribution Go are set to <= 2, which is the mean of embedding data, T= 1, b d, and Ω-1 0.001 d x Id, where d is the dimension of the embedding, which is 256 in model. K is chosen with 100 for all the datasets. The VB algorithm, well as KMeans and KMeans initialization, for our GBNC model is implemented by adapting the DPM implementation provided in the scikit-learn library (Pedregosa et al.) 2011 All experiments are conducted on a server with AMD EPYC 7413 24-Core processors and eight NVIDIA RTX A5500 GPUs, using PyTorch (Pszkk et al. 2019
and 100 for VisDA to
Additional Results
This section presents additional results, including tables, figures, and sensitivity analyses.
D.1 Additional Results for OPDA
We report the mean accuracy of all methods under the OPDA settings, as shown in Table A1 and Table A2 for the Office-Home, Office-31, and VisDA datasets. These results are consistent with the trends observed
H-scores and NMI metrics (Tables la 2a 1b 2bj. Our method achieves the highest average mean accuracy on Office-Home and Office-31, and performs comparably to GLC, the best-performing method, on VisDA.
Table A1: Mean Accuracy (%) on the Office- Home dataset under OPDA seltings.
Methods
SF FG A2C
A2P A2R
C2A
C2P
C2R
P2A
P2C
P2R
R2A
R2C
R2P Avg
Best Epoch
SHÖT-O [iang et al.
2020
x
36.9
55.9
58.1
52.0
55.2
62.0
50.7
41.0
62.7
53.1
36.9
56.5
51.8
41.8
40.5
+3.0
=3.
42.1
42.7
40.8
112
40.6
20.6
GLC {Qu et al. 2023
v x
44.5
74.4
89.1
57.8
68.5
89.2
70.3
47.8
87.9
74.5
47.6
79.7
69.3
10.4
11.7
11.1
202
14.9
10.5
10.9
21.0
10.2
10.7
10.5
20.0
ABC
50.6
82.8
90.1
73.9
82.2
88.6
72.0
86.9
79.0
50.5
81.8
73.9
41.7
12.0
102
21.
41.0
20.3
10.2
21.8
10.6
10.8
1111
21.1
Final Epoch
SHOT-O [Liang et al.
2020
x
41.0
56.0
58.1
54.7
54.4
62.0
53.9
42.6
60.7
55.3
42.9
57.7
53.3
10.8
10.8
139
20.
11.
10.2
11.
20.3
12.0
19.5
11.
GLC Qu et al. 2023
47.3
74.5
90.9
59.3
68.5
89.9
70.1
30.8
88.2
77.3
38.3
81.9
+0.2
+.6
+0.5
-18
+5.0
+0.2
+0.3
-1.5
+0.2
+0.9
+25
-0.0
GBNC-ouly
44.6
77.4
90.1
65.9
66.7
82.7
66.3
43.8
86.4
74.6
46.7
82.4
69.0
429
105
11.
10.6
10.
274
11 1
ABC
48.3
77.7
88.5
73.5
71.6
86.9
72.7
46.9
87.7
77.9
49.2
74.0
71.2
40.1
#4.0
22.
=18
48.7
+0.3
+0.4
20.6
412
114
22.
#2.4
To further assess clustering quality on the discovered unknown classes, we additionally report NMI (Vinh
et al. 2010) and Purity (Manning, 2008 compuled exclusively on the unknown-class samples identified by and A6 Since GLC and SHOT do not directly produce individual unknown-class labels, we follow the same procodure used for computing NMI on the full datasct: we use the cluster assignments obtained by applying DPM to the unknown samples detected by these methods, and then compute NMT and Purity based these assignments. This more fine-grained analysis complements
ABC, GLC, and SHOT Figures A3 A4
A5
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Table A2: Mean Accuracy (%) on the Office-31 and VisDA datasets under OPDA settings.
Methods
SF
FG
VisDA
Office-31
S2R
A2D
A2W
D2A
D2W
W2A
W2D
Avg
Best Epoch
SHOT-O (Liang al.
2020
29.5
58.5
55.6
56.6
76.9
55.5
65.6
61.5
+1.0
#2.4
=0.5
+1.7
+3.00
+2.3
+00
GLC [Qu et al.
2023
X
70.6
81.1
84.8
88.4
92.8
87.1
95.6
88.3
11.3
ABC
61.5
90.0
92.8
89.3
91.3
89.6
94.0
91.2
+1.2
+0.4
+1.6
+0.6
+0.7
+0.2
+1.0
Final Epoch
SHOT-O (iang et al.
2020
x
34.3
59.1
62.1
55.2
75.5
55.1
65.7
62.1
GLC Qu et
2023
/
x
73.2
80.4
88.2
90.7
93.7
90.8
92.5
89.4
+0.9
+1.0
-0.7
+0.2
+0.1
+0.3
+0.3
CBNC-only
29.5
80.4
89.1
84.1
83.6
80.1
94.3
85.3
40.2
1.0.0
22.7
13.6
2.5 5
10.4
1.000
ABC
/
63.4
88.7
92.3
89.9
89.5
89.8
94.4
90.8
+0.3
40.3
40.4
#12
the standard evaluation metrics and demonstrates that ABC, well as the DPM module when applied to different baseline methods, achieves reasonable performance in distinguishing individual unknown classes.
Overall, ABC achieves the highest average NMI in most settings: Final Epoch on Office-31, Best Epoch on Office-Home, and both settings on VisDA. Although this evaluation is conducted on the discovered unknown-class samples of each method, the results suggest that a unified Bayesian nonparametric framework that jointly detects known classes and separates unknown classes can yield better separation than performing separate BNC step on the unknown samples produced by existing source-free universal domain adaptation methods. On Office-31 and Office-Home, ABC attains average NMT of approximately 65% the unknown subsets, indicating good agreement between ground-trute truth and estimated labels. On VisDA, the lower NMI highlights the greater difficulty of this dataset, which is consistent with its lower overall classification performance reported in the main results. For Purity, we observe similar trend on Office-Home, where ABC achicves moderate agrecment with an average value around 60%. On VisDA and Office-31, ABC attains higher average Purity scores (approximately 67% and 87%, respectively) than NMI. Since Purity emphasizes cluster homogeneity, the gap between NMT and Purity suggests that clusters are relatively homogeneous but more numerous than the true classes, meaning some true classes are split into multiple smaller clusters. A similar discrepancy between Purity and NMI is also observed when applying the BNC module, DPM, to SHOT and GL.C. This behavior is consistent with the well-known tendency of Bayesian nonparametric clustering (BNC) methods to produce numerous small clusters that are often difficult to interpret (Müller eet al. 2013 Miller & Harrison 2013). Because ABC relies on a BNC module to cluster unknown samples, this clustclug phenomenon also appears in ABC's results. In the BNC literature, it is common to apply post-processing to filter out tiny clusters and focus on larger, meaningful clusters for downstream analysis (Wang et al. 2021 Ni et al., 2020a; Guha et al. 2021). Additionally, several methods handle small clusters through cluster merging using "clustering the clusters" strategy. In our downstream analyses (Appendices D.3 and D.4 we do not integrate this merging step, and thus our post-processing focuses solely on filtering. Incorporating merging stralegies will be considered as future work.
post- proseprocessing step; for example, SIGN (Ni et al.) 2020ch merges clusters
D.2 Runtime and Memory Analysis
The computational cost of ABC is primarily dominated by the VB procedure in the GBNC step. Assuming the truncation level K* is chosen a multiple of the expected number of clusters K, cach VB itcration has time complexity OdN), where N denotes the number of samples and d is the embedding dimension. In contrast, popular clustering-bart based domain adaptation methods (Qu et al, 2023 Li et al.) [022]] typically rely on KMcans or similar centroid-basod algorithms to detect unknown-class samples, with per-iteration complexity (d).)). Thus, both approaches scale linearly with respect to N; however, VB exhibits quadratic complexity in d, whereas KMeans scales linearly in d. This difference explains why our method is generally
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Table A3: NMI score (%) for discovered unknown-class samples on the Office-Home dataset under OPDA settings.
Methods
A2C
A2P
A2R
C2A
C2P
C2R
P2A
P2C
P2R
R2A
R2C
R2P
Avg
Best Epoch
SHOT-O Liang et al.
2020
46.6
68.8
62.8
54.0
64.6
62.0
52.9
47.2
63.7
55.4
47.2
69.7
57.9
DPM
10.4
10.3
108
208
103
110
110
10.7
112
10.
10.3
10.3
GLC QQu et al.
2023
DPM
47.7
71.9
69.1
56.6
72.3
69.5
57.4
47.5
69.0
58.1
48.7
72.0
61.7
49.6
75.6
72.1
61.9
75.2
71.2
63.6
49.6
72.4
65.1
48.0
76.8
65.1
20.8
20.9
21.0
21.
21.0
20.7
20.6
20.6
31.0
20.9
20.8
20.8
Final Epoch
SHOT-O [Lang et al.
2020
53.3
62.6
58.3
54.0
64.1
58.8
53.5
52.8
57.0
54.6
53.6
63.8
57.2
DPM
+1.1
+1.4
+13
+0.8
+0.8
+1.1
+0.5
GLC QQu et al.
2023
+DPM
72.5
72.3
69.0
77.4
72.3
69.5
58.9
66.8
68.6
59.3
65.6
71.6
68.7
ABC
64.5
20.3
21.1
20.9
20.7
20.6
20.9
20.8
20.2
10.5
11.2
20.8
20.3
Table A4: NMI score (%) for discovered unknown-class samples on the Office-31 and VisDA datasots under OPDA settings.
Methods
VisDA
Office-31
S2R
A2D
A2W
D2A
D2W
W2A
W2D
Avg
Best Epoch
SHOT-O (Liang al. 2020
26.9
72.3
75.2
50.0
71.8
48.7
70.3
64.7
DPM
+1.0
11.3
10.33
21.8
10.8
21.7
10.3
GLC (Qu al. 2023
DPM
26.1
74.4
74.0
49.9
72.1
50.3
70.2
65.2
10.3
1:0.7
1:0.9
21.3
1:02
ABC
34.8
69.0
74.2
50.9
74.7
51.0
70.6
65.1
10.2
10.8
1:0.3
20.2
1:0.7
20.8
2.3.5
Final Epoch
SHOT-O [Llang al.
2020 +
25.3
68.4
70.3
47.6
70.3
50.6
67.1
62.4
DPM
40.2
#1:2
#:111
1:0.6
1:0.8
-:2.5
+:07
GLC (Qu et al.
2023
+DPM
24.4
71.4
72.8
48.4
71.4
49.4
70.2
64.0
1:1.4
1:0.4
1:0.6
1:011
ABC
34.5
71.2
74.7
53.1
75.3
49.1
66.5
65.0
10.5
11.2
1:0.9
11.8
10.9
20.7
11.3
Table A5: Purity score (%) for discovered unknown-class samples on the Office- Homee dataset under OPDA
settings.
Methods
A2C
A2P
A2R
C2A
C2P
C2R
P2A
P2C
P2R.
R2A
R2C
R2P
Avg
Best Epoch
SHOT-O (Liang et 2020
36.4
69.1
61.1
43.2
61.2
58.2
42.1
36.9
61.4
45.6
36.4
69.5
DPM
40.4
+1.7
+22
20.8
42.3
GLC Quuer et
2023
+DPM
38.0
71.4
68.7
46.6
71.1
68.6
50.5
36.3
67.9
51.3
36.7
71.0
56.5
11.3
10.6
10.
20.7
103
4033
11
203
10.6
11.
11.
10.0
ABC
39.7
73.9
73.0
56.1
73.3
69.7
58.2
40.8
71.9
56.7
38.3
75.5
60.6
11.7
21.
Final Epoch
SHOT-O (Liang et
60.2
41.3
56.0
52.6
41.1
41.1
51.8
61.2
48.2
DPM
11.4
11.9
131
20.4
11.6
13.
114
20.8
11.9
11.7
10.6
11.7
GLC Qu
2023
+DPM
62.2
66.9
52.5
67.6
70.7
62.6
12.1
10.4
10.9
23.8
103
402
107
233
12.4
11.1
20.
10.0
ABC
41.2
73.4
71.9
55.4
71.8
68.4
58.6
39.9
70.4
56.0
39.4
73.8
60.0
203
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Table A6: Purity score (%) for discovered unknown-class samples on the Office-31 and VisDA datasets under OPDA settings.
Methods
VisDA
Office-31
S2R
A2D
A2W
D2A
D2W
W2A
W2D
Avg
Best Epoch
SHOT-O [Liang al.
2020:
57.9
99.8
98.7
66.3
98.7
65.6
100.0
88.2
DPM
+0.9
+0.4
+00.4
+1.4
+-0.4
+3.2
+0.0
GLC QQu et al.
2023
+DPM
63.1
99.1
98.1
66.1
98.7
65.1
100.0
87.9
40.7
+00.7
1:0.4
19.6
+:0.9
#1.4
+0.0
ABC
67.4
96.6
98.6
67.2
97.0
67.2
95.8
87.1
20.5
11.3
1:0.3
20.3
11.0
21.55
20.8
Final Epoch
SHOT-O [Liang et al.
2020
52.8
100.0
99.6
65.2
98.9
69.6
100.0
88.9
DPM
+0.2
+:0.0
+:0.8
+:0.6
+:0.7
+3.6
+0.0
GLC (Qu et al. 2023
+DPM
62.6
100.0
98.2
66.9
99.5
67.6
100.0
88.7
43.5
2:0.2
20.7
4:0.5
=2.0
+0.0
ABC
66.8
98.5
99.0
70.1
97.8
66.1
96.2
87.9
+0.4
+:08
+:0.2
+2.3
#111
#0.6
#0.4
slower than (Means-based approaches in the runtime comparisons (Tables A7a and A7b). Nevertheless, the linear scalability with N ensures that our method remains practical for large-scale datasets. For example, on the VisDA dataset with tens of thousands of target-domain images, much larger than the other two datasets, our method achieves a reasonable runtime, approximately twice that of GLC/SHOT in average time per epoch, and requires about 2.5 hours of total training time compared to 2 hours for GLC/SHOT, demonstrating good scalability practice.
Furthermore, as discussed in the introduction, the true number of unknown clusters is not known a priori. Unlike VB, which automatically infers the effective number of clusters given only an upper bound K*, KMeans requires a fixed pre-specified value of K. In practice, this often necessitates repeated clustering over multiple candidate values of K, resulting in additional computational overhead. If clustering is performed over M candidate values, the total complexity becomes O(N When M scales proportionally with K. (e.g., searching over a range such as [K/2, 2K] with unit step size), the overall complexity increases to d() leading to quadratic dependence on K. Even with more efficient search strategies, the cumulative cost of repeated clustering can be substantial. In this sense, the proposed method may exhibit increasing computational advantages as K grows when finer granularity in estimating K is required. Furthermore, the quadratic dependence on d in VB arises from modeling the full precision matrix, which captures covariance structure in the embedding space, information that KMeans does not incorporate. This richer representation can improve cluster quality in practice. If computational efficiency is prioritized, the precision matrix in our mothod can be casily constrained to be diagonal, reducing the complexity to O(NKd) while retaining automatic cluster number estimatiin and eliminating the need for repeated clustering.
Next, we evaluate both the training time and memory consumption of ABC and compare them with two bascline SFDA methods, SHOT and GLC, which are also included in performance comparison. Tables 77 and A7b reports both total training time (in minutes) and average time per epoch (in seconds). Despite modeling the covariance structure across features using a Dirichlet Process Gaussian Mixture Model, ABC remains computationally efficient. On Office-31 and Office-Home, entire training completes in under 10 and approximately 20 minutes on average, respectively, comparable to SHOT and GLC, a clustering- based approach using K-mcans. On the larger-scale VisDA-C datasot, ABC requires around 2.5 hours compared to GLC's hour, demonstrating reasonable scalability despite the added modeling complexity. While ABC is slightly slower than GLC, both methods exhibit similar orders of magnitude for total and per-epoch training time, indicating that ABC achieves a favorable balance between computational cost and modeling capability. Table A7c reports peak memory usage during training. ABC consumes roughly twice the memory of SHOT and GLC, likely due to caleulations involving the precision mairix. However, memory usage remains comparable to baseline methods and scales similarly across datasets different sizes, suggesting that ABC also exhibits good scalability in terms of memory. It is worth noting that GLC accelerates several of its KMeans steps using the FAISS EeeaaryJohnson et al.) 2219)), a highly optimized implementation with GPU acceleration and vectorized operations. In contrast, the iterative updates of our VB procedure are
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Table A7: Runtime and memory comparison under OPDA settings.
(a) Runtime comparison:
Office-Home
Methods
A2C
A2R C2A
C2P
C2R
P2A
P2C
P2R
R2A
R2C
R2P
Avg
Total Training Time (min)
SHOT-O (Lanne
2020
~ 1451555-01
13.
GLC (Qu
25.5-~274-22
ABC
11..2-17.11 1...01111..0.115--11111
Average Time per Epoch (5)
SHOT-O [Liang et al GLC QQu ét al. 2023
2020
~5 ~22
~20
-11
~22
~208
~-3
208
~62
~85
~11
~33
~:0
~13
~26
~22
~2
~22
ABC
~
~103
~213
~75
~02
~213
~7
-10
~104
~ 103
112
(b) Runtime comparison: Office311 and VisDA
(c) Memory comparison
Methods
VisDA
Office-31
Methods
Office-
Office- Home
VisDA
S2R
A2D
A2W
D2A
D2W
W2A
W2D Avg
31
Total Training Time (min)
Peak Memory (GB)
SHOT-0 Liang et al.
121.3
~4.2
~3.
~7.9
33.
~7.8
~4.2
~5.2
SHOT-
~1.7
Liang
2020
Qu 2023
117.6
~4.5
+152
~5.8
~14
~84
2020
ABC
146.0
~3.7
~8.3
~3.9
~8.4
~3.7
~5.
~1,9
~27
~21
Average Time per Epoch (s)
SHOT-O Liang et al.
448
~>17
~13
~32
114
~31
~21
2020
~5
~110
ABC
875
~22
~2
~00
2/3
~50
~22
implemented in standard Python without specialized acceleration. Therefore, ABC's runtime could be further reduced through optimized implementations leveraging high-performance computing techniques such GPU parallelization or optimized linear algebra. libraries.
D.3 Finding the Number of Estimated Clusters
As part of our downstream analysis, we report the estimated number Kank of unknown clusters and compare it with the true value. Figure A1 shows this comparison, with results reported separately for the best epoch and the final epoch. As discussed in Appendix D.1 BNC models tend to generate many tiny clusters, and thus post-processing steps to filter out such clusters are commonly adopted. Following the same practice as in (Wang et al., 2021), in Figure A1 we focus only on the major clusters with 1% of the total images when counting Kank- As shown in Figure A1 for Office-31 and VisDA, the estimated number of unknown clusters closely matches the ground truth, indicating that ABC reliably estimates Kunk across multiple transfer tasks on Office-31 and on the VisDA transfer task. In contrast, the number of clusters is underestimated for Home. While estimating Kank without prior knowledge is inherently challenging, ABC produces accurate estimates in some tasks and generally provides a reasonable approximation across datasets.
D.4 Visualization of Discovered Unknown Clusters
In this section, we present t-SNE visualizations of discovered unknown clusters based on their learned embeddings. The t-SNE algorithm produces a low-dimensional representation that preserves local structure by maintaining the relative proximity of similar points from the original high-dimensional embedding space (Van der Maaten & Hinton 2008 Specifically, we apply t-SNE to obtain nonlinear two-dimensional mapping for visualizing the sample distribution of the major unknown clusters described in Appendix D.3 The resulting visualizations are shown in Figures A2 and A3 corresponding to the Best Epoch and Final Epoch, respectively. In each figure, individual points are colored according to their estimated cluster labels, Across most settings, the visualizations exhibit well-separated groups that align closely with the estimated labels, indicating that ABC effectively partitions samples from discovered unknown classes and supports fine-grained discrimination.
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True vs Estimated Number of Unknown Clusters (Final Epoch)
Office-Ntmme-
Office-11 Thus
Number of Unkracen Clusters
VisDa Est
G2A
Transfer Tasks
(a) Final epoch
Estimated
Epoch)
OfficeHome Est
Number of Unknooenn Clesters
VisDa True
VisDa Est
WSA
W20
588
Transter Tasks
(b) Best epoch
Figure A1: Evaluation of Unknown Cluster Number Estimation. The hatched bars represent the true number of unknown clusters, while the solid bars represent the estimated number.
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aa) Office-31
(b) Office-31
(c) Office-31
(d) Office-31 31
(e) Office-31
Office-31
(g) VisDA-C
(h) Home
Office- Home
Office- Home
(k) Office- Home
(1) Office- Home
dlear Read Werd
Aut
Pnodct Clasrt
Podect -lat, Word
(m) Office-Homee
(n) Office-Homme
Office-Home
(p) Office-Home
(q) Office-Home
(r) Office-Home
(s) Office-Home
Figure A2: t-SNE visualization of discovered unknown classes (Best Epoch). Each point is colored according to its predicted cluster label.
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comppnentt
(a) Office-31
(b) Office-31
(c) Office-31
(d) Office-31 31
(e) Office-31
(f) Office-31
(g) VisDA
(h) Office- Home
(i) Office Home
Office- Home
(k) Office- Home
(1) Office- Home
dlear rest Werrd
Hodeed Aut
Poduct -lat, Worr
(m) Office-Homne
nn) Office-Home
Office-Home
(p) Office-Home
(q) Office-Home
(r) Home
(s) Office-Home
Figure A3: t-SNE visualization of discovered unknown classes (Final Epoch). Each point is colored according to its predicted cluster label.
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D.5 Results for OSDA
In this section, present results under the OSDA setting for the Office-31 dataset, reporting H-score, mean accuracy, and NMI in Tables A8 A9 and A10 respectively. We follow the standard experimental split used in prior work (Qu ct al.) 2023), with 10 shared, O sourco-private, and 11 target-private classes. The results are consistent with our observations from the OPDA settings, with our method achieving solid performance across metrics. Notably, SHOT shows significantly improved performance under the OSDA setting, achieving the highest average mean accuracy.
Table A8: H-score (%) on the Office-31 dataset under OSDA settings.
Methods
SF FG
Office-31
A2D
A2W
D2A
D2W
W2A
W2D
Avg
OSBP
SSito et al
2018
82.4
82.7
75.1
97.2
73.7
91.1
83.7
ROS
[Buce et al 2020
82.4
82.1
77.9
96.0
77.2
99.7
85.9
CMU
2020
52.6
55.7
76.5
75.9
65.8
64.7
65.2
DANCE CE Salto el al
2020
X
84.9
78.8
79.1
78.8
68.3
88.9
79.8
DCC
cf al.
58.3
54.8
67.2
89.4
80.9
72.6
OVANet Satto & Sãenko
X
90.5
88.3
86.7
98.2
88.3
98.4
91.7
2021
GATE
Chen al. 2022)
88.4
86.5
84.2
95.0
86.
96.7
89.5
Best Epoch (Best H-score)
SHOT-- (Liagg et al.
2020
89.1
86.4
82.7
89.2
74.3
86.0
84.6
#1.6
+1.1
+0.6
GLC QQu et al.
2023
83.2
76.7
92.5
95.3
92.9
86.0
87.8
10.3
10.4
10.4
10.3
ABC
90.1
91.4
91.6
20.8
20.6
41-1
21-1
11.7
41.3
Final Epoch
SHOT-O (Liang et al. 2020
85.4
82.0
68.1
78.4
66.8
85.7
77.7
11.0
13.1
43.0
11.6
13.0
10.5
GLC (Qu et
/
75.4
92.4
95.3
87.0
-0.3
+0.5
+0.4
+0.4
+0.2
+0.2
GBNC-only
89.3
87.9
87.7
89.3
83.9
94.1
88.7
10.7
88.9
88.4
87.3
91.2
88.7
=12
#0.0
+8.0
#0.9
#0.0
#1.0
Table A9: Mcan Accuracy (%) on the Offico-31 dataset under OSDA scttings.
Methods
SF
FG
Office-31
A2D
A2W
D2A
D2W
W2A
W2D
Avg
Best Epoch
SHOT-O [Llang al. 2020
x
89.9
90.9
87.1
91.7
74.6
85.6
86.6
1:0.7
+1.9
13.2
11.8
15.0
GLC QQu et al.
2023
x
76.9
67.7
92.0
94.2
91.3
77.7
83.3
+0044
+0.2
+0.2
ABC
91.2
90.4
92.7
+0.5
+1.6
+1.2
+1.8
+0.4
+1.8
Final Epoch
SHŌT-O [Langg et al.
2020
X
92.7
94.3
90.2
94.2
77.2
86.7
89.2
+0.2
GLC QQu al. 2023
X
74.8
65.1
92.0
94.2
91.5
75.0
20.6
10.6
10.2
10.2
1:0.2
1.0.2
GBNC-only
93.1
83.9
82.2
83.5
80.4
92.2
85.9
ABC
87.3
90.0
87.0
81.9
89.7
92.8
88.1
20.3
$1.9
13.1
11.3
10.8
$1.5
34

---

Published in Transactions on Machine Learning Research (04/2026)
Table A10: NMI (%) on the Office-31 dataset under OSDA settings.
Methods
Office-31
A2D
A2W
D2A
D2W
W2A
W2D
Avg
Best Epoch
SHOT-O (Liang al.
2020
80.5
81.1
70.5
81.0
68.8
80.0
77.0
{ DDM
+0.2
10.5
2.000
#0.3
10.6
20.3
GLC Qu
2023
DPM
79.2
78.6
69.0
83.3
69.0
80.6
76.6
#0.5
#0.9
20.2
+-0-1
+0.3
#0.1
ABC
80.4
83.7
70.1
84.3
70.5
82.4
78.6
+1.8
Final Epoch
SHOT-O Liang al. 2020
80.7
81.4
69.9
79.8
68.2
79.9
76.7
{ DPM
+0.7
#0.7
+0.3
#0.6
+0.66
#0.1
GLC Qu
2023
DPM
79.4
79.1
83.3
68.8
80.3
76.7
20-4
2001
10.3
20.3
GBNC-only
79.8
82.5
69.6
83.6
69.6
81.8
77.8
10.0
1.0.6
10.4
10.9
10.1
ABC
80.1
83.3
69.5
81.8
78.0
10.4
20.5
20.2
20.9
10.4
20.7
D.6 Additional Ablation Study and Sensitivity Analysis Results
In this section, we present supplementary figures for the ablation studies and sensitivity analyses discussed in the main text. We first show comparison between the Beta mixture detector and the OOD detectors in terms of NMI and mean accuracy for our ablation study (Figure A4). The results based NMI lead to conclusions consistent with those obtained using HOS in the main text, whereas the mean accuracy results reveal a slight difference: on Office-Home, the OOD detectors achieve marginally better performance across transfer tasks. This difference expected, as the OOD detectors tend to retain more samples as known classes, while mean accuracy places less emphasis on unknown-class performance by treating the aggregated unknown class a single category, equivalent to each individual known class.
We further provide supplementary figures and extended discussion the sensitivity analysis of key hyperpa- rameters in our model under the OPDA setting, including Atee: Km, and 8. These results are visualized across multiple figures (Figures A3 A10 and cover metrics such as H-score, NMI, and mean accuracy at the Final Epoch on the Office-31 and Office- HooceeHHoee&e datasets.
To provide a comprehensive view of hyperparameter effects, we present two complementary visualization formats. Specifically, line plots (Figures A5 A7 illustrate per-task performance variations as each hyperpa- rameter changes, highlighting the response patterns across different domain adaplation scenarios. In contrast, bar plots (Figures A8 A10 summarize the average performance across all tasks, offering high-level overview of model robustness.
Overall, the results show that the performance of our model remains stable across a broad range of hyper- parameter values, with only moderate sensitivity observed in specific cases. For instance, the performance (measured by NMI and H-score) remains stable when varying a, while is slightly more sensitive to the choice of Kmn- The results validate our hyperparameter choices and indicate that ABC performs well without. extensive tuning, making it practical for real-world deployment.
35

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Published in Transactions on Machine Learning Research (04/2026)
CUMMIR 10PFoN-311
CANVVEIA LUTTION (OTTOIOOOTT
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exanelic
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628
(b) Mean Accuracy
Figure A4: Beta mixture detector vs. OOD detectors
36

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Published in Transactions on Machine Learning Research (04/2026)
80
HO5
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(h) Office- Home: Sensitivity 5
Figure A5: Hyperparameter sensitivity analysis per task (H-score) of Alocs a, K Knn, and ô on Office-31 and Oliie-Home under the OPDA setting.
37

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Published in Transactions on Machine Learning Research (04/2026)
95
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Home / Final Epoch
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(g) Office-Home: Sensitivity on Kmn
(h) Office-Home: Sensitivity 5
Figure A6: Hyperparameter sensitivity analysis per task (NMI) of Aioes a, Knns and d on Office-31 and Olfie-Home under the OPDA setting.
38

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Published in Transactions on Machine Learning Research (04/2026)
ACC (8p
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(g) Office-Home: Sensitivity on Kmn
(h) Office-Home: Sensitivity 5
Figure A7: Hyperparameter sensitivity analysis per task (Mean Accuracy) of Alees a, Kmn and å on Office-31 and Office-fHooeeee under the OPDA setting.
39

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Published in Transactions on Machine Learning Research (04/2026)
Office-31 / Final Epoch
Office-Home / Final Epoch
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(g) Office-31: 8
(h) Office-Home: 8
Figure A8: Hyperparameter sensitivity (H-sccrre) of Moees Knn, and 6 on Office-31 and Office- under OPDA.
40

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Published in Transactions on Machine Learning Research (04/2026)
Office-31 / Final Epoch
Office-Home / Final Epoch
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(g) Office-31: 8
(h) Office-Home: 8
Figure A9: Hyperparameter sensitivity (NMI) of Xioes a, Knn, and 8 on Office-31 and Office- under OPDA.
41

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Published in Transactions on Machine Learning Research (04/2026)
Office-31 / Final Epoch
Office-Home / Final Epoch
90
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(h) Office- Home: 8
Figure A10: Hyperparameter sensitivity (Mean Accuracy) of Xioes a, Knn, and 8 on Office-31 and Office-Home under OPDA.
42


Reviews:
[{"review_id": "idPn9aBzMY", "reviewer": "Reviewer_tY5x", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposes Adapt via Bayesian Nonparametric Clustering (ABC) for source-free domain adaptation under category shift, where unknown target classes are present. Unlike prior SFDA methods that treat all unknown classes as a single category, ABC discovers fine-grained clusters among unknown samples without requiring the number of clusters a priori. The method detects high-confidence known-class samples via a Beta mixture model on cosine similarities, applies a guided Dirichlet Process Mixture clustering using these as anchors, and refines the source model through prototype-based and local consistency regularizers. Experiments on Office-31, Office-Home, and VisDA-C show competitive H-scores against SFDA and non-source-free baselines, with additional NMI results demonstrating effective fine-grained clustering of unknowns.\n\nKey Strengths:\n1. The paper addresses an underexplored yet practical aspect of SFDA—fine-grained discovery of unknown classes rather than collapsing them into a single category. Integrating Bayesian nonparametric clustering into the SFDA pipeline, guided by high-confidence known-class anchors, is technically sound and represents a meaningful contribution to the field.\n2. The evaluation covers three standard benchmarks under OPDA settings, reports both classification (H-score, mean accuracy) and clustering (NMI) metrics, and provides extensive sensitivity analyses across multiple hyperparameters (δ, α, K_nn, λ_loc), supporting robustness claims.\n3. The DPM-based clustering, prototype learning, and neighborhood consistency are combined in a unified iterative framework, reducing error propagation between clustering and adaptation compared to post-hoc clustering approaches applied to existing methods.\n\nKey Weaknesses:\n1. he paper does not report the estimated number of unknown clusters versus ground truth, nor does it provide ARI or purity metrics specifically on the unknown subset, making it difficult to assess over- or under-clustering behavior. Runtime and memory comparisons against baselines are also absent.\n2. The anchor-guided mechanism lacks analysis of failure scenarios when high-confidence labels are incorrect or when the number of discovered common classes diverges from source classes. The remapping procedure between cluster indices and known-class labels is not fully detailed.\n3. The Gaussian likelihood with Normal-Wishart prior may not be well-suited for L2-normalized embeddings lying on a hypersphere, and robustness to non-Gaussian cluster structures in the feature space is not empirically examined.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The main claims regarding competitive H-score performance and effective fine-grained clustering are supported by experiments on three standard benchmarks with appropriate metrics and sensitivity analyses. However, the evidence would be more convincing with runtime comparisons, variance reporting across seeds, and diagnostics on the estimated number of unknown clusters versus ground truth.", "audience_yn": "Yes", "audience_explanation": "Fine-grained discovery of unknown classes in source-free domain adaptation is a practical and underexplored problem relevant to researchers in transfer learning, domain adaptation, and Bayesian nonparametrics.", "requested_changes": "Report the estimated number of unknown clusters versus ground truth along with ARI/purity on the unknown subset, and include runtime/memory comparisons against baselines. Strengthening: Add variance reporting across multiple seeds, ablate the Beta-mixture detector against alternative OOD criteria, and clarify the failure modes and remapping procedure for the anchor-guided mechanism.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "y007p4yTl3", "reviewer": "Reviewer_B4mX", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper introduces a unified framework for source-free domain adaptation (SFDA) that leverages Bayesian nonparametric clustering (specifically, Dirichlet Process Mixtures with variational Bayes inference) to discover latent structure within unknown classes. The authors argue that treating all unknown classes as a single category is limiting, and propose integrating clustering and model adaptation in a joint optimization framework. Key strengths include the unified design (which minimizes error propagation between clustering and adaptation), a thorough sensitivity analysis, and a principled theoretical foundation. However, the work does not convincingly demonstrate technical advantages over recent state-of-the-art methods, and the evaluation lacks comparison with the latest USDA benchmarks. The related work section also does not sufficiently position this approach relative to other clustering-based SFDA methods.", "claims_and_evidence_yn": "No", "claims_explanation": "While the paper provides a principled approach and some empirical evidence, the claims regarding the superiority of the proposed method are not fully supported. The evaluation is limited to comparisons with older baselines (2020–2023), omitting recent state-of-the-art methods such as those reported in \"[P1] Revisiting Source-Free Domain Adaptation: Insights into Representativeness, Generalization, and Variety\" (CVPR 2025), which achieves higher performance on standard benchmarks (e.g., 74.1% on Office-Home with ResNet-50, compared to 72.9%/69.9% for the proposed method). Furthermore, the paper does not provide compelling experimental scenarios where the proposed technique clearly outperforms prior arts, nor does it address or introduce challenging settings (e.g., Class-Incremental Domain Adaptation, ECCV 2020) where its benefits would be more apparent.", "audience_yn": "Yes", "audience_explanation": "The problem of unknown class discovery in source-free domain adaptation is of practical and theoretical interest to the TMLR audience. The integration of Bayesian nonparametric clustering with model adaptation is a reasonable incremental step, and the sensitivity analysis may provide useful insights for researchers working on related problems. However, the impact of the work is currently limited by the lack of compelling empirical results and insufficient comparison with recent advances.", "requested_changes": "Critical:\n1. Provide comprehensive experimental comparisons with recent state-of-the-art SFDA methods, especially those reported in \"[P1] Revisiting Source-Free Domain Adaptation: Insights into Representativeness, Generalization, and Variety\" (CVPR 2025) and other 2024–2025 works. Clearly state where the proposed method stands relative to these.\n2. Demonstrate use cases or experimental scenarios (e.g., class-incremental domain adaptation) where the proposed technique offers clear advantages over prior arts, or provide a discussion if such cases do not exist.\n3. Enhance the related work section to explicitly position this approach against other clustering-based SFDA methods, such as \"Universal Source-Free Domain Adaptation\" and \"Domain Consensus Clustering for Universal Domain Adaptation,\" clarifying the unique contributions and differences.\n\nWould Strengthen the Work:\n1. Clarify the rationale for reporting both \"best epoch\" and \"final epoch\" results, and discuss the stability/convergence of the method.\n2. Consider moving part of the theoretical contributions (e.g., variational Bayes inference) from the appendix to the main text if they represent a good theretical contribution.", "broader_impact_concerns": "I do not have significant concerns regarding the broader impact or ethical implications of this work. The paper addresses a methodological advance in domain adaptation and does not raise obvious ethical or societal risks. The authors may wish to briefly discuss potential misuse or limitations in the Broader Impact Statement.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "gTNrrS7dWI", "reviewer": "Reviewer_wERe", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper addresses Source-Free Domain Adaptation (SFDA) under category shift, where the target domain contains classes not present in the source domain. The authors propose Adapt via Bayesian Nonparametric Clustering (ABC), a framework that moves beyond treating all unknown classes as a single group. Instead, it performs fine-grained classification of unknown target classes by automatically discovering their latent structure.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The authors provide extensive experimental evidence across three standard benchmarks: Office-31, Office-Home, and VisDA. They compare ABC against both SFDA and non-SFDA baselines using multiple metrics (H-score, mean accuracy, and NMI). The inclusion of ablation studies and hyperparameter sensitivity analyses demonstrates that the performance gains are due to the proposed components and are robust to parameter settings.", "audience_yn": "Yes", "audience_explanation": "The paper addresses the highly relevant and practical problem of Source-Free Domain Adaptation, which is crucial for privacy-preserving machine learning. By introducing fine-grained classification for unknown classes, it pushes the boundaries of standard \"unknown detection\" and opens new avenues for open-set recognition and deep clustering. Researchers in domain adaptation, transfer learning, and Bayesian nonparametrics would find these results significant.", "requested_changes": "1. Clarification on Scalability: Provide a more detailed discussion or complexity analysis regarding the Variational Bayes inference compared to simpler SFDA methods, especially for the VisDA dataset where performance was slightly lower than the top baseline.\n\n2. Visualizations of Discovered Clusters: Including t-SNE visualizations of the discovered unknown classes (the fine-grained clusters) would more intuitively demonstrate the \"fine-grained\" claim.\n\n3. Comparison of Computational Time: A table comparing the per-epoch training time of ABC versus SHOT/GLC would help quantify the \"cost\" of the nonparametric clustering.", "broader_impact_concerns": "There are no significant ethical concerns. The paper focuses on Source-Free adaptation, which inherently promotes privacy by avoiding the need for raw source data during the adaptation process. The potential applications mentioned (medical imaging, robotics, security) are beneficial, though as with any classification model, users should be cautious about biases in the pretrained source model.", "additional_comments": "N/A", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)