Prior-free Tabular Test-time Adaptation
Authors: Rundong He
Jieming Shi
Venue: ICLR 2026 Poster (2026)
Keywords: Tabular Test-time Adaptation
Prior-free
Primary area: transfer learning, meta learning, and lifelong learning
TL;DR: Our method addresses both label and feature shifts in tabular data under source-free and prior-free constraints.

Abstract: Deep neural networks (DNNs) have been effectively deployed in tabular data modeling for various applications. However, these models suffer severe performance degradation when distribution shifts exist between training and test tabular data. While test-time adaptation (TTA) serves as a promising solution to distribution shifts, existing TTA methods primarily focus on visual modalities and demonstrate poor adaptation when directly applied to tabular modality. Recent efforts have proposed tabular-specific TTA approaches to mitigate distribution shifts on tabular data. Nevertheless, these methods inherently assume the accessibility of source domain or prior and fail to fundamentally address feature shift while overlooking unique characteristics of tabular data, leading to suboptimal adaptation. In this paper, we focus on the problem of \textit{prior-free tabular test-time adaptation} where no access to source data and any prior knowledge is allowed, and we propose a novel method, \underline{P}rior-\underline{F}ree \underline{T}abular \underline{T}est-\underline{T}ime \underline{A}daptation (PFT$_3$A), which has three designs to simultaneously address label shift and feature shift without source domain or prior access. Specially, PFT$_3$A contains the \textit{Class Prior Estimating} module for estimating source-target class priors to calibrate prediction, eliminating dependency on source class prior and mitigating label shift; the \textit{Robust Feature Learning} module for learning robust feature by aligning source-like and target-like features to mitigate feature shift; the \textit{Representative Subspace Exploration} module for eliminating redundant features by projecting feature into subspace to enhance feature alignment. Extensive experiments demonstrate the effectiveness and generalization of PFT$_3$A in tabular TTA tasks. The implementation is at \url{https://github.com/rundohe/PFT3A}.

Published as a conference paper at ICLR 2026
PRIOR-FREE TABULAR TEST-TIME ADAPTATION
Rundong He Jieming Shi
Department of Computing, The Hong Kong Polytechnic University he he com, jieming. shi epwlyu.
ABSTRACT
Deep neural networks (DNNs) have been effectively deployed in tabular data mod- eling for various applications. However, these models suffer severe performance degradation when distribution shifts exist between training and test tabular data. While test-time adaptation (TTA) serves as a promising solution to distribution shifts, existing TTA methods primarily focus on visual modalities and demonstrate poor adaptation when directly applied to tabular modality. Recent efforts have proposed tabular-specific TTA approaches to mitigate distribution shifts on tabular data. Nevertheless, these methods inherently assume the accessibility of source domain or prior and fail to fundamentally address feature shift while overlooking unique characteristics of tabular data, leading suboptimal adaptation. In this paper, we focus on the problem prior-free tabular test- test-time adaptation where access to source data and any prior knowledge is allowed, and propose a novel method, Prior-Free Tabular Test-Time Adaptation (PFT3A), which has three designs to simultaneously address label shift and feature shift without source domain or prior access. Specially, 3FT contains the Class Prior Estimating module for estimating source-target class priors calibrate prediction, eliminating dependency on source class prior and mitigating label shift; the Robust Feature Learning module for learning robust feature by aligning source-like and target- like features to mitigate feature shift; the Representative Subspace Exploration module for eliminating redundant features by projecting feature into subspace enhance feature alignment. Extensive experiments demonstrate the effectiveness and generalization of PFT&A tabular TTA tasks. The implementation is at nttps::/githiei com com/runddoe//PF33..
INTRODUCTION
Deep neural networks (DNNs) have achieved remarkable success in modeling tabular data, deliv- cring statc-of-the-arr performance in critical applications such as fraud detection and healthcare diagnostics (Hollmann al. 2022). However, their deployment in real-world scenarios is often challenged by distribution shifts of labels and features between training (source) and test (target) tabular data (Gardner et al.) 2023). These shifts, caused by temporal changes, geographic variations, or sampling biases, can lead to significant performance degradation. For example, a model trained on 2024 economic data may perform poorly when predicting 2025 market trends due shifts in economic policies or geopolitical events that alter underlying data distribution (Okeleke et al., 2024).
Test-time adaptation (TTA) has emerged as promising solution to address distribution shifts by adapting model parameters using unlabeled test data during inference, without requiring retrain- ing (Liang et al. 2020p. While methods like Tent (Wang et al., 2020) and EATA (Niu et al., 2022) have shown success, their development has primarily focused on visual data. However, directly applying these methods to tabular data results suboptimal performance (Zhou et al. 2024), as they do not consider the distinct characteristics of tabular data.
The Tableshift benchmark (Gardner et al.) 2023) identifies two key types of distribution shifts in tabular data: feature shift,, where feature distributions differ between training and testing, and label shift, where label distributions are mismatched. Fig. [(b) demonstrates that the performance of TabPFN (Hollmann et al. 2025). tabular foundation model, degrades significantly under distribution
"Corresoonding author

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100
Teburar Data
tabular datz
12 terget
Xhi
Ps: sounce class prior
batebsize
the index batch
6
21-3-
unisbeled baich how data
Tabular Data
Talutar Dota
Tabuter Data
20
Hyperwssoo
Datsents
(b)
Figure 1: (a) The introduction of prior-free free test-time adaptation tabular data. (b) Performance comparison of the tabular foundation model (TabPEN) on test data with (without) distribution shift.
shifts. Recent tabular-specific TTA methods, like AdapTaale (Kim et al. 2024 and TabLog (Ren
al. 2024) address label shift and identify invariant rules for tabular data. Cai & Ye (025) optimize
time-aware data splits and model periodicity via Fourier series to tackle degraded generalization under temporal distribution shifts. Drifi-Resilient TabPFN (Helli al. 2024 integrates causal inference with meta meta-learning to handle temporal distribution shifts in tabular data. However, these methods assume access to training data, limiting their real-world applicability. FTAT (Zhou al., (202)) mitigates label shift by optimizing label distributions, addresses feature shift by filtering low-quality predictions, and employs online ensemble learning for robust predictions without requiring source data. While FTAT reduces reliance on training data, it still depends on domain -specffc priors. As
illustrated in Fig. [(a) real-world applications frequently require adapting source-trained model to unlabeled test data with distribution shifts, without access source data and domain-specifie priors.
In this work, we focus on the problem of prior-free tabular test-time adaptation where no access to source data and any prior knowledge is allowed, and we propose novel method, Prior-Free Tabular Test-Time Adaptation (PFT3A), which has three designs to simultancously address label shift and feature shift without source domain access filtering test data. Specially, PFT; contains the Class Prior Estimating module for estimating source-target class priors to calibrate prediction, eliminating dependency on source class prior and mitigating label shift; the Robust Feature Learning module for learning robust feature by minimizing the Kullback-Leible (KL) divergence between source-like and target-like features mitigate feature shift; the Representative Subspace Exploration module for eliminating redundant features by projecting feature into subspace to enhance feature alignment. To summarize, the contributions of this paper are fourfold:
We introduce novel problem, prior-free tabular test-time adaptation, and propose the PFT method to address this challenge.
We design a Class Prior Estimating module to mitigate label shift by estimating source-target class priors, eliminating dependency source class prior.
We enhance feature alignment through Robust Feature Learning and Representative Subspace Exploration, addressing feature shift and eliminating redundant features.
Extensive experiments demonstrate that PFT outperforms state-of-the-art TTA methods.
2 RELATED WORK
Test-Time Adaptation (TTA). TTA adapts a pre-trained source model to distribution shifts in test data without accessing source data. Existing methods primarily address feature shifts, where conditional distributions remain consistent but marginal distributions differ. Approaches include leveraging class prototypes or pseudo-labels (Chen al. 2022, Dang et al.] 2002], Goyal al.. 2022, Liang et al., 2020), and employing self-supervised learning (SSL) on auxiliary tasks like rotation prediction (Liang et al., 2021 or masked autoencoding (Gandelsman et al. 2022 Ren et al. 2023) to enhance robustness. Test-Time Training methods, such as TTT et al. 20200 and TTT+ et al. 2021), ), jointly train models on primary and auxiliary SSL tasks, enabling updates with unlabeled test data. but its reliance source data limits applicability. Fully TTA methods, such as Tent (Wang et al. 2020) and EATA (Niu et al. 2022), adapt models without source data by updating batch normalization (BN) layers employing sample selection strategies. Similar BN
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adaptation techniques are explored in (Goyal et al. 2022). TDA (Karmanov et al. 2024) enables effective and efficient test-time adaptation with vision- language models. While effective in vision tasks, these methods remain largely unexplored for tabular data.
Recent works like TdapTablc (Kim ct al. 2024) and TabLog (Ren et al, 2024) address label shifts and identify invariant rules for tabular data. Cai & Ye 2025) optimize time-aware data splits and model periodicity via Fourier series to tackle degraded generalization under temporal distribution shifts. Drift- PrifttResilieet TabPFN (Helli al. 2024) integrates causal inference with meta-learning to handle temporal distribution shifts in tabular data. However, these methods assume access to training data, limiting their real-world applicability, FTAT (Zhou al. 2024) mitigates label shift by optimizing label distributions, addresses feature shift by filtering low-quality predictions, and employs online ensemble learning for robust predictions without requiring source data, While FTAT reduces reliance on training data, it still depends on domain-specific priors. In contrast, we propose prior-agnostic test-time adaptation framework for tabular data, eliminating dependencies on training data and domain-specific priors.
Deep Tabular Learning.
Learning on tabular data focuses on applying advanced techniques to tasks like classification and regression. Unlike image or text data, which exhibit spatial or sequential patterms, tabular data is often high-ding figh-dimmessioal and heterogeneous, posing unique challenges for traditional models. Recent works have introduced specialized deep learning architectures to address these challenges. FT- FTT-Trasformmer (Gorishniy et al. 2021) employs feature tokenizer to process diverse feature columns and generate optimal embeddings. TabTransformer (Huang et al. 2020 leverages self-attention to model complex feature interactions, while TabNet (Arik & Plister 2021
integrates decision trees with deep learning for enhanced interpretability. Other methods, such as Deep Feature Interaction Network (DeepFIN) (Klambauer et al., (017) and TabCNN (Gorishniy
al. 2022). further explore effective representation learning for tabular data. TabPFN (Hollmann et al. 2022; 2025), transformer- based foundation model, excels in supervised classification on
small tabular datasets by using in-context learning and a causal prior for efficient Bayesian inference.
However, despite their success in i.i.d. settings, these models often struggle under distribution shifts.
PROBLEM AND ANALYSIS
In this section, define the prior-free tabular test-time adaptation problem, introducing its notations and formulation (Section 3.1). We then identify the core challenges of tabular TTA and highlight the limitations of existing methods through three focused analyses (Section 3.2.
3.1 PROBLEM FORMULATION
Definition (Test-time Adaptation (TTA).) Let D (xi, 3k) } be N₂ labeled samples from source distribution Q over X x Y, where X is the input space and y f1,..., K, is the label space with K classes. During adaptation, unlabeled target data Dr = )=, sampled from a different distribution P (P + Q). arrives sequentially in batch D.. Given source model fe, X + y trained on D2 with initial parameters fu TTA dynamically updates fe, using only the incoming unlabeled batch D/, without accessing D., to address distribution shifts.
Definition 2 (Prior-free Tabular Test-time Adaptation.) Extending Definition 7 this setting focuses on tabular data, where both D2 and D, belong to the tabular modality. Given a source model fe, X +y trained D, with initial parameters 8G, the goal is adapt fe, using only the incoming unlabeled tabular batches DL, without access D, or source class prior Ps (i.e., prior- free), to address distribution shiftss Here, X C Ra represents the tabular input space, where d denotes the number of columns. each being either continuous or discrete.
3.2 ANALYSIS
Feature shift and label shift are two common types of distribution shifts in tabular data (Gardner et al. 2023). Feature shift arises when the feature distributions between training and testing data differ. For instance, in ASSIST (Gardner et al.) 2023), cross cross-school generalization suffers accuracy drop due to disparities in input feature distributions (e.g., problem-solving behaviors, study habits)
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00.11%
Adspiatio
FTT nur pitrr
To/
18%
70-
LAVE
50.12%
800
94%
11:00
TENT
Non-ddutstton
60.77%
58.0 56.5 39
58.5
ni.
60.5
01.0
81.5
HELOC
Heath Dutasets
ASSIST
Accurscy (%)
(b)
Figure 2: (a) The average accuracy results of various classic TTA methods and Non-Adaptation on five tabular datasets. Accuracy Comparison of Non-Adaptation, FTAT with prior, and FTAT without prior across HELOC, Health Ins., and ASSIST.
across schools. Label shift occurs when the label distribution varies between domains. Existing TTA methods struggle with tabular data. Fig. 2(a) compares the average accuracy of classic TTA methods, including TENT (Wang et al.) 2020), EATA Niu et al. 2022), CoTTA (Wang et al. 2022). SAR (Niu) et al. 2023), LAME (Boudiaf et al. 2022). ODS (Zhou et al. 2023). and Non-Adaptation (direct evaluation without TTA) on five tabular datasets. These methods often underperform Non-Adaptation, with average accuracies of 58% (TENT) and 57.56% (ODS) compared to 60.77% for Non-Adaptation. Originally developed for visual data, these methods struggle with tabular TTA. Moreover, existing tabular TTA methods face the following three major limitations: (i) Ineffectiveness in prior-free scenarios. Current methods like AdapTaabl (Kim et al.) 2024) and TabLog (Ren et al., (022) address label and covariate shifts but rely on access source data, which often unavailable in real-worth applications. While FTAT (Zhou et al. 2024) climinates the need for source data, it still depends on class priors derived from the source distribution, limiting its effectiveness in prior-free fior-frre settings. Fig. 2(b shows that the absence of class priors leads to a significant accuracy drop for FTAT across datasets such as HELOC, Health Ins., and ASSIST. This underscores the need for TTA methods that are both source-free and prior-free for robust adaptation in real-world tabular scenarios. (ii) Limitations of filtering low-confidenee samples. Feature shift arises from discrepancies between source and target feature distributions. Filtering low-confidence target samples excludes target-specific data without addressing the underlying mismatch. High-con high-coofidence samples often resemble the source domain, while low-confidence ones capture target-specific traits. Discarding the latter biases the model towards cource-like representations, limiting generalization. Feature alignment, instead, bridges the source-target gap by learning invariant features, effectively mitigating feature shift (Chen et al. 2019). (iii Over-alignment of all feature dimensions. In tabular tasks with limited class diversity (e.g.. binary classification in Tableshift (Gardner al. 2023)) ) empirical findings (Zhang et al. 2023) highlight significant feature space redundancy, where only subset of features is predictive. Over- aggressive feature alignment leads to two key issues: reliance on redundant, non-discriminative
features, fostering spurious correlations; and neglect of critical discriminative features, degrading adaptation performance. Selectively aligning discriminative features, as demonstrated Table improves performance across datasets.
4 METHODOLOGY
In this section, we introduce our proposed method, Prior-Free Tabular Test-Time Adaptation ())),A). which addresses the major challenges in tabular TTA analyzed in Section 3.2 PFT,A consists of three modules, as shown in Figure (1) Class Prior Estimating, which estimates the class priors of the source and target domains by identifying lokr and target-like data from unlabeled batched target data, without requiring access to source data or class priors; (2) Robust Feature Learning, which mitigates feature shift by aligning the feature distributions between the source-like and target-like data, without relying on filtering low- cwwfiidieeece predictions; (3) Representative Subspace Exploration, which identifies and aligns representative subspaces using subspace detection methods, leveraging the unique characteristics of tabular data and the Tableshift benchmark, without aligning all feature dimensions. In what follows, will provide detailed introduction these three modules.
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Representative Subspace Exploration
Takadaa
TAlAdAY
TabLERI
Class Prior Estimating
Cinl
Tomoyy
Robust Feature Learning
prior
Subaganl
dim2
Schepac
Source Model
calibration
dml
update
Figure 3: The framework PFT for prior-free tabular test-time adaption. contains the Class Prior Estimating for estimating source-target class priors to calibrate prediction, Robust Feature Learning for aligning feature to mitigate feature shift, and Representative Subspace Exploration for eliminating redundant features to enhance feature alignment.
4.1 CLASS PRIOR ESTIMATING
3.2. existing TTA methods that use class priors on tabular data suffer from degraded performance in the prior-free setting. the prior-free TTA Definition 2 the source model fea (trained source data D2) should adapt to unlabeled target data D, without access to any prior knowledge (e.g., source data D, and class priors).
As analyzed in Section
Aiming to estimate the class priors, we propose Class Prior Estimating module during testing time. The main challenge here is how to estimate the class priors of the source and target domains without access the source data. Our idea is to leverage the model trained on the source domain to identify the source-like and target-like data from the unlabeled target data. Specifically, the model trained on the source domain tends be more confident when encountering samples resembling the source domain. Thus, we treat samples with low prediction uncertainty as source-like examples to approximate the source proxy distribution, and samples with high prediction uncertainty as targer-like examples to approximate the target proxy distribution (Section 4.1.I. Then we estimate the class priors of the source and target domains based on the identified source-like and target-like data and calibrate the model's 's predictions to mitigate label shift during test-time adaptation (TTA) (Section 4.1.2
4.1.1 ESTIMATING PROXY DISTRIBUTIONS
Firstly, we feed the data x, in the j-th unlabeled batched target tabular data D into the model fø,-. to obtain the predicted probabilities p, (X,, fa._.) by
fo, (x,)
(1) p;
(2)
.....PP (K)
D ((j 1)b, (j 1)6 1,...,, .b.......,............... (1)
where denotes the size of batch, p! (8) denotes the predicted probability that example x, belongs to k-th class (k- 1, .., K), K denotes the number of category.
We use entropy to quantify the prediction uncertainty of the model. The entropy of the probabilities
P. is defined below. Following Zhou et al. (2024), data arrives in an online fashion, processed in batches.
(p,) - Pi log (())
For j-th batch data DJ. we mine source-like set SO and target-like set T by
Ši [x/xx E Dj, (p.) < e}, T {x//x; D/. (p.) e),
where denotes threshold and j denotes the index of the j-th batch.
4.1.2 ESTIMATING THE CLASS PRIORS
We initially estimate the class priors of the source and target domains based on S1 and g in the first unlabeled batched data D.. Specifically, we estimate class prior Ps of source domain by
Ps Ng. Eiesi P.:
(4)

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Published as a conference paper at ICLR 2026
where Ni denotes the number of examples in the source-like set St. Similarly, target domain's class prior Py can be estimated initially by
Eieri P..
(5)
where Ny: denotes the number of examples in the first target-like set 7'
We use only the first unlabeled batch from the target domain obtain the source-like set. This is because the source model, trained solely on source data, better encapsulates the source domain s knowledge before being updated with target data. Since the source model has not encountered target data, its predictions on target-like data may lack accuracy, leading to biased estimates of the target domain's class priors. To mitigate this bias, we iteratively refine the target domain's class priors:
p Norm C Pss),
where Cj p's represents the estimated bias correction term derived from the j-th batch data DJ, Cj the covariate matrix computed on Dj. and Norm() ensures the resulting distribution sums to one. p is defined as:
p
No Eies: P.
Using the estimated class priors P& and Pr for the source and target domains, we calibrate the model's predictions address label shift during test-time adaptation. Specifically, for example x; in the j-th batch D., the model's prediction f0z-1 (x:) is adjusted obtain the calibrated prediction (x;) as:
(x, fo, (x,)
P1
(8)
Ps
where (x,- is the raw model prediction for the data point x, in j-th batched data DJ.
4.2 ROBUST FEATURE LEARNING
In this section, we introduce the Robust Feature Learning (RFL) module, which aims learn robust features to mitigate feature shift.
From Eq. 3 we derive the source-like set S and target-like set T for the j-th batch D/_ By passing Si and 7 through the feature extractor g. obtain the source-like feature set 9(S²) and target-like feature set 9(fv). Assuming the feature distributions follow Gaussian distribution Adachi al. (2024). we estimate the proxy source and target feature distributions based on g(St) and g(T²), The mean ut's and variance (o")² the proxy source feature distribution are computed as:
1
Σ X,ES1
Zí (o²)s
Σ X,ES}
[z. p
(z. 1²)),
N 91
where z, = Day 1 (x,) E IRd, & denotes the parameters of feature extractor g, d denotes the dimension of feature, and @ denotes the element-wise product.
Similarly, we compute the mean pi and variance (a²)² of proxy source feature distribution by
Σ Zi (02) N/w x
Σ (z, - (o=-)) @ (z: - m4)
N
(10)
X
Then, we align feature distributions to learn robust feature by minimizing the Kullback-Leible (KL) divergence between proxy source feature distribution and proxy target feature distribution:
LKI. KL (Ni''s (o 230)) ( (a²)²)
(11)
|log(( (a 2 /0 (3) f(p3 22,)²² ( 11/2.
In the Tableshift benchmark (Cai Ye 2025), which focuses on binary classification, the features often less diverse compared to multi-clan classification. They typically distributed within

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Published as a conference paper at ICLR 2026
small subspace of the feature space, many dimensions exhibit variance (Zhang al. 2023
Adachi et al. 2024). This dimensional sparsity poses two key challenges for feature aligument: I) The computation of KL divergence in Eq. becomes numerically unstable due to the inclusion of variance terms from underutilized dimensions; 2) The alignment effectiveness reduced, as most dimensions contribute negligibly to the representative subspace. To mitigate these issues, we propose to explore the representative subspace of the feature space, which is detailed in the next section.
4.3 REPRESENTATIVE SUBSPACE EXPLORATION
As analyzed in Section 3.2 aligning features across the full feature space can be suboptimal, as not all dimensions contribute meaningfully to tabular data TTA. To address this, we focus on identifying and aligning the most informative subspace that captures the key dimensions relevant for adaptation. employ a subspace detection method inspired by Principal Component Analysis to explore the representative subspace for prior-free tabular TTA. First, we compute the covariance matrix for the proxy source features as:
Specifically,
Σ
Σ (2; N5 x;ES:
12) (2)
(12)
where the proxy source mean jr's is the same as Eq. The subspace spanned by the eigenvectors of the covariance matrix >',, denoted by Vs (Vs = [v's vI ..... D. The corresponding eigenvalues As (As = [Ag. Ag. ... represent the variance of the source features along the direction Vs. We the top-m largest eigenvalues X3. A3,- ... Ag" the corresponding eigenvectors vs. v ... v
We project the feature - (x:) of example x; into the subspace by
z goo
V (x)),
(13)
where p000
mm Vs [V V
vSl E R.xdd
Then, we compute the projected mean و and variance (0²)'s proxy source domain according to
Eq. and compute the projected mean jut and variance ( of proxy target domain according to
Eq. T0 After that, we align the projected feature distributions the proxy source and target domains
in the subspace by
CKL = KL (W( ((pp..
(14)
Moreover, similar to (Zhou et al. 2024). we employ entropy minimization loss in accordance with classical TTA methods, defined by
Lent
- Ps log (k)
(15)
where p denotes the predicted probability that example x; belongs to class it (k = 1,2,
K).
K denotes the number of category.
Jointly considering Eq. 14 and Eq. 15 the final optimization objective is defined as follows,
Call 31CKL + 82Cent
(16)
we can effectively mitigate label shift and feature shift, enabling tabular test-time adaptation under prior-free scenarios.
By minimizing Eq. 16
Assuming Gaussian distributions Eq. 14 reasonable for the following reasons: First, we can easily compute the KL divergence in closed form by assuming the Gaussian distribution. Second, features follow a Gaussian-like distribution when projected onto the feature subspace under subspace. This is due to the central limit theorem, i.e., the features are more likely to follow Gaussian distribution in the subspace as the number of the original feature dimensions increases. Moreover, since our method uses the PCA, the features projected onto the subspace decorrelated. KL divergence provides an information theooreti measure of distribution discrepancy, which aligns with our goal minimizing the information loss when adapting between domains.
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Table 1: Performance comparison with TabTransformer backbone. The best is in bold.
HELOC
ANES
Health Ins.
ASSIST
Hyperiension
Avg
Method
BAce.
Acc.
BAoc.
Asc.
[BAcc.]
[AAce
F1
Acc.
[BAcc]
Acc.
[BAcc]]
Non-Adaptation
55.66
59.60 6k)
44.
78.95
75.30
84.23
66.35
70.11
65.88
49.04
53,07
[58.92]
54,87
59.24
46.25
[0.77
63:46
59.922
TENT
56.37
59.60
50.34
78.82
75.18
84.14
65.22
70.07
65.62
47.83
53.11
61.27
11.74
50.12
0.78
58.00
61.62
52.43
52.57
78.82
61.40
54.86
62.60
LAME
51.71
59.56
44.30
78.57
74.77
84.04
65.35
70.11
65.88
45.12
51.30
61.40
54.87
59.24
46.25
59.12
63.00
60.37
CoTTA
56.37
59.60
50.34
78.82
75.18
84.14
65.35
70.11
65.88
45.51
51.64
61.56
54,87
59.24
46.25
60.18
63.15
61.63
ODS
64.75
61.35
SAR
56.37
59.60
50.34
78.82
75.18
84.14
65.35
70.11
65.88
45.12
51.30
61.40
54.87
59.24
46.25
60.11
63.09
61.60
PTAT
60:54
63.22
55.81
79.46
76.29
84.34
66.31
70.84
67.19
53.17
55.85
58.94
61.78
61.65
65.62
64.22 25
65.57
66.18
PFT&A (ours)
66.17
65.17
70.91
|80.3]
78.72
84.06
774.33
72.67
79.33
$9.29
59.15
59..73
63.03
61.39
69.20
68.59
67.42
72.65
Table 2: Performance comparison with MLP as backbone. The best is in bold.
Method
HELOC
ANES
Health Ins.
ASSIST
Hypertension
Aug
Ace.
BAcc.
F1
Acc.
BAcc.
F1
Aoc.
[Aac.
F1
Acc.
[/Acc.
F1
Ace.
BAcc.
F1
Apc.
[Aac.
Fl
Non-AAaatation
54.37
58.25
40.02
79.11
75.66
84.24
65.79
70.68
66.21
55,86
60.81
66.44
58.76
61.69
55.46
62.78
65.42
62.47
TENT
54.35
58.23 24
39:95
78.07
74.00
64.30
69:79
63.87
50.87
56.41
63.99
41.67
50.07
0.49
57.88
61.72
50.41
EATA
54.37
58.25
40.02
78.13
74.20
83.79
65.78
70.68
66.21
55.86
60.81
66.42
57.81
61.19
52.57
62.39
65.03
61.86
LAME
43.10
50.00
30.10
63.50
54.60
46.80
63.44
69.14
62.61
45.12
51.50
61.40
58.63
61.64
55.12
54.76
57.34
51.21
COTTA
58.25
4003
78.13
65.79
70.68
66.21
60.81
58.76
55.46
65.13
ODS
43.10
50.00
30.10
63.50
54.60
46.80
63.45
69.14
62.62
45.12
$1.30
61:40
57.12
60.80
51.41
54.46
57.17
50.47
SAR
52.32
56.74
33.
13
74.30
83.79
65.79
70.68
66.21
55.86
60.81
66.42
58.21
61.50
53.81
62.06
64.79
60.68
59.14
79.29
84.42
71.60
68.38
57.26
61.45
63.28
66.11
PFT&A (OUrS)
65.26
62.87
72.43
79.84]
79.13
82.94
73,09
73.63
77.220
63.54
65.57
666.45
64.53
61.83
71.93
69.25
68.63
74.19
5 EXPERIMENTS
We begin by detailing the experimental setup, followed by a comparative evaluation of 3A against existing TTA methods on five benchmark datasets. Finally, we present an ablation study and analyze the results, emphasizing the strengths and insights of our approach.
5.1 EXPERIMENTAL SETUP
Datasets, Following FTAT (Zhou et al. 2024). we evaluate our prior-free TTA approach on five benchmark datasets from the TableShift benchmark Gardner al. (003)) HELOC, ANES, ASSIST, Hypertension, and Health Ins. These datasets exhibit significant distribusion shifts, with sample sizes ranging from 10K 5M and feature dimensions varying from 26 365. This diversity enables comprehensive evaluation of our method's 's robustness across wide range of tabular data scenarios under distribution shifts.
Compared Methods. We first compare PFTzA with the non-adapted source model, referred to as Non-Adaptation. Then, we compare PFT with various TTA methods, including typical TTA methods (i.e., TENT (Wang et al. (020) and EATA (Niu et al., (022)). continual TTA methods (i.e..
COTTA (Wang et al. 2022)), ), robust FTTA methods (i.e., SAR (Niu et al. 2023 LAME (Boudiaf) al. 2022). ODS (Zhou al. 2023 ). and tabular TTA method (i.e., FTAT (Zhou et al. 2024).
Backbone Models. We use three representative deep tabular models: MLP, TraTrrosformer (Huang
al.
2020 and FT-Transformer (Gorishniy et al. I the backbone.
Metrics. Following FTAT (Zhou et al. 2024), we use accuracy (Acc), balanced accuracy (BAcc), and Fl score to evaluate the performance. More experimental details and analyses can be found in the Appendix.
5.2 MAIN RESULTS
Tables 6 g and report the performance of PFT and baselines on the five datasets using TabTrans- former, MLP, and FT-Transformer as backbones, respectively. We observe that PFT, consistently outperforms the baselines under most metrics across all datasets. For example, as shown in Table 6 P improves avg Acc, avg BAcc, and avg Fl by 7.82%. 3.96%, and 12.73%, respectively. com- pared to Non- Non-Adaptation, demonstrating the necessity of adapting the model on unlabeled test data to mitigate distribution shifts effectively. Compared to typical TTA methods (e.g., EATA), PFT,
8

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Published as a conference paper at ICLR 2026
Table 3: Performance comparison with FT-Transformer backbone. The best is in bold.
HELOC
ANES
Health Ins.
ASSIST
Hypertcnnion
Avg
Method
BAce.
F1
Acc.
BAac..
Acc.
[BAcc]]
[AAcc.
F1
Acc.
[BAcc]
Acc.
[BAcc]]
Non-Adaptation
46,26
52.48
13.32
75.47
71.50
81.80
58.33
65.44
[44,06]
59.32
62.99
66.66]
58.88
61.84
55.71
19.45
62.85
54.50
TENT
44,98
51.45
8.11
63.02
51.52
76.19
36.44
50.05
0.24
58.25
62.91
67.57
17.01
53.85
18.83
54.05
57.84
48.68
EATA
12:27
74.65
62.60
58.84
60.24
52.85
LAME
43.14
50.03
0.20
75.37
71.35
81.73
59.08
65.44
55.91
56.54
62.98
67.63
58.78
61.78
55.47
59.40
62.06
51,16
CoTTA
46.26
52.48
10.67
75.47
71.50
81.80
58.33
65.44
54.06
58.25
62.91
67.57
58.88
61.84
55.71
59.44
62.83
53.96
ODS
0.20
75.41
67.1
58.77
62.18
SAR
43.30
50.20
30.50
75.47
71.50
81.80
58.33
65.44
54.06
58.25
62.91
67.57
59.64
62.24
57.52
59.00
62.46
58.31
PTAT
59.20
61.51
55.52
76.06
73.29
81.38
66.45
70.50
67.85
58.32
62.95
67.56
62.34
63.30
64.13
64.47
66.31
67.29
PFT&A (ours)
65.46
62.70
73.17
76.62
75.42
80.60
73.88
72.84
78.87
59.36
63.53
667.43
64.74
63.07
70.74
68.00
67.51
74.16
achieves improvements of 8.65%, 4.82%, and 10.6% in avg Acc, avg BAcc, and avg F1, respectively, highlighting the limitations of directly applying typical TTA methods to tabular data, which often underperform Von-Adaptation. Similarly, PFT outperforms continual TTA methods (e.g., CoTTA) by 8.41%, 4.27%, and I 1.02% in the same metrics, indicating that naive application of continual TTA methods to tabular data fails to yield significant improvements. Robust TTA methods (e.g.. ODS) achieve avg Acc, avg BAcc. and avg Fl scores of 57 57.56%. 61.35%, and 57.53%, respectively. which are lower than all other approaches. confirming their ineffectiveness for tabular TTA. FTAT, a tabular-specific 'TA method, achieves 64.25%, 65.57%, %, and 66.38% in avg Acc, avg BAcc, and avg F1, respectively, surpassing Non- Non-Adape Adaptation and other TTA methods, underscoring the importance of tabular-specific strategies. Notably, 3FT further exceeds FTAT by 4.34%, 1.85% and 6.27% in these metrics, demonstrating its superior effectiveness in prior-free TTA scenarios. Overall, PFTzA achieves consistent performance gains across datasets and metrics, validating its effectiveness.
As shown in Table S with the MLP backbone, PFT&A demonstrates strong performance across most datasets. For example, in the Health Insurance dataset, it achieves accuracy of 73.09% and balanced accuracy (BAcc) of 73.63% highlighting its effectiveness in both overall and balanced classification metrics. Similarly, in the ASSIST dataset, 3F achieves accuracy of 63.54%, showcasing its capability even with a simpler architecture like MLP. When applied with the FT- Transformer backbone, PFT continues to perform robustly, as shown in Table 9 For instance, in the Health Insurance dataset, it achieves an accuracy of 73.88% further validating its adaptability and effectiveness. The consistent performance improvements across datasets and backbones in Tables 6 g. underscore the generalizability of 3FT in addressing the challenges of tabular TTA.
5.3 EXPERIMENTAL. ANALYSIS
Ablation Study. We ablate the three compo- nents PFT Class Prior Estimating (CPE),
Table 4: Ablation (Acc) with Tab TabTransformer.
Robust Feature Learning (RFL), and Represen- tative Subspace Exploration (RSE) to analyze their contributions. The results are in Table 4 Without each component, the performance is degraded, indicating that they are essential for the performance of PFTzA. This highlights the effec- tiveness of the proposed components in Section 4.1 priors, aligning feature distributions, and exploring representative subspaces.
Method
|EELOC
ANES
ASSIST
Hypertension
PFTSA CPE
60.46
79.41
58.3
53.14
59.45
PFTSA wio RFL
65.94
79.33
73.42
58.39
62.71
PPTSA
65.74
80.11
23.40
62.58
PFT.A
66.17
80.33
74.13
59.29
63.03
Section 4.2, and Section
4.3 for estimating class
Varying Parameters. We analyze the impact of PFS hyperparameters, including 31. B2, Ç. and m. on perfor- mance. 3 and B2 control the weights of the feature align- ment loss and entropy minimization loss Eq. [6] respec- tively. Ç is associated with c, which influences class prior estimation as defined in Eq. 3 while m determines the dimensionality of subspaces in the Representative Sub- space Exploration module. The results in Fig, show that performance improves initially and then declines as these parameters vary, highlighting the importance of proper tuning to balance the contributions of the components.
60.0
Anunnc P3
39.5
Opina.
59.5
Opizal
94.0
valle
Mounayy Ph)
29.
04.0
(4) 10 vale
Figure 4: Sensitivity of B1, B2. Ç. m.

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Published as a conference paper at ICLR 2026
6 CONCLUSION
In this paper, we developed PF,,A, novel tabular test-time adaptation (TTA) method that operates without prior knowledge of the source domain. 3F is designed address the challenges of label shift and feature shift in tabular data, which are often exacerbated by the lack of access to source domain data or priors. By incorporating Class Prior Estimation module, a Robust Feature Learning module, and Representative Subspace Exploration module, PFTxA effectively mitigates the impact of these shifts, enabling robust and accurate predictions in target domains. Extensive experiments demonstrate the effectiveness of PFT across various tabular TTA tasks, showcasing its ability to adapt to dynamic environments without relying on prior knowledge or source data.
7 ACKNOWLEDGMENT
This work is supported by grants from the Research Grants Council of Hong Kong Special Ad- ministrative Region, China (No. PolyU 15205224), and Smart Cities Research Institute (SCRI) P0051036-P0050643.
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A APPENDIX
A.1
REPRODUCIBILITY
Data Availability. All real-world datasets used in experiments are based Tableshift (Gaddner
ct al. 2023).
A.2
USE OF LLMS
We only sought assistance from LLMs for language polishing.
A.3 DETAILED EXPERIMENTAL SETUP
A.3.1 DETAILED METRICS
Following FTAT (Zhou et al. 2024). to evaluate the performance. Accuracy measures the proportion of correctly classified instances out of the total instances, providing general overview of model performance. However, it may be misleading in imbalanced datasets where one class dominates. Balanced accuracy addresses this limitation by averaging the recall of each class, ensuring fair evaluation across imbalanced classes. Fl score combines precision and recall into a single metric, offering a balanced measure of a model's ability to correctly identify positive instances while minimizing false positives and false negatives. Together, these metrics provide comprehensive assessment of model performance across different aspects, particularly in scenarios involving class imbalance or varying misclassification costs.
accuracy (Acc), balanced accuracy (BAcc), and F1 score
A.3.2 DETAILED HYPERPARAMETER SET
In our experiments, we intentionally used the same hyperparameter values across all datasets to demonstrate the generalizability and robustness of 3F Specifically, we maintained identical hy- perparameters (31=1.0,, 12=0.11 m=5, (=0.7) for all five tabular datasets in the Tableshift benchmark. The entropy threshold plays critical role in distinguishing between source-like and target-like data samples. Rather than using a fixed threshold value across all datasets, we employed data-adaptive approach. For each incoming batch of target data D/. we calculated the entropy distribution of model predictions and set threshold as a specific percentile this distribution. Through empirical validation, we found that the 70th percentile (ç=0.7) consistently provided balanced separation between confident and uncertain predictions across various tabular datasets.
A.3.3 DETAIL DATASETS
Based on Tableshift (Gardner et al. 2023), 3 a summary datasets we use shown in Table We give detailed overview of each dataset, including task target, shift source, Acc Gap, feature shift level,
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and label shift level. Acc Gap Accenotss accuracy difference between test set with distribution shift DoOn and without distribution shift D!", which is defined by
Ace = Aco(fe. D(P) - Acc(fe, DOOD),
(17)
where fog denotes the model trained on source data D,. Ace incurred when training a classifier comprised of changes in p(æ) ("feature shift") and changes in p(y) ("label shift"). The feature shift level is measured with Optimal Transport Dataset Distance with the Gaussian approximation Alvarez-Melle Mells Fusi (2020). The label shift level is measured based on the label distribution of source and target data.
Table 5: Summary of datasets and their associated distribution shifts.
Dataset
Task Target
Shift Source
Acc Gap
feature shift
label shift
ASSIST
Next Answer Correct VotedinU. S...nUU...ppeeee preeideentaal election Geographic Re-
School
-34,49%
24.054.59 13.60
0.0670
ANES
-2.58%
0.0025
gion
HELOC
Repayment of Home Equity
Est. third-party
-22.58%
19.35
0.0983
Line Credit loan Hypertension diagnosis for high- risk age(50+)
risk level
Hypertension
BMI Category
4.36%
4.69
0.0022
Health Ins.
Coverage Mon-Medicare eligi- Disability Status
-14.46%
5.79
0.1701
ble low-income individuals
HELOC. The Home Equity Line of Credit (HELOC) is a part of credit secured by the applicant's home. A HELOK provides access revolving credit line with lower interest rate than other types of loans. To assess an applicant's suitability for HELOC, lender evaluates an applicants' financial background to predict whether given applicant islikely to repay line of credit and, if so, how much credit should be extended. In order to accurate credit risk predictions for their overall utility for both lenders and borrowers and achieve equal treatment, HELÓC dataset which contains 10,459 samples need to predict whether a consumer is 90 days past due or worse at least once over period of 24 months using 38 features varying from financial activity to credit inquiries.
ANES. Understanding participation in elections is critical task for policymakers, politicians, and those with an interest in democracy. Predicting which individuals will vote in an electio, widely acknowledged as critical to polling and campaigning in U.S. politics. For better understanding individual activity in presidential election, ANES dataset predict whether an individual will vote in the U.S presidential election using 365 features including voting behavior, elections, public opinion and attitudes. The ANES dataset includes 60,377 samples.
ASSIST. ASSISTMENTS dataset in education field (abbreviated as ASSIST). The ASSISTments tutoring platform is a free, web-based, data-driven tutoring platform for students in grades 3-12. ASSISTMENTS dataset contains affect predictions such as such as boredom, confusion, frustration, and engaged problem-solving behavior on students who use the ASSISTMENTS tutoring platform. The numbers of features and samples in ASSISTMENTS dataset are 26 and 2.667,776.
Hypertension. Hypertension, or systolic blood pressure (lypically systolic pressure 130 mm Hg or higher or diastolic 80 or higher) affects nearly half of Americans. When left untreated, hypertension is associated with the strongest evidence for causation of all risk factors for heart attack and other cardiovascular disease (Fuchs and Whelton 2020). As result, it is important to predict blood pressure accurately and efficitively. Hypertension dataset has a goal to achieve efficitive blood pressure measurement and increase the prediction accuracy. Hypertension dataset contains 846,781 samples with 100 features related to several risk factors for hypertension.
Health Ins. Public health insurance makes a significant performance in providing affordable and accessible medical care for individuals. A high level of health insurance ownership is important for the healthy development of the individual. So, it is important to raise the rate of owning health insurance. Health Ins. dataset is related to public coverage field and the goal is to predict whether an individual is covered by public health insurance using 135 features. The number of samples in Health Ins. dataset is 5,916,565.
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Table 6: Performance comparison with TaaTrenfformer backbone. The best is in bold.
Method
HELDC
ANES
Health las.
Acc.
BAcc.
FI
Asc.
BAce
F1
Aec.
BAce.
Fi
Nom Adaeptationn
55.06
1.54
50
60
1.11
46.30
5.08
78.05
0.227
75.30 1 0.45
84.25
0.12
65.55
1:08
70.11
1 0.67
65.85
1.63
TENT
56.37
1.53
50.60
1.11
00.34
5.91
73.82
0.38
15.18 0.56
84.14
0.19
65.
1.18
70.07 = 0.70
05.62
1.82
EATA
56.37
1.55
57
4.04
52.57
4.42
78.62
0.38
75. 18
1:3.::00 0.56
84.14
0.19
65.
1.08
70.11 1: 0.87
65.85
59.56
1.51
6.64
14.77
0.30
65.
1.08
0.67
CoTTA
56,37
59.00
1.11
50.34
78.82
0.58
15.15 0.36
65.
1.08
70.11
0.87
18,
ODS
56.77
3.50
74.29
5.22
3.25
FIAT
0.15
79:40
76.
94.34
0.00
0.012
PFISA (ours)
60.17 0.17
70.91
80.33
0.16
74.33
72.00 +: 0.30
79.33
1.08
Method
ASSIST
Hyperiension
Acc:
BAcc
Apc.
BAcc.
F1
Apc.
BA
F1
AdtsAAdiptaionn
18.04
53.07
2.12
08.32
54.87
0.59
10.24 + 0.63
46.25
2.16
60:77
1.56
63.40
1.00
1o.92
1.87
TENT
17.85 5.39
53.1
2.18
61.27
0.32
41.74
0.01
50.12 0.01
0.78
0.06
58.00
1.30
61,62
0.91
52:43
1.66
BATA
15.28 0.16
6.14
61:80
54.86
0.80
59.24 1 0.63
46.24
2.15
59.3
0.81
62.60
1: 1.21
62:08
1.70
01
2:20
54.87
53.24 0.63
08:12
2.12
1.16
64
0.63
0.56
0.96
2.20
01:20
0.63
2:16
1.05
63
FTAT
53.17
2.02
58.01
1.60
61.78
81:65 0.05
65.02
61
0.44
65.57
0.45
68 0:30
PFT,A (ours)
59.299 1: 0.31
59.13 |
59.75 1.13
63.03
61.39
0.08
69:20
0.37
668.59
0.30
67.42
0.25
72.65
A.3.4 DETAIL COMPARED METHODS
We compare our 3. with various TTA methods, including typical TTA methods (i.e., TENT
Wang et al. 2020) and EATA (Niu et al. 2022)). continual TTA methods (i.e., CoTTA (Wang et al.
2022 ), robust FTTA methods (i.e., SAR (Niu et al. 2023), LAME (Boudiaf et al. 2022). ODS (Zhou
et al. 2023)) and tabular TTA method (i.e., FTAT (Zhou al. 2024)).
TENT Wang et al. 2020) updates the model parameters with entropy minimization loss.
EATA Nuu al.
2022
combines active sample selection with Fisher regularization enhance
prediction performance while mitigating catastrophic forgetting.
mitigates error accumulation in streaming data by leveraging weight- and-augmentation averaged pseudo-labels and stochastic parameter restoration.
CoTTA (Wang et al. 2022
SAR (Niu et al. 2023) filters samples based on test entropy and optimizes model parameters toward flat minima to enhance robustness and performance.
LAME (Boudiaf et
2022 adjusts model predictions through a cautious adaptation strategy.
ODS (Zou et al.
2023) disentangles the combined distribution shift, tackling covariate and label
shifts independently.
2024 optimizes label distributions, filters low-quality predictions, and employs online ensemble learning for robust predictions.
FTAT (Zhou al.
A.4
DETAILED EXPERIMENTS AND ANALYSIS
A.4.1 DETAILED EXPERIMENTAL RESULTS
Table 6 Table and Table show the mean and standard deviation with TabTransformer (Huang al. 2020). MLP, and FT-Transformer (Gorishniy et al. (202)) by three repeated experiments. The results show that our PFT,A achieves the best performance on majority of datasets and metrics, demonstrating the effectiveness of approach.
Table 7: Cost analysis on PFT, and FTAT.
Metric
PF (Ours) FTAT (Baseline) Difference Relative Improvement
Accuracy (ACC)
59.29%
53.17%
+6.12%
11.5%
Runtime (s)
1.0161
0.9346
+0.0815
8.7%
Memory (MB)
1074.62
1050.46
+24.16
2.3%
14

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Published as a conference paper at ICLR 2026
Table 8: Performance comparison with MLP backbone. The best is in bold.
Method
HELOC
ANES
Health lns.
Acc.
BAucc.
FI
Asc.
BAce
F1
Acc.
BAoc.
FI
Nom Adaeptation|
5d.37 1 5.55
56.22 25
3.56
10.02 1 16.8
75.
1 0.31
75.66
1 0.46
84.24
0.16
65.77
79
0.63
70,65
1 0.64
96
21
0.00
TENT
54.85 1.35
58.24
3.58
39.35
16.9
78.07
0.335
74.00 + 0.65
83.76
0.13
64
30-00+
0.70
68.79 = 0.47
[13.87
1.06
EATA
54.57 5:55
25 1:3.6
00.02 1: 16.8
78.13
1:30 0.30
74.20 1: 0.59
83.70
0.10
65.
0.63
70.08 2: 0.64
06.21
1:0:0
LAME
08.10
50.00
0.00
63.50
0.00
54.50
0.00
63.44
1.09
1.09
62261
4
CoTTA
54.36 5.35
58.23
13356
40.05
16.8
78.13
0.30
14.20 0.39
83.79
65.79 0.63
70.08 4 0.44
08.21 0.90
ODS
42.10+00.0
50.00 0.00
63.50
0.00
1.07
02:62
56.77
0:90
FIAT
02.67
0.15
09.14
0.23
79:29
75.83
44.42
1.10
0.33
71.60
0.15
10.
PFTAA (ours)
66.26 + 0.00 62.87 0.25
72.43 4: 0.36
79.84
0.019
79.23 d: 0.02
0:15
78.09 0.08
73.63 +: 0.01
77.20 0.12
Method
ASSIST
Hyperiension
Acc:
BACc
F1
Apc.
BAcc.
F1
Apc.
BA
F1
06,80 + 3.81
00.81 + 3.37
00.42
56.70
1,08
61.00 + 0.95
55.46
4.03
02.
70.77-55
2.36
65 1.76
02:47
4.76
TENT
50.87 1 0.52
56.41
0:22
63.99 1 0.15
41.67
0.08
50.07
0.05
0.40
0.36
57.
1.37
61.72
1.01
50.41
3.3.2
BATA
55.86 0.18
00.81
0.16
66.42
0.08
57.81
2.52
61.19
1 1.38
52.87
5.82
62
1.76
65.05
1.25
61
4.74
LAME
46.12
00 0:18
58.63
01.03=1.600
1.60
61.54 0.52
54.76
57.34
0.44
51
CoTTA
00:81
0.95
62:
1.14
02.35
ODS
0.18
52
60.80
0.53
51.41
54.
57.17
0.44
50.47
SAR
06.86
00:81 0.16
00.02
0.08
58.21
61.50 0.77
58.5 88.81=
1.778
64.79
1.19
90 00.08-1
FTAT
51.84
57 26
1.18
04:65 6: 0.50
63.28
0.54
63.
0.52
68.
1.10
61
0.75
66.
0.63
68
PFT,A (ours)
633.54 1: 0.90 65.37
1:22
68.45
1: 0.94
64.53
0.22]
81.83 0.35
T1.
1.22
669
0.11
68.63
0.37
7.419 19 0.52
Table 9: Performance comparison with FT-Transformer as backbone. The best in bold.
Method
TTLLOC
ANES
Health Ins.
Acc.
BACe.
Ft
Avc.
BAcc.
F1
Acc.
DAoc.
F1
Non Adaptation
46,26 à 1.05
52 48
0.78
13.32 1 4.50
70,47
1,31
71.50 1 2.06
81.80
1 0.45
58.
4.05
05.44 L 2.56
54.06 à: 7.72
TENT
44,98 2: 1,83
51 48 1:30
8.11
7,50
03,02
=: 11.99
14.32 4: 1.15
76.19
01
36.
26.44
0.03
56.00 =: 0.112
0.24
0.
FATA
45,05 1.00
52:23
+0.74
12.27
+ 4.38
74.65
1.66
70.16
+ 2.49
81.51
0.67
57 00.40-
4.36
64.86
+ 2.70
12:25
LAME
18.14
50.00 1.00
0.20
0.14
75.37
1.34
11.35
2:12
81.73
0.48
59.
4.57
65.44
2.80
53.91
9:04
COTTA
52
0.78
7.65
76.47
2.00
0.45
58
2.56
54.06
ODS
13.14
50.03
2.15
50
50:20 0.00
73.47
71
2.00
81.80
58
2.56
FTAT
50.20
0.16
51
0.13
02
0.34
76.00
73.29
0.37
81.38
0:23
05:45
0.03
70.50
0.02
07
PFT,A (ours)
65.46 + 0.12
62.70
0.25
79.17 +: 0.20
76.62 2: 0.17
75.42 0.45
80.60
0.06
73.88 0.67
72.84 +: 0.19
78.87 1.05
Mithod
ASSIST
Hyperiension
Avg.
Acc:
RAce
F1
Auc.
BAce
F1
Acc.
RADe:
F1
Non- Adieptationn
58.32 0.07
62 08:90:11 0.09
667.63
:: 0.00
58.88
0.28
01.31
+ 0.14
56.71
0.79
50.00
1.35
85 + 1,15
51.30
2.71
TENT
58.25 0.07
62.91
1:0.0
67.57
1: 0.00
47.01
6.30
55.88
4.52
18.80
20.50
54.05
1.84
57.84
1.65
68
BATA
53.85
6.19
62,80
58.84
0.27
0.38
56.62
57.
1.61
1.27
52.85
2
LAME
0.06
67.63
0.07
58.78
0.35
56.47
50
0.30
51
CoTTA
0.00
0.34
55.71
50.
62.63
1.15
OUS
1.04
67.14
0.38
57
0.34
58
1.27
62.
1.38
52
1.78
SAR
58.25
0.07
62:91
0.09
67.57
0.00
30.64-1
0.65
62 24
0.29
57.62
1.63
50.00-
62.46
1.00
58
FTAT
58.32
1 0.05
62:96
0.05
67.56
1 0.00
62.34
0.07
63.30
1 0.08
61.13
0.06
64.47
0.10
00.31
1 0.09
67
29
0.14
PPTSA (ours)
50.36 1: 0.15
63.53
1: 0.11|
67.43
0.22
64.74
0.29
63.07
4: 0.38
70.74
4: 1.00
68.01
0.27
67.51
4: 0.28
74.16
0.663
0.63
A.4.2 DETAILED COST ANALYSIS
To ensure a fair and reproducible comparison about cost, we evaluated both our method (PFT3A) and the baseline method (FTAT) on ASSIST with TabTransformer. The quantitative comparison in Table confirms that PF achieves significantly improved accuracy with minimal additional resource consumption. This balance makes our method particularly suitable for practical applications where prediction quality is paramount. The results strengthen our claims regarding the method's practical utility and deployment readiness.
A.4.3 DETAILED ABLATION ANALYSIS
Class Prior Estimating (CPE). When CPE is disabled (PFT3A w/o CPE), performance sharply deteriorates in Health Insurance (Acc drops from 74.13% to 58. 29%) and Hypertension (Ace decreases from 63.03% to 59.45%), indicating that direct adaptation without class prior estimation amplifies prediction errors. Notably, in Health Insurance, the absence of CPE even underperforms the Non- Adaptation baseline (58.28 29% vs. 65.35%), suggesting that naive feature alignment without class prior estimation still shows poor performance and Health Insurance exhibits larger label shift compared with other datasets.
Robust Feature Learning (RFL). Robust Feature Learning (RFL) proves essential for handling covariate shift in tabular data. By aligning feature distributions between source and target domains, RFL enables effective adaptation unseen data. The results clearly demonstrate its impact: on
15

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Published as a conference paper at ICLR 2026
Table 10: Ablation (Ace) with TraTrrnsformer.
Method
|HELOC
ANES Health Ins.
ASSIST Hypertension
Non-Adaptation
55.66
78.95
65.35
49.04
54.87
P w/o CPE
60.46
79.41
58.29
53.14
59.45
P wo RFL
65.94
79.33
73.42
58.39
62.71
3 w/o RSE
65.74
80.11
73.40
58.53
62.58
PFT&A
66.17
80.33
74.13
59.29
63.03
ANES, accuracy improves from 79.33% (w/o RFL) to 80.33% (with RFL), while ASSISTMENTS shows gains from 58.39% to 59.29%. While the performance gains from RFL appear less pronounced. this primarily reflects the Tableshift benchmark's characteristic where label shift dominates feature shift. Nevertheless, consistent improvements of RFL across datasets confirm RFL's critical role in mitigating feature shifts. Moreover, RFL helps subsequent subspace exploration by providing well-aligned feature representations.
Representative Subspace Exploration (RSE). The ablation results in Table TO demonstrate RSE's indispensable role in refining feature alignment for tabular TTA. Disabling RSE (PFT,A w/o RSE) leads consistent performance drops across all datasets, most notably in Health Insurance (Ace: 74.13% to 73,40%) and Hypertension (Ace: 63.03% to 62.58%). These results reflect RSE's unique ability to eliminate redundant features and enhance feature alignment.
A.4.4 HYPERPARAMETER SENSITIVITY AND SELECTION
We determine single default hyperparameter configuration for PFTzA via grid search on the ASSIST dataset using a TabTransformer backbone. The search space is defined as: 31 E {0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.8). 32 E {0.05, 0.15, 0.2, 0.25, 0.3, 0.5), Ç E (0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85). and m (2. 4, 5, 6, 7,8.. The configuration achieving the best average target-domain performance on ASSIST is selected the default: 33 = 1.0, 82 5. Once selected, this configuration is fixed and directly applied all other
0.10, 0.70, datasets (HELOC, ANES, Health Insurance, and Hypertension) without any dataset-specific tuning. This protocol strictly follows the realistic TTA setting, where target labels are unavailable and hyper- parameter adaptation per dataset infeasible. Figure shows that while extreme values can degrade performance, PFT&A exhibits relatively stable performance plateau around the selected default configuration. The selected hyperparameters lie within this stable region, indicating that the method not overly sensitive moderate variations and does not require fine-grained tuning.
To verify that P does not rely on dataset-specific tuning, we compare the performance of the fixed ASSIST-tuned configuration with -ppesct- optimal configurations obtained using the same search space on each dataset, as shown in Table I]
Table 11: Comparison between the fixed ASSIST-tuned configuration and dataset-specific optimal hyperparameters.
Dataset
FTAT
Fixed Config
Dataset-Specifie Best
Gap
HELOC
60.54
66.17
66.27
0.10
ANES
79.46
80.33
80.42
0.09
Health Ins.
66.31
74.13
74.34
0.21
Hypertension
61.78
63.03
63.09
0.06
According to Table I1 the performance gap between the fixed configuration and dataset-specific optimal settings remains small, demonstrating that PFT generalizes well across domains without requiring per-dataset hyperparameter tuning. These findings confirm the practical applicability of PFT&A in realistic test-time adaptation scenarios. Furthermore, regardless of whether the fixed configuration or dataset-spechs optimal settings are used, the performance of PFT,A consistently outperforms the current state-of-the-art baseline, FTAT, by significant margin.
16

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Published as a conference paper at ICLR 2026
Table 12: Comparison of our estimated source domain class priors with the ground truth.
HELOC
ANES
Health Ins.
ASSIST
Hypertension
Ground Truth (0.74, 0.26) (0.31, 0.69)
(0.78, 0.22)
(0.31, 0.69)
(0.60, 0.40)
Estimation
(0.89, 0.11) (0.31, 0.69)
(0.63, 0.37)
(0.29, 0.71)
(0.66, 0.34)
Error
0.15
0.15
0.06
A.4.5
CLASS PRIOR ESTIMATION ANALYSIS
compares the true source class priors with the class priors estimated by our CPE module. The estimation errors of our CPE module across the five datasets are 0.15, 0.00, 0.15, 0.02, and 0.06, respectively, demonstrating its reliability in estimating class priors.
Table T2
A.5 LIMITATIONS AND FUTURE WORK
When the source model is manipulated by adversarial attacks, the performance of PFT3A may be compromised since the target model relies on the source model. As future work, we plan to investigate the robustness of PFT against adversarial attacks and explore methods to enhance its resilience such scenarios. cases of severe distributional shifts, PFT&A may experience performance degradation. Dynamic thresholds that adjust based on shift severity detection could improve robustness. applications where test data arrives very small batches, PFT may face several challenges. Maintaining sliding window of recent batches could provide more stable statistical estimates.
17


Reviews:
[{"review_id": "ugvjuV1L6z", "reviewer": "Reviewer_hW3a", "summary": "The paper proposes Prior-Free Tabular Test-Time Adaptation (PFT3A) to solve distribution shifts in Tabular data by test-time adaptation. Specifically, they achieve prior-free test-time adaptation by estimating the source data prior through low-entropy target data at the first test batch, and learn robust and representative representations by aligning pseudo-source and target features during test-time adaptation. Experiments on the TableShift benchmark demonstrate the effectiveness of the proposed method.", "questions": "1. From Figure 4, it seems that the method are sensitive on some hyperparameters (e.g., beta_2 and m). It is not clear whether different dataset need specific hyperparameters. And how does these hyperparameters set for different datasets?\n\n2. In Section 4.2, why do the author assume feature as Gaussian distributions? motivation and advantages? How about other distributions or just deterministic features with alignment by L2?\n\n3. How about the costs of the method on test-time adaptation?", "limitations": "", "rating": 2, "confidence": 5, "soundness": 2, "presentation": 3, "contribution": 1, "strengths": "1. The paper is easy to follow.\n\n2. Experiments demonstrate the effectiveness of the proposed method.", "weaknesses": "1. The novelty of the proposed method is limited. The idea of using high-confidence target samples as source-like samples have already been explored in many source-free adaptation or test-time adaptation papers [1]. The idea of aligning source and target features for test-time adaptation has also been widely used [2, 3]\n\n2. The class-prior estimating module seems highly relies on the threshold of the entropy. But it is not clear how does the threshold set for various datasets.\n\n3. Following the above question, there is no guarantee that the estimated source prior can cover the real source data. If the first batches are very bad (e.g., heavily shifted or extremely class-imbalance, which can usually happen in real applications), the estimation can be biased and misclassified. And the error will also be accumulated to the following adaptation and prediction, leading to worse and worse results. Including experiments on bad first-batch test data is also necessary for more insights of this problem.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "zPitmGOPyn", "reviewer": "Reviewer_vak8", "summary": "This paper tackles test-time adaptation (TTA) for tabular data in a realistic, prior-free setting where no source data or distributional priors are available. The proposed method, PFT₃A, comprises three key modules: (1) a Class Prior Estimation module that addresses label shift via unsupervised entropy-based techniques; (2) a Robust Feature Learning module that aligns features using KL divergence without relying on confidence thresholding; and (3) a Representative Subspace Exploration module that identifies and adapts discriminative subspaces through PCA-inspired methods. Comprehensive experiments on five datasets with various backbones demonstrate consistent superiority over existing TTA baselines, including prior-free and tabular-specific ones. Ablation studies and sensitivity analyses validate the efficacy of each component.", "questions": "1). Could you clarify if the Gaussian assumption for feature representations was empirically validated across all evaluated tabular datasets, especially those with high-cardinality categorical variables? \n\n2). For the class prior update equation in Section 4.1.2 ($\\tilde{\\mathbf{p}}_T^j = \\operatorname{Norm}(\\tilde{\\mathbf{p}}_T^{j-1} - \\hat{C}^{j-1} \\tilde{\\mathbf{p}}_S^j$), please provide a detailed derivation, intuition, and procedure for computing and regularizing the batch covariate matrix, particularly in cases of low-rank or ill-conditioned features.\n\n3). Have you evaluated the runtime and memory footprint of PFT₃A on larger batch sizes or datasets with hundreds of features, and how does it compare to baseline methods?\n\n4). The \"Limitations and Future Work\" section (Appendix A.5) emphasizes adversarial robustness but overlooks scenarios where the method underperforms, such as extreme distributional shifts or small-batch settings. Could you elaborate on these failure modes and potential mitigations?", "limitations": "", "rating": 4, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1). The paper identifies and formalizes an under-explored challenge in tabular TTA: the fully prior-free and source-free scenario. This is motivated by empirical evidence in Figure 2, highlighting limitations of prior methods under real-world constraints.\n\n2). PFT₃A integrates unsupervised class prior estimation from prediction entropy (to handle label shift), KL-based feature alignment (for covariate shift), and a principled subspace selection strategy via PCA, which mitigates overfitting to non-discriminative features.\n\n3). The method is evaluated on five TableShift benchmark datasets using three deep tabular backbones, showing improvements over a range of baselines. The inclusion of ablations and analyses enhances the credibility of the results.", "weaknesses": "1). Although the method is compared to various prior-free and vision-inspired TTA approaches, it lacks direct comparisons or discussions with recent tabular-specific test-time augmentation (TTAug) techniques, such as those in Kozodoi (2021) or Brownlee (2020). These augmentation-focused methods could serve as competitive baselines or complementary strategies, and their omission limits the benchmarking scope.\n\n2). The paper under-explores connections to emerging training-free TTA adapters in vision-language or cross-modal domains (e.g., Karmanov et al., 2024). Incorporating such perspectives in the Related Work section or as experimental baselines could reveal transferable insights for tabular adaptation.\n\n3). In Sections 4.2 and 4.3, the KL divergence is computed assuming Gaussian-distributed feature projections for alignment. However, the justification for this Gaussian assumption is insufficient, particularly for tabular data with high-cardinality categorical features. Details on handling low-variance or near-singular subspaces—such as eigenvalue thresholding or covariance regularization—are not explicitly described, despite mentions of numerical instability. Furthermore, the bias correction in class prior estimation (Section 4.1.2, Eq. for $\\tilde{\\mathbf{p}}_T^j$) references a batch-specific covariate matrix without a full explanation of its computation, regularization, or derivation, which could hinder reproducibility.\n\n4). The entropy-based sample selection for distinguishing source-like and target-like instances may introduce bias in severe label shift scenarios (e.g., as observed in Table 10 for HELOC/Health Ins. datasets), where initial model uncertainty might not reliably indicate domain alignment. This affects the accuracy of class prior estimation and suggests the need for additional calibration or robust alternatives.\n\n5). The method's per-batch covariance computations and eigen-decompositions could incur high computational costs on large-scale or high-dimensional datasets. A quantitative comparison of runtime and memory usage against baselines would strengthen the practical claims.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "6eYEdTf0Ec", "reviewer": "Reviewer_B7xd", "summary": "This paper focuses on the tabular TTA problem without the accessibility of the source domain or prior. Based on the analysis, this paper proposes PFT3A method, which consists of a Class Prior Estimating module for estimating source-target class priors, Robust Feature\nLearning module for learning robust features by aligning source-like and target-like features to mitigate feature shift, and Representative Subspace Exploration module for selecting informative features. Experiments conducted in this paper show the effectiveness of PFT3A under prior-free tabular test-time adaptation problem.", "questions": "See Weakness above.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1. This paper is well-written, which makes it easy to follow. The motivation is clear, and the math symbol is easy to follow.\n2. The method introduced in this paper is novel; The idea of optimizing the Kullback-Leibler (KL) divergence of the source distribution and the target distribution with informative columns provides insights for tabular machine learning.\n3. The experiment conducted in this paper is well-designed, showing the effectiveness in performance and robustness in parameters of the PFT3A method.", "weaknesses": "1. The motivation behind the method’s design needs to be explained. In Eq. 6, the estimation of the prior leverages both the model’s predicted outputs and the covariance matrix of the features. This design links the predicted probabilities with the feature information of the data; however, the paper does not clarify the rationale for combining these two components.\n2. Typos: \n\na. In line 298, the cite format would be better using \\citep: \n>  Assuming the feature distributions follow a Gaussian distribution Adachi et al.\n(2024), --> Assuming the feature distributions follow a Gaussian distribution (Adachi et al. 2024).\n\nb. The symbol $\\zeta$ does not appear until section 5.3, and it is not clearly defined. According to the explanation in line 466, does it refer to $\\epsilon$, or what is the relationship between $\\zeta$ and $\\epsilon$?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)