Data Distribution Valuation Using Generalized Bayesian Inference

Cuong N. Nguyen; Cuong V. Nguyen

cs.LGApr 7, 2026

Data Distribution Valuation Using Generalized Bayesian Inference

Authors: Cuong N. Nguyen, Cuong V. Nguyen

Organizations: Department of Mathematical Sciences Durham University

Abstract

We investigate the data distribution valuation problem, which aims to quantify the values of data distributions from their samples. This is a recently proposed problem that is related to but different from classical data valuation and can be applied to various applications. For this problem, we develop a novel framework called Generalized Bayes Valuation that utilizes generalized Bayesian inference with a loss constructed from transferability measures. This framework allows us to solve, in a unified way, seemingly unrelated practical problems, such as annotator evaluation and data augmentation. Using the Bayesian principles, we further improve and enhance the applicability of our framework by extending it to the continuous data stream setting. Our experiment results confirm the effectiveness and efficiency of our framework in different real-world scenarios.

Figures & tables

Component	Annotator evaluation	Data augmentation
$\mathcal{S}$	$\{s_{1},\ldots,s_{M}\}$ (set of annotators)	$\{s_{i}\}$ , where $s_{i}=(\psi_{i},\alpha_{i})$ (set of augmentors)
$\mathcal{D}_{s}$	$\mathcal{D}_{s}$ (given noisy sample set from $s$ )	$\{(s(x),y)\,\|\,(x,y)\in\mathcal{D}^{\mathrm{tr}}\}$ (transformed training set using $s$ )
$\mathcal{D}^{*}$	$\mathcal{D}^{*}$ (given validation set)	$\mathcal{D}^{\mathrm{tr}}$ (given training set)
$\phi(s,\mathcal{D}_{s},\mathcal{D}^{*})$	$m_{s}$ (small model trained on $\mathcal{D}_{s}$ )	$m^{u}$ (pre-trained universal model)
$\varphi(s,\mathcal{D}_{s},\mathcal{D}^{*})$	$\mathcal{D}^{*}$ (validation set)	$\mathcal{D}_{s}$ (transformed training set using $s$ )
$L(s,\mathcal{D}_{s},\mathcal{D}^{*})$	$-T(m_{s},\mathcal{D}^{*})/\tau$	$-T(m^{u},\mathcal{D}_{s})/\tau$

Table 1: Summary of GBV components for two problems in Section 4.2 with a general transferability measure

T

Method	Dataset
Method	CIFAR-10	CUB-200-2011
Uniform	74.37 $\pm$ 0.23	52.45 $\pm$ 0.85
DAVINZ ( 2022 )	74.82 $\pm$ 0.62	52.06 $\pm$ 0.38
LAVA ( 2023 )	74.74 $\pm$ 0.91	-
MMD ( 2024 )	75.95 $\pm$ 0.91	52.62 $\pm$ 0.80
GBV (quick $\tau$ )	77.94 $\pm$ 0.08*	57.58 $\pm$ 0.96*

Table 2: Test accuracy (%) of different methods for annotator evaluation. Bold numbers and asterisks (*) indicate the best and second best accuracies on each dataset respectively. Our GBV method outperforms the baselines on both datasets.

Method	Dataset
Method	CUB-200-2011	Stanford-Dogs
AutoAugment ( 2019 )	67.30 $\pm$ 0.39	65.64 $\pm$ 0.58
RandAugment ( 2020 )	67.73 $\pm$ 0.23	67.12 $\pm$ 0.31
TrivialAugment ( 2021 )	69.43 $\pm$ 0.49	67.64 $\pm$ 0.23
EntAugment ( 2024 )	72.38 $\pm$ 0.40	72.17 $\pm$ 0.27
SRA ( 2025 )	66.53 $\pm$ 0.42	66.26 $\pm$ 0.42

Table 3: Test accuracy (%) of different methods for data augmentation. Bold numbers and asterisks (*) indicate the best and second best accuracies on each dataset respectively. Our GBV method outperforms the baselines on both datasets.

Figure 1: Test accuracy of different methods for continual annotator evaluation. Our CGBV method consistently outperforms the baselines on this problem.

Method	Time (s)	Method	Time (s)
DAVINZ	10.68 $\pm$ 0.4	MMD	1.05 $\pm$ 0.58
LAVA	370.21 $\pm$ 5.37	GBV	0.85 $\pm$ 0.17

Table 4: Running time of different methods.

Figure 2: Effects of different transferability measures (left) and

\tau

(right) on test accuracy. The red column on the right is for the quick

\tau

value.

Figure 3: Test accuracy of GBV with respect to sample size.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

augmentor	range	augmentor	range
equalise	-	rotate	$-90^{\circ}$ - $90^{\circ}$
solarise	0 - 256	color	0.0 - 5.0
posterise	2 - 8	contrast	0.0 - 0.9
brightness	0 - 5	sharpness	0.0 - 5.
shear_x	0.0 - 0.3	shear_y	0.0 - 0.3
translate_x	0 - 32	translate_y	0 - 32

Appendix

Table 5: Data augmentation space used in our experiment.

Method	CIFAR10	CUB-200-2011
MMD	0.99	0.93
GBV	0.99	0.98

Appendix

Table 6: Pearson correlation coefficients between valuation methods’ solutions and test accuracy with a labeled reference set. The best results for each dataset are highlighted in bold.

Method	Unlabeled	No reference set
MMD	0.76	0.85
GBV	0.83	0.87

Appendix

Table 7: Pearson correlation coefficients between valuation methods’ solutions and test accuracy on CIFAR-10 with unlabeled and entirely unavailable reference sets. The best results in each setting are highlighted in bold.

Universal model	Accuracy (%)
ResNet-50 (ImageNet)	$74.45\pm 0.16$
ViT-S/16 (DINOv3)	$73.99\pm 0.60$
ViT-Base (CLIP)	$74.80\pm 0.30$

Appendix

Table 8: Final test accuracy (%) for data augmentation on CUB-200-2011 when using different universal models

m^{u}

for GBV.

Data Valuation

Data valuation estimates how examples, datasets, or contributors affect model performance to guide selection, auditing, and fair compensation.

See all 43 papers

TimeLAVA: Learning-Agnostic Valuation for Time Series Data
Jun 17, 2026Wenqin Liu, Weizhi Quan, Aoqi Zuo +5Data Valuation
School of Mathematics and Statistics, The University of Melbourne · School of Mathematics and Statistics, University of Sydney · Responsible AI Research Centre, Australian Institute for Machine Learning +3
From Detrimental to Beneficial: Dynamic Influence-based Valuation and Editing
Aug 23, 2026Adrian Nyakairu, Hongfu LiuTraining Data Curation Data Valuation
Department of Computer Science, Brandeis University
Challenges in Enabling Private Data Valuation
Feb 27, 2026Yiwei Fu, Tianhao Wang, Varun ChandrasekaranData Valuation Privacy-Utility Tradeoff
University of Illinois Urbana-Champaign · ∗University of Virginia

Jun 17, 2026J/K move · Enter open · S save

TimeLAVA: Learning-Agnostic Valuation for Time Series Data

Wenqin Liu, Weizhi Quan, Aoqi Zuo, Erdun Gao+4

School of Mathematics and Statistics, The University of Melbourne · School of Mathematics and Statistics, University of Sydney · Responsible AI Research Centre, Australian Institute for Machine Learning+3

Data Valuation

Open paper AskPDF arXiv

Data valuation quantifies the intrinsic quality of individual samples to enable principled data curation, quality control, and robust learning. For time series in critical domains such as healthcare, finance, and industrial monitoring, effective valuation methods are essential yet fundamentally lacking. Existing approaches are either model-dependent, limiting their generalizability, or designed for i.i.d. data and thus fail to capture temporal dependencies, multi-scale patterns, and non-stationary dynamics inherent to sequential data. We introduce TimeLAVA, a learning-agnostic framework that values temporal segments by their marginal contribution to minimizing distributional discrepancy between evaluated and reference data. At its core is a novel Selective Wavelet-based Wasserstein discrepancy combining multi-scale wavelet transforms for temporal localization with unbalanced optimal transport for robustness to distributional shifts. Segment values are efficiently computed via sensitivity analysis without requiring model training and aggregated into point-wise scores. We provide theoretical guarantees linking valuation to model-agnostic generalization and prove bounded sensitivity to outlier contamination. Extensive experiments across anomaly detection, data pruning, and label noise detection demonstrate that TimeLAVA produces significantly more informative value scores than existing methods on diverse real-world datasets.

Abstract

Data Valuation

Explore similar work

TimeLAVA: Learning-Agnostic Valuation for Time Series Data

From Detrimental to Beneficial: Dynamic Influence-based Valuation and Editing

Challenges in Enabling Private Data Valuation