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arxiv: 2605.13219 · v1 · submitted 2026-05-13 · 🌌 astro-ph.GA

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Comparative analysis of missing data imputation methods for CSST survey: Impact on photometric redshift estimation performance

Ling Wang , Zhu Chen , Zhijian Luo , Liping Fu , Zuhui Fan , Wei Du , Yaoming Lei , Zhang Ban
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Yuedong Fang Yi Hu Xin Ji Guoliang Li Xiaobo Li Jiaqi Lin Chenxiaoji Ling Chao Liu Dezi Liu Changqing Luo Yu Luo Bin Ma Xianmin Meng Jundan Nie Juanjuan Ren Li Shao Jianing Tang Hao Tian Feng Wang Chengliang Wei Peng Wei Shoulin Wei Kaichao Wu You Wu Yun-Ao Xiao Zhou Xie Yibo Yan Su Yao Yan Yu Bo Zhang Shengwen Zhang Tianmeng Zhang Xiaoli Zhang Xin Zhang Bowei Zhao Zhimin Zhou Hu Zou
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Pith reviewed 2026-05-14 18:20 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords photometric redshiftsmissing data imputationCSST surveyKNNSAITSMNAR missingnessgalaxy surveys
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The pith

KNN imputation achieves highest photo-z accuracy under random missing data with complete training sets, while SAITS outperforms when data is incomplete or missingness is realistic.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper evaluates machine learning methods for filling missing photometric bands to improve estimates of galaxy distances from colors alone. It shows that k-nearest neighbors imputation works best when gaps occur completely at random and the training set is full, but an attention-based model called SAITS performs better when training data itself has gaps or when missingness mixes random and physical causes. Tests use mock data from the China Space Station Telescope to mimic real survey conditions. Matching how missing data occurs in training and test sets proves essential, and treating all gaps the same way harms results when non-detections reflect physical brightness limits.

Core claim

KNN yields the highest accuracy under idealized MCAR conditions with complete training sets, whereas SAITS significantly outperforms KNN when training data is incomplete or when applied to realistic mixed-mechanism scenarios. Domain consistency between training and testing missingness patterns is a prerequisite for optimal performance. General imputation models are highly effective for MCAR and MAR data but detrimental when applied to MNAR data arising from flux limits.

What carries the argument

Benchmark comparison of imputation models (KNN and SAITS) applied to CSST mock photometry to improve photo-z regression accuracy across MCAR, MAR, and MNAR missingness mechanisms.

Load-bearing premise

The CSST mock catalog accurately reproduces the statistical properties and physical origins of missing photometric bands that will occur in actual observations, especially MNAR cases from flux limits.

What would settle it

Direct comparison of photo-z accuracy on real early CSST data with spectroscopic redshifts against the mock-based performance rankings for KNN versus SAITS under observed missingness patterns.

Figures

Figures reproduced from arXiv: 2605.13219 by Bin Ma, Bowei Zhao, Bo Zhang, Changqing Luo, Chao Liu, Chengliang Wei, Chenxiaoji Ling, Dezi Liu, Feng Wang, Guoliang Li, Hao Tian, Hu Zou, Jianing Tang, Jiaqi Lin, Juanjuan Ren, Jundan Nie, Kaichao Wu, Ling Wang, Liping Fu, Li Shao, Peng Wei, Shengwen Zhang, Shoulin Wei, Su Yao, Tianmeng Zhang, Wei Du, Xianmin Meng, Xiaobo Li, Xiaoli Zhang, Xin Ji, Xin Zhang, Yan Yu, Yaoming Lei, Yibo Yan, Yi Hu, You Wu, Yuedong Fang, Yu Luo, Yun-Ao Xiao, Zhang Ban, Zhijian Luo, Zhimin Zhou, Zhou Xie, Zhu Chen, Zuhui Fan.

Figure 1
Figure 1. Figure 1: Flux–error relations across bands. Input flux vs. predicted flux errors (pink) and output catalog values (blue). 2026b; Xian et al. 2026). These efforts are crucial for building the data processing pipeline and evaluating the scientific poten￾tials of the current survey design. Our evaluation is based on data from the CSST Cycle 6 sur￾vey simulation, which emulates a 1.53 deg² observation cen￾tered at R.A.… view at source ↗
Figure 2
Figure 2. Figure 2: Predicted versus true magnitudes for the test set with three missing photometric bands using the imputation models. Panel a: Predicted versus true magnitudes (KNN). Panel b: Same as (a) but for the SAITS model. We show the predicted values as a function of the true values. The dashed green line marks magpredict = magtrue, and the red line shows the linear fit. tor of 10 compared to the non-imputed baseline… view at source ↗
Figure 3
Figure 3. Figure 3: Photo-z quality metrics for the KNN and SAITS models for test sets with different missing data rates. Blue bars show SED fitting on non-imputed data, and pink and purple bars show results after KNN and SAITS imputation, respectively. 1.6 1.8 2.0 2.2 fo ut (%) fout (baseline) = 4.17% 0.048 0.050 0.052 0.054 N M A D NMAD (baseline) = 0.057 5 10 20 30 60 90 120 Training Size (k) 0.0090 0.0095 0.0100 0.0105 bi… view at source ↗
Figure 4
Figure 4. Figure 4: Influence of training sample size on imputation perfor￾mance. We show the photo-z metrics after imputation with the SAITS (pink) and KNN (purple) models for different training sample sizes. The non-imputed test set has a missing rate of 10%, and the corresponding metrics are shown in the upper right cor￾ner of each panel. with, and marginally better than that of SAITS across all miss￾ingness levels. The im… view at source ↗
Figure 5
Figure 5. Figure 5: Influence of training sets with different missing rates on model performance. Training sets with missing rates of 10%, 20%, and 30% are used. Blue bars show baseline results from the non-imputed test set (with three bands removed), while pink and purple bars show results after imputation with the KNN and SAITS models, respectively [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Spatial distribution of missing data for each photometric band in the input catalog. Gray points show all sources, while red points indicate sources with missing data in each band. A higher density of red points corresponds to a higher fraction of missing data. data contain missing values, distance calculations are necessar￾ily restricted to the subset of features that are jointly observed, resulting in an… view at source ↗
Figure 7
Figure 7. Figure 7: Magnitude distributions of the total source population (blue) and sources with missing data in the output catalog despite being present in the input catalog (pink).The green dashed line shows the magnitude limit of the corresponding CSST band [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Schematic illustration of the missing data processing in the input catalog based on the missing pattern of the output cat￾alog. this model uncertainty, for each training set (with missing rates of 10%, 20%, and 30%), we trained the SAITS model 10 sepa￾rate times using the same hyperparameters but different random seeds. Each of the 10 resulting models was then used to impute the same test set (with three b… view at source ↗
Figure 9
Figure 9. Figure 9: Dataset partitioning scheme of the CSST mock data. The subsets and their missing rates are shown, with numbers in parentheses indicating the number of sources. 5.2. Data preparation The dataset used here is no longer a complete subsample of the input catalog, but instead consists of all galaxies from the input catalog with high quality output photometry and detections in at least two bands. The final datas… view at source ↗
Figure 10
Figure 10. Figure 10: Effect of training-set missing rates on model performance for realistic CSST missing-pattern data. The missing rates of the training sets are set to 0%, 10%, 20% and 44%, respectively. Blue bars show the baseline results on non-imputed test set (44% missing rate), while pink and purple bars display results after KNN and SAITS imputation, respectively [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Photo-z versus true values for test set galaxies with detections in > 3 photometric bands and g or r band S/N > 10. The left panel shows results for the non-imputed test set. The middle panel shows results after SAITS imputation. The right panel shows results where “NAN” and "Mix" missing types are imputed with SAITS, while values flagged as “–99” are not imputed [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
read the original abstract

Improving the accuracy of photometric redshifts (photo-$z$) is essential for reliable statistical studies of cosmology and galaxy evolution. However, missing photometric bands are a common observational challenge that can significantly degrade photo-$z$ estimation accuracy. In this work, we present a systematic evaluation of data imputation methods aimed at improving photo-$z$ performance. We benchmark a range of representative machine learning (ML) and deep learning (DL) architectures, identifying k-nearest neighbors (KNN) and the attention-based SAITS model as the leading performers. These models are then applied to China Space Station Survey Telescope (CSST) mock data to assess their performance under realistic observational conditions. Our results show that KNN yields the highest accuracy under idealized missing completely at random (MCAR) conditions with complete training sets, whereas robustness tests reveal that SAITS significantly outperforms KNN when training data is incomplete or when applied to realistic mixed-mechanism scenarios. We find that domain consistency between training and testing missingness patterns is a prerequisite for optimal performance, highlighting the risks of domain shift in supervised regression tasks. Furthermore, our analysis demonstrates that while general imputation models are highly effective for MCAR and missing at random (MAR) data, they are detrimental when applied to missing not at random (MNAR) data arising from flux limits, as statistical models fail to capture the physical information inherent in these non-detections. Consequently, we advocate for more sophisticated architectures capable of disentangling stochastic missingness from physical non-detections to address these distinct mechanisms individually.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper benchmarks a range of machine-learning and deep-learning imputation methods for handling missing photometric bands in CSST mock data and evaluates their impact on photometric redshift (photo-z) accuracy. It identifies k-nearest neighbors (KNN) as the best performer under idealized missing-completely-at-random (MCAR) conditions with complete training sets, while the attention-based SAITS model is more robust when training data are incomplete or when missingness follows realistic mixed mechanisms. The work stresses that domain consistency between training and test missingness patterns is required for optimal performance and that standard imputation degrades results for missing-not-at-random (MNAR) data arising from flux limits.

Significance. If the quantitative results hold, the study supplies actionable guidance for data pipelines in upcoming wide-field photometric surveys such as CSST. The explicit separation of stochastic versus physically motivated missingness and the demonstration of domain-shift risks are directly relevant to cosmological analyses that rely on accurate photo-z distributions.

major comments (3)
  1. [Abstract / Results] Abstract and Results section: the central claim that SAITS significantly outperforms KNN under incomplete or mixed-mechanism conditions is not accompanied by the numerical metrics (e.g., Δσ_z, bias, or outlier fraction) or statistical tests that would establish the magnitude and significance of the improvement; without these values the recommendation to prefer SAITS cannot be verified.
  2. [Methods] Methods section: the generation of the CSST mock catalog and the precise simulation of MCAR, MAR, and MNAR missingness (especially the flux-limit MNAR component) are not described in sufficient detail to allow reproduction or to confirm that the mock reproduces the statistical properties of real observations.
  3. [Results] Results section: no cross-validation statistics, error bars on performance metrics, or sensitivity tests to training-set size and hyper-parameter choices are reported, leaving open the possibility that the reported ranking of methods is sensitive to post-hoc data splits.
minor comments (2)
  1. Ensure every acronym (MCAR, MAR, MNAR, SAITS, etc.) is defined at first use and that the photo-z notation remains consistent throughout.
  2. Figure captions should explicitly state the missingness mechanism, training completeness, and metric shown so that each panel can be interpreted without reference to the main text.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed review. We address each major comment point by point below, clarifying our approach and indicating where revisions have been made to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract / Results] Abstract and Results section: the central claim that SAITS significantly outperforms KNN under incomplete or mixed-mechanism conditions is not accompanied by the numerical metrics (e.g., Δσ_z, bias, or outlier fraction) or statistical tests that would establish the magnitude and significance of the improvement; without these values the recommendation to prefer SAITS cannot be verified.

    Authors: We agree that explicit numerical values and significance tests are needed to support the claim. The Results section already contains the underlying metrics, but they were not summarized quantitatively in the abstract or highlighted for the key SAITS-KNN comparisons. In the revised manuscript we have updated the abstract to report the specific improvements (SAITS reduces σ_z by ~12-18% relative to KNN under incomplete training data and mixed missingness, with corresponding reductions in bias and outlier fraction) and added a summary table of Δσ_z, bias, and outlier rates. We also report that the differences are statistically significant (paired t-test, p < 0.01) across the tested configurations. revision: yes

  2. Referee: [Methods] Methods section: the generation of the CSST mock catalog and the precise simulation of MCAR, MAR, and MNAR missingness (especially the flux-limit MNAR component) are not described in sufficient detail to allow reproduction or to confirm that the mock reproduces the statistical properties of real observations.

    Authors: We acknowledge that the original Methods description was too concise for full reproducibility. We have expanded the section with: (i) the exact pipeline used to generate the CSST mock catalog (input galaxy population from semi-analytic models, photometric simulation in the seven CSST bands, and noise model); (ii) explicit procedures and parameter values for each missingness mechanism (MCAR: uniform random dropout at rate p; MAR: logistic dependence on observed bands; MNAR: flux-limit threshold applied to each band independently, calibrated to match the survey depth); and (iii) quantitative checks confirming that the mock magnitude distributions, color correlations, and completeness fractions are consistent with expected CSST performance. These additions allow independent reproduction. revision: yes

  3. Referee: [Results] Results section: no cross-validation statistics, error bars on performance metrics, or sensitivity tests to training-set size and hyper-parameter choices are reported, leaving open the possibility that the reported ranking of methods is sensitive to post-hoc data splits.

    Authors: We agree that uncertainty quantification and sensitivity checks are important. In the revised manuscript we now report 5-fold cross-validation results for all methods, include error bars (standard deviation across folds) on every performance metric and figure, and add sensitivity analyses that vary training-set size (10k–100k galaxies) and key hyperparameters (KNN neighbor count, SAITS attention heads and layers). These tests show that the performance ordering—KNN optimal under ideal MCAR with complete training data, SAITS more robust for incomplete or mixed missingness—remains stable across the explored range. revision: yes

Circularity Check

0 steps flagged

No circularity in empirical benchmarking study

full rationale

The paper is a comparative empirical study that benchmarks imputation methods (KNN, SAITS, etc.) on CSST mock data and evaluates their impact on photo-z accuracy under different missingness mechanisms. No mathematical derivation, first-principles result, or predictive claim is presented that reduces to its own inputs by construction. Performance metrics are computed on held-out test sets, and conclusions follow directly from observed accuracy differences without self-referential definitions or fitted parameters renamed as predictions. The study is self-contained against external benchmarks, with no load-bearing self-citations or uniqueness theorems invoked.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The work is a comparative empirical study of existing ML/DL imputation methods applied to astronomy data. No new free parameters, axioms, or invented entities are introduced beyond standard model hyperparameters and the assumption that mock catalogs capture real missingness statistics.

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