An Interdisciplinary and Cross-Task Review on Missing Data Imputation

Jicong Fan

arxiv: 2511.01196 · v3 · submitted 2025-11-03 · 📊 stat.ML · cs.AI· cs.LG

An Interdisciplinary and Cross-Task Review on Missing Data Imputation

Jicong Fan This is my paper

Pith reviewed 2026-05-18 01:54 UTC · model grok-4.3

classification 📊 stat.ML cs.AIcs.LG

keywords missing data imputationimputation methodsmachine learningdeep learninglarge language modelsmissingness mechanismsdownstream tasksdata preprocessing

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The pith

This review synthesizes fragmented research on missing data imputation from classical statistics through deep learning to large language models.

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

The paper tries to establish a unified map of missing data imputation by first defining core ideas such as missingness mechanisms, single versus multiple imputation, and different goals for filling in gaps. It then sorts methods into groups that run from older statistical tools like regression and the EM algorithm to newer ones including matrix completion, autoencoders, GANs, diffusion models, graph networks, and large language models, while paying attention to tricky data forms like time series, graphs, and multimodal records. The review further shows how imputation can be chained or jointly trained with later tasks such as classification, clustering, and anomaly detection. A sympathetic reader would care because missing entries routinely block reliable conclusions in healthcare, commerce, and monitoring systems, and a clear organization of the options can reduce wasted effort and point to better choices.

Core claim

The central claim is that missing-data work has stayed scattered across fields and that a single review can connect its statistical roots to current machine-learning practice by laying out a taxonomy that runs from classical regression and the EM algorithm, through low-rank and high-rank matrix completion, to deep models such as autoencoders, GANs, diffusion models, and graph neural networks, plus large language models, with extra sections on tensors, time series, streaming, graph, categorical, and multimodal data, followed by discussion of sequential versus joint pipelines that link imputation to downstream classification, clustering, and anomaly detection, plus notes on theory, benchmarks,

What carries the argument

the categorization of imputation methods that groups approaches by generation and by data type while separating single-imputation from multiple-imputation goals

If this is right

Joint training of imputation and downstream tasks such as clustering can produce higher accuracy than running imputation first and analysis second.
Privacy-preserving imputation built on federated learning will become necessary for healthcare and other regulated domains.
Models designed to generalize across data types and fields will lower the cost of adapting imputation to new problems.
Clearer benchmarking resources and metrics will make it easier to compare classical and modern methods on equal footing.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The taxonomy could be turned into a decision tree or automated selector that matches a dataset's traits to suitable imputation methods.
Work on multimodal imputation may borrow architectural ideas from vision-language models that were not yet mature when the review was written.
The identified challenges around streaming data suggest direct links to online learning settings that the paper leaves for later exploration.

Load-bearing premise

The review assumes that its selection and categorization of methods and literature accurately captures the fragmented state of the field without major omissions in coverage of techniques or domain-specific considerations.

What would settle it

A broad literature search that finds a widely adopted imputation technique for streaming industrial data or a domain-specific method in bioinformatics that is absent from the presented taxonomy would show the synthesis is incomplete.

Figures

Figures reproduced from arXiv: 2511.01196 by Jicong Fan.

**Figure 2.** Figure 2: Taxonomy of methods for handling missing data [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: Missing values (marked as "?") in survey data (row: subject; column: question). tions [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

**Figure 4.** Figure 4: Possible missing values (marked as zero) in scRNA-Seq data (log-transformed). [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

**Figure 5.** Figure 5: Two examples of the missing data problem of images. The original complete images are from [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

**Figure 6.** Figure 6: Examples of collaborative filtering (a) and link prediction (b). The question marks indicate missing values. [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗

**Figure 7.** Figure 7: Examples of missing data patterns in industrial process: (a) sensor breakdown; (b) process shutdown; (c) [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗

**Figure 8.** Figure 8: Examples [Fan et al., 2020a] of data forming high-rank matrices in 3D space (left: union of subspaces; middle: one nonlinear manifold; right: union of nonlinear manifolds). where S ∈ R n×n is the coefficient matrix and is usually assumed to be sparse. Given an incomplete data matrix X˜ , Fan and Chow [2017b] proposed the following matrix completion method: minimize Xˆ ,S ∥S∥ℓS + λ 2 ∥Xˆ − XSˆ ∥ 2 F subject… view at source ↗

**Figure 9.** Figure 9: Toy examples of tensors. Each grid or cell denotes a scalar. Actually, it is impossible to directly visualize a [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗

**Figure 10.** Figure 10: An intuitive example of multimodal data imputation (three modalities, ten subjects). Each cell represents a [PITH_FULL_IMAGE:figures/full_fig_p028_10.png] view at source ↗

read the original abstract

Missing data is a fundamental challenge in data science, significantly hindering analysis and decision-making across a wide range of disciplines, including healthcare, bioinformatics, social science, e-commerce, and industrial monitoring. Despite decades of research and numerous imputation methods, the literature remains fragmented across fields, creating a critical need for a comprehensive synthesis that connects statistical foundations with modern machine learning advances. This work systematically reviews core concepts-including missingness mechanisms, single versus multiple imputation, and different imputation goals-and examines problem characteristics across various domains. It provides a thorough categorization of imputation methods, spanning classical techniques (e.g., regression, the EM algorithm) to modern approaches like low-rank and high-rank matrix completion, deep learning models (autoencoders, GANs, diffusion models, graph neural networks), and large language models. Special attention is given to methods for complex data types, such as tensors, time series, streaming data, graph-structured data, categorical data, and multimodal data. Beyond methodology, we investigate the crucial integration of imputation with downstream tasks like classification, clustering, and anomaly detection, examining both sequential pipelines and joint optimization frameworks. The review also assesses theoretical guarantees, benchmarking resources, and evaluation metrics. Finally, we identify critical challenges and future directions, emphasizing model selection and hyperparameter optimization, the growing importance of privacy-preserving imputation via federated learning, and the pursuit of generalizable models that can adapt across domains and data types, thereby outlining a roadmap for future research.

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.

Desk Editor's Note private letter to a colleague

A broad literature survey on missing data imputation that connects classical methods to recent deep learning and LLM work but skips any description of its own search process.

read the letter

This review organizes imputation techniques from regression and EM through matrix completion, autoencoders, GANs, diffusion models, GNNs, and LLMs, while also covering data types like tensors, time series, graphs, and multimodal inputs. It does a decent job showing how imputation can be handled separately or jointly with tasks such as classification, clustering, and anomaly detection, and it flags practical issues like privacy via federated learning and the need for better model selection. That cross-task and cross-domain angle is the part that could actually help someone pick an approach without reading dozens of scattered papers first. The summaries of existing theoretical guarantees and evaluation metrics are straightforward and useful for orientation. The main limitation is that the paper claims a thorough categorization without describing any literature search protocol, databases, keywords, time bounds, or inclusion criteria. That absence makes it difficult to judge whether important recent work or domain-specific methods were missed, which undercuts the strength of the synthesis claim. The citations appear wide but the lack of transparency on selection leaves room for bias. This is the kind of paper that works best for applied researchers or students who want an updated map of the field rather than for specialists already deep in one sub-area. It could fit a reading group focused on practical method choice. I would send it to peer review because the scope is timely and the connections it draws have value, even if referees will likely ask for more detail on coverage and possibly additional references.

Referee Report

1 major / 1 minor

Summary. This review synthesizes the literature on missing data imputation across disciplines. It covers core concepts such as missingness mechanisms, single vs. multiple imputation, and imputation goals; categorizes methods from classical regression and EM to matrix completion, autoencoders, GANs, diffusion models, GNNs, and LLMs; addresses complex data types including tensors, time series, graphs, and multimodal data; examines integration with downstream tasks via sequential or joint frameworks; and discusses theoretical guarantees, benchmarks, metrics, and open challenges such as model selection, privacy via federated learning, and generalizability.

Significance. A well-executed interdisciplinary review could usefully connect statistical foundations with recent deep learning and LLM-based methods while highlighting cross-task considerations. However, the absence of a documented search protocol limits the ability to evaluate whether the claimed thorough categorization accurately reflects the fragmented field without major omissions, reducing the potential impact.

major comments (1)

[Abstract / Introduction] The central claim of providing a 'thorough categorization' of imputation methods (from classical techniques through LLMs) and domain considerations requires a transparent literature search protocol. No description of databases, keywords, time bounds, inclusion/exclusion criteria, or selection process appears in the abstract or is referenced in the provided manuscript structure, making it impossible to assess completeness or selection bias (e.g., coverage of recent privacy-preserving or LLM approaches).

minor comments (1)

[Integration with downstream tasks] Clarify whether the review distinguishes between single and multiple imputation consistently when discussing integration with downstream tasks such as classification or anomaly detection.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive feedback and for recognizing the interdisciplinary scope of our review. We appreciate the opportunity to improve the manuscript's transparency regarding literature selection and will address this point directly.

read point-by-point responses

Referee: [Abstract / Introduction] The central claim of providing a 'thorough categorization' of imputation methods (from classical techniques through LLMs) and domain considerations requires a transparent literature search protocol. No description of databases, keywords, time bounds, inclusion/exclusion criteria, or selection process appears in the abstract or is referenced in the provided manuscript structure, making it impossible to assess completeness or selection bias (e.g., coverage of recent privacy-preserving or LLM approaches).

Authors: We agree that documenting the literature curation process would strengthen the manuscript and allow readers to better evaluate its scope and potential biases. Although the review is framed as an interdisciplinary synthesis informed by expertise across statistics, machine learning, and domain applications rather than a formal PRISMA-style systematic review, we will revise the Introduction to include a dedicated subsection describing our approach. This will specify the primary sources consulted (Google Scholar, arXiv, PubMed, IEEE Xplore, and domain-specific repositories), representative search terms (e.g., combinations of 'missing data imputation', 'matrix completion', 'GAN-based imputation', 'diffusion models for imputation', 'LLM imputation'), the time frame (foundational works through late 2024), and inclusion considerations (peer-reviewed contributions, impactful preprints, and relevance to methods or cross-task integration). We will also note how recent privacy-preserving and LLM-based works were incorporated. This addition will directly address concerns about completeness and selection bias while preserving the review's narrative structure. revision: yes

Circularity Check

0 steps flagged

Review paper with no internal derivation chain or self-referential reductions

full rationale

This is a literature review synthesizing concepts, mechanisms, and methods for missing data imputation from classical statistics through deep learning and LLMs. No new equations, fitted parameters, predictions, or uniqueness theorems are derived within the paper itself. The categorization and integration discussions rely on external literature citations rather than reducing to self-defined inputs, self-citations as load-bearing premises, or ansatzes smuggled via prior author work. Absence of a documented search protocol affects verifiability of completeness but does not create circularity under the defined patterns, as no claim reduces by construction to the paper's own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The review rests on standard domain assumptions about the fragmentation of the imputation literature and the utility of interdisciplinary synthesis, without introducing free parameters, new entities, or ad-hoc axioms beyond those common in the field.

axioms (1)

domain assumption The literature on missing data imputation remains fragmented across disciplines, necessitating a comprehensive synthesis.
Directly stated in the abstract as the motivation for the review.

pith-pipeline@v0.9.0 · 5788 in / 1221 out tokens · 47629 ms · 2026-05-18T01:54:53.888134+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

systematically reviews core concepts including missingness mechanisms... categorization of imputation methods spanning classical techniques to modern deep learning models and large language models
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

low-rank and high-rank matrix completion, deep learning models (autoencoders, GANs, diffusion models, graph neural networks)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages · 1 internal anchor

[1]

eckart-young

doi: https://doi.org/10.1016/j.chaos.2021.111236. URL https://www.sciencedirect.com/science/ article/pii/S0960077921005907. Abdo Y Alfakih, Amir Khandani, and Henry Wolkowicz. Solving euclidean distance matrix completion problems via semideﬁnite programming. Computational optimization and applications , 12:13–30, 1999. Majed Alwateer, El-Sayed Atlam, Mahm...

work page doi:10.1016/j.chaos.2021.111236 2021
[2]

URL https://www.sciencedirect.com/science/ article/pii/S1574013724001035

doi: https://doi.org/10.1016/j.cosrev.2024.100720. URL https://www.sciencedirect.com/science/ article/pii/S1574013724001035. Marine Le Morvan, Julie Josse, Thomas Moreau, Erwan Scornet, and Gael V aroquaux. Neumiss networks: dif- ferentiable programming for supervised learning with missing values. In H. Larochelle, M. Ranzato, R. Had- sell, M. F. Balcan, ...

work page doi:10.1016/j.cosrev.2024.100720 2024
[3]

URL https://www.sciencedirect.com/science/ article/pii/S003132032200526X

doi: https://doi.org/10.1016/j.patcog.2022.109046. URL https://www.sciencedirect.com/science/ article/pii/S003132032200526X. Feng Xiao and Jicong Fan. Unsupervised anomaly detection in the presence of missing values. In A. Globerson, L. Mackey, D. Belgrave, A. Fan, U. Paquet, J. Tomczak, and C. Zhang, edi- tors, Advances in Neural Information Processing S...

work page doi:10.1016/j.patcog.2022.109046 2022
[4]

Tensor Ring Decomposition

doi: https://doi.org/10.1016/j.neucom.2017.07.016. URL https://www.sciencedirect.com/science/ article/pii/S0925231217312535. Qibin Zhao, Liqing Zhang, and Andrzej Cichocki. Bayesian cp factorization of incomplete tensors with automatic rank determination. IEEE transactions on pattern analysis and machine intelligence , 37(9):1751–1763, 2015. Qibin Zhao, G...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.neucom.2017.07.016 2017

[1] [1]

eckart-young

doi: https://doi.org/10.1016/j.chaos.2021.111236. URL https://www.sciencedirect.com/science/ article/pii/S0960077921005907. Abdo Y Alfakih, Amir Khandani, and Henry Wolkowicz. Solving euclidean distance matrix completion problems via semideﬁnite programming. Computational optimization and applications , 12:13–30, 1999. Majed Alwateer, El-Sayed Atlam, Mahm...

work page doi:10.1016/j.chaos.2021.111236 2021

[2] [2]

URL https://www.sciencedirect.com/science/ article/pii/S1574013724001035

doi: https://doi.org/10.1016/j.cosrev.2024.100720. URL https://www.sciencedirect.com/science/ article/pii/S1574013724001035. Marine Le Morvan, Julie Josse, Thomas Moreau, Erwan Scornet, and Gael V aroquaux. Neumiss networks: dif- ferentiable programming for supervised learning with missing values. In H. Larochelle, M. Ranzato, R. Had- sell, M. F. Balcan, ...

work page doi:10.1016/j.cosrev.2024.100720 2024

[3] [3]

URL https://www.sciencedirect.com/science/ article/pii/S003132032200526X

doi: https://doi.org/10.1016/j.patcog.2022.109046. URL https://www.sciencedirect.com/science/ article/pii/S003132032200526X. Feng Xiao and Jicong Fan. Unsupervised anomaly detection in the presence of missing values. In A. Globerson, L. Mackey, D. Belgrave, A. Fan, U. Paquet, J. Tomczak, and C. Zhang, edi- tors, Advances in Neural Information Processing S...

work page doi:10.1016/j.patcog.2022.109046 2022

[4] [4]

Tensor Ring Decomposition

doi: https://doi.org/10.1016/j.neucom.2017.07.016. URL https://www.sciencedirect.com/science/ article/pii/S0925231217312535. Qibin Zhao, Liqing Zhang, and Andrzej Cichocki. Bayesian cp factorization of incomplete tensors with automatic rank determination. IEEE transactions on pattern analysis and machine intelligence , 37(9):1751–1763, 2015. Qibin Zhao, G...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.neucom.2017.07.016 2017