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Order-Agnostic Autoregressive Modelling with Missing Data

T0 review · 0 major / 2 minor · reviewed 2026-06-30 · grok-4.3

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Pith's one-line read Order-agnostic autoregressive models can be trained directly on incomplete data under general missingness and outperform standard imputation.

desk verdict The paper gives a direct training method for order-agnostic autoregressive models on incomplete data under general missingness, with the claim that standard training already handles MCAR implicitly. read the letter →

arxiv 2605.06355 v2 pith:EFRRHSDO submitted 2026-05-07 cs.LG stat.ML

Ignacio Peis , Pablo M. Olmos , Jes Frellsen This is my paper · ORCID
classification cs.LGstat.ML
keywords order-agnosticautoregressivemodelsmissingdataimputationmissingnessmechanismsactiveinformationacquisitiondeepgenerativeincompletedatasets
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper reinterprets order-agnostic autoregressive models as already performing imputation when trained on complete data, because their variable ordering acts like random masking under a missing completely at random process. It then supplies the first training procedure that works on incomplete observations without assuming the data are fully observed. The same models support active selection of which missing entry to observe next by using their conditional densities to rank information gain. Across real benchmarks the resulting MO-ARM version beats established imputation methods. Readers would care because many practical datasets arrive with missing entries and embedding the handling inside the generative model removes an extra preprocessing stage.

What carries the argument

The Missingness-Aware Order-Agnostic Autoregressive Model (MO-ARM), which folds the observed missing pattern into the autoregressive factorization so that each conditional is trained only on the actually observed preceding variables.

What would settle it

On a dataset generated with a known non-random missingness pattern, compare MO-ARM imputation error against a baseline trained only on complete data; if the errors are statistically indistinguishable, the advantage of the new framework is falsified.

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Extended reading notes

Core claim

Order-agnostic autoregressive models trained on fully observed data implicitly perform imputation under a missing completely at random mechanism and retain robust performance at high missing rates. The authors introduce a missingness-aware training framework that extends the same models to arbitrary missingness mechanisms, allowing direct learning from incomplete data while preserving the ability to perform amortized conditional density estimation for active information acquisition.

Load-bearing premise

Missingness can be separated from the data-generating process so that the autoregressive conditionals remain unbiased when trained only on observed entries.

Editorial extensions

If this is right

  • Standard training on complete data already produces competitive imputation under high missing rates via the order-agnostic property.
  • A single training procedure works for any missingness mechanism without requiring complete observations.
  • The learned conditionals enable sequential choice of the next most informative variable to observe.
  • MO-ARM records lower imputation error than common baselines on multiple real-world datasets.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Generative modeling pipelines could skip separate imputation steps and train end-to-end on raw incomplete records.
  • The active acquisition routine could be paired with budgeted data collection where each observation carries a cost.
  • Similar missingness adjustments might apply to other order-agnostic sequence models beyond the architectures tested here.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 2 minor

Summary. The manuscript reinterprets order-agnostic autoregressive models for missing-data settings. It argues that standard training on fully observed data implicitly performs imputation under an MCAR mechanism, yielding robust out-of-sample imputation. It then introduces a principled training framework for incomplete data under general missingness mechanisms and applies the resulting amortized conditional densities to active information acquisition (sequentially choosing the most informative missing variables). The proposed MO-ARM model is reported to outperform established imputation baselines across real-world benchmarks.

Significance. If the empirical claims are substantiated, the work supplies a coherent extension of order-agnostic autoregressive models to missing data, together with an implicit-imputation observation and an application to active acquisition. These elements could be useful for generative modeling pipelines that routinely encounter incomplete observations. The manuscript does not report machine-checked proofs or fully reproducible code artifacts, but the high-level logic appears internally consistent.

minor comments (2)
  1. [Abstract] Abstract: the specific real-world benchmarks, missingness rates, and quantitative margins of improvement are not stated; these details belong in the experimental section (presumably §4 or §5) to permit assessment of the outperformance claim.
  2. The notation used for the missingness mechanisms and the precise definition of the new training objective should be introduced with explicit equations early in the methods section to avoid ambiguity with standard missing-data terminology.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their review of our manuscript. We appreciate the recognition that the high-level logic appears internally consistent and that the elements could be useful for generative modeling pipelines encountering incomplete observations. The report does not enumerate specific major comments, so we have no individual points to rebut at this stage. We remain available to provide further clarification, additional experiments, or revisions should the referee or editor request them.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity identified

full rationale

The paper reinterprets order-agnostic autoregressive models for missing data by showing that standard training on fully observed data implicitly performs MCAR imputation and by introducing a framework for general missingness mechanisms. These steps are logical extensions of existing model properties rather than reductions to self-definitions, fitted inputs renamed as predictions, or load-bearing self-citations. The central outperformance claim rests on benchmark comparisons, and the derivation chain remains self-contained without any quoted equation or premise equating outputs to inputs by construction.

Assumptions & free parameters 0 free parameters · 0 assumptions · 0 invented entities

Abstract-only review provides no information on free parameters, axioms, or invented entities used in the framework.

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Cite this review

Pith. "Pith review of Order-Agnostic Autoregressive Modelling with Missing Data." pith.science (2026). https://pith.science/paper/EFRRHSDO

@misc{pith2026260506355,
  author       = {Pith},
  title        = {Pith review of: Order-Agnostic Autoregressive Modelling with Missing Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EFRRHSDO}},
  note         = {Machine review of arXiv:2605.06355}
}
read the original abstract

Order-Agnostic autoregressive models have demonstrated strong performance in deep generative modeling, yet their use in settings with incomplete data remains largely unexplored. In this work, we reinterpret them through the lens of missing data. First, we show that their standard training procedure on fully observed data implicitly performs imputation under a missing completely at random mechanism, resulting in robust out-of-sample imputation performance in settings with high missingness. Second, we introduce the first principled framework for training them directly on incomplete datasets under general missingness mechanisms. Third, we leverage their amortized conditional density estimation to perform active information acquisition, i.e., sequentially selecting the most informative missing variables for downstream prediction or inference. Across a suite of real-world benchmarks, our Missingness-Aware Order-Agnostic Autoregressive Model (MO-ARM) consistently outperforms established imputation baselines.

Figures

Figures reproduced from arXiv: 2605.06355 by the authors.

Figure 1
Figure 1. Graphical models used throughout the paper. Boxes denote collections of variables. The view at source ↗
Figure 2
Figure 2. Image inpainting comparison. The leftmost panel shows incomplete images at different rates. view at source ↗
Figure 3
Figure 3. Average test imputation performance at a 50% missing rate across the nine UCI tabular view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Sequential active information acquisition with MO-ARM and baselines on UCI datasets.
Figure 5
Figure 5. Figure 5: Per-dataset average test imputation RMSE of MCAR missing data at a 50% missing rate
Figure 6
Figure 6. Figure 6: Per-dataset average test imputation MAE of MCAR missing data at a 50% missing rate
Figure 7
Figure 7. Figure 7: Per-dataset average test imputation accuracy of MCAR missing data at a 50% missing rate
Figure 8
Figure 8. Figure 8: Per-dataset average test imputation RMSE of MNAR missing data at a 50% missing rate
Figure 9
Figure 9. Figure 9: Per-dataset average test imputation MAE of MNAR missing data at a 50% missing rate
Figure 10
Figure 10. Figure 10: Per-dataset average test imputation accuracy of MNAR missing data at a 50% missing

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