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arxiv: 2511.04333 · v1 · submitted 2025-11-06 · 💻 cs.LG · cs.AI

LUME-DBN: Full Bayesian Learning of DBNs from Incomplete data in Intensive Care

Federico Pirola , Fabio Stella , Marco Grzegorczyk This is my paper

Pith reviewed 2026-05-18 01:02 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords dynamic bayesian networksmissing datagibbs samplingintensive carebayesian inferencetemporal modelsimputation
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The pith

A Gibbs sampling procedure learns dynamic Bayesian networks from incomplete intensive care data by sampling missing values as Gaussian parameters.

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

The paper presents a full Bayesian method for learning dynamic Bayesian networks when longitudinal clinical data contain missing entries. It folds imputation directly into the learning process by treating each unobserved value as an unknown Gaussian parameter and drawing it from its full conditional distribution at every Gibbs step. This produces both network parameters and imputed values together with uncertainty estimates that respect the temporal structure of the data. The method is demonstrated on simulated sequences and on real records from critically ill patients, where it achieves higher reconstruction accuracy and more stable convergence than separate imputation tools such as MICE. The approach therefore supplies a practical route to reliable temporal models in settings where incomplete observations are routine.

Core claim

A Gibbs sampler jointly infers DBN parameters and missing data by modeling each unobserved entry as a Gaussian random variable whose full conditional is directly available, thereby performing principled imputation and uncertainty quantification inside the same iterative procedure used for network learning.

What carries the argument

Gibbs sampling over the joint posterior of DBN parameters and missing values, with each missing observation treated as an unknown Gaussian parameter that is resampled from its full conditional at every iteration.

Load-bearing premise

Missing values can be treated as unknown parameters that follow a Gaussian distribution whose full conditional can be sampled directly within the Gibbs procedure for DBNs.

What would settle it

Mask known values in a complete longitudinal dataset generated from a known DBN, run the sampler, and check whether the recovered posterior means and credible intervals for the masked entries are well calibrated against the true hidden values.

Figures

Figures reproduced from arXiv: 2511.04333 by Fabio Stella, Federico Pirola, Marco Grzegorczyk.

Figure 1
Figure 1. Figure 1: Area Under the Precision-Recall Curve for different experimental settings (sam￾ple sizes, missingness rates and imputation methods). The p-values of the paired t-test LUME-DBN AUC vs Baseline Method AUC are computed for each experimental con￾dition, highlighting p-values < 0.05 with colored ’⋆’ based on the baseline method. Confidence bars represent the 95% confidence intervals for each experimental settin… view at source ↗
Figure 2
Figure 2. Figure 2: Reconstructed DBNs for each ICU type, averaged over five independent simu￾lations after local data standardization. A threshold of 0.8 is applied to the averaged inclusion probabilities. Arcs are meant to represent temporal relationship with a single temporal lag, namely between nodes at time t − 1 and nodes at time t [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
read the original abstract

Dynamic Bayesian networks (DBNs) are increasingly used in healthcare due to their ability to model complex temporal relationships in patient data while maintaining interpretability, an essential feature for clinical decision-making. However, existing approaches to handling missing data in longitudinal clinical datasets are largely derived from static Bayesian networks literature, failing to properly account for the temporal nature of the data. This gap limits the ability to quantify uncertainty over time, which is particularly critical in settings such as intensive care, where understanding the temporal dynamics is fundamental for model trustworthiness and applicability across diverse patient groups. Despite the potential of DBNs, a full Bayesian framework that integrates missing data handling remains underdeveloped. In this work, we propose a novel Gibbs sampling-based method for learning DBNs from incomplete data. Our method treats each missing value as an unknown parameter following a Gaussian distribution. At each iteration, the unobserved values are sampled from their full conditional distributions, allowing for principled imputation and uncertainty estimation. We evaluate our method on both simulated datasets and real-world intensive care data from critically ill patients. Compared to standard model-agnostic techniques such as MICE, our Bayesian approach demonstrates superior reconstruction accuracy and convergence properties. These results highlight the clinical relevance of incorporating full Bayesian inference in temporal models, providing more reliable imputations and offering deeper insight into model behavior. Our approach supports safer and more informed clinical decision-making, particularly in settings where missing data are frequent and potentially impactful.

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

2 major / 2 minor

Summary. The paper proposes LUME-DBN, a Gibbs sampling procedure for full Bayesian learning of Dynamic Bayesian Networks from incomplete longitudinal data. Missing entries are treated as unknown parameters drawn from Gaussian distributions and sampled from their full conditionals inside the DBN Gibbs sweep; the method is evaluated on simulated data and real ICU records, with the central claim that it yields superior reconstruction accuracy and convergence relative to model-agnostic imputation such as MICE.

Significance. A sound implementation would advance principled uncertainty quantification for temporal clinical models by folding imputation directly into DBN parameter learning. The approach correctly emphasizes the temporal structure that static BN methods ignore, and the provision of a joint posterior over structure, parameters, and imputations is a genuine technical contribution if the distributional assumptions can be justified.

major comments (2)
  1. [Abstract] Abstract: the assertion that the Bayesian approach 'demonstrates superior reconstruction accuracy and convergence properties' is unsupported by any numerical results, dataset sizes, missingness fractions, statistical tests, or ablation details, rendering the central empirical claim unverifiable from the manuscript text.
  2. [Method] Method section (Gibbs sampling for missing values): the full conditional for each missing entry is derived under an unconditional Gaussian model. ICU variables routinely include binary flags, integer counts, bounded lab values, and censored observations; sampling from a Gaussian produces probability mass outside valid support, so the imputed draws are not from the true posterior and the comparison with MICE (which admits per-variable conditional models) is not on equal footing.
minor comments (2)
  1. [Abstract] The abstract states that the method 'supports safer and more informed clinical decision-making' without any downstream clinical-task evaluation (e.g., prediction of outcomes or treatment effects) that would substantiate this claim.
  2. [Method] Notation for the DBN transition and emission distributions is not introduced before the Gibbs sweep is described, making it difficult to follow how the full conditionals are obtained.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and insightful comments on our manuscript. We have addressed each major comment point by point below, making revisions where appropriate to improve clarity, rigor, and transparency.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that the Bayesian approach 'demonstrates superior reconstruction accuracy and convergence properties' is unsupported by any numerical results, dataset sizes, missingness fractions, statistical tests, or ablation details, rendering the central empirical claim unverifiable from the manuscript text.

    Authors: We agree that the abstract would be strengthened by including concrete details to support the empirical claims. In the revised manuscript, we have updated the abstract to reference specific quantitative results from the experiments, including reconstruction accuracy metrics, dataset sizes (number of patients and time steps), missingness fractions, and the statistical comparisons performed against MICE. These additions make the central claims directly verifiable while preserving the abstract's conciseness. revision: yes

  2. Referee: [Method] Method section (Gibbs sampling for missing values): the full conditional for each missing entry is derived under an unconditional Gaussian model. ICU variables routinely include binary flags, integer counts, bounded lab values, and censored observations; sampling from a Gaussian produces probability mass outside valid support, so the imputed draws are not from the true posterior and the comparison with MICE (which admits per-variable conditional models) is not on equal footing.

    Authors: We appreciate this observation on the distributional assumptions. Our derivation of the full conditionals for missing values assumes Gaussian distributions, which is appropriate for the continuous physiological variables (e.g., heart rate, blood pressure) that form the primary focus of our ICU datasets and evaluations. We acknowledge that this assumption does not enforce valid support for binary, count-based, or censored variables and that MICE can employ variable-specific models. In the revision, we have added explicit discussion of this modeling choice and its limitations in the Methods and Limitations sections, clarified that comparisons were restricted to continuous variables for fairness, and outlined extensions to mixed-type models as future work. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper describes a Gibbs sampling procedure that treats missing values as Gaussian parameters whose full conditionals are sampled inside the DBN learning sweep. No equations, derivations, or self-citations are shown that reduce the claimed reconstruction accuracy or convergence properties to a quantity fitted from the same data by construction. The method is presented as a direct application of standard conditional sampling, and performance claims rest on empirical comparisons to MICE on simulated and real ICU data rather than tautological redefinitions or imported uniqueness results. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The method rests on the modeling choice that missing entries are Gaussian parameters and that the DBN conditional distributions permit direct sampling; these are domain assumptions rather than derived results.

axioms (1)
  • domain assumption Missing values follow a Gaussian distribution and can be sampled from their full conditional given the current DBN parameters.
    Explicitly stated as the core of the imputation step in the proposed method.

pith-pipeline@v0.9.0 · 5791 in / 1089 out tokens · 27558 ms · 2026-05-18T01:02:35.737535+00:00 · methodology

discussion (0)

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Reference graph

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