Quantifying Confounding Bias in Neuroimaging Datasets with Causal Inference

Anna Rieckmann; Benjamin Gutierrez Becker; Christian Wachinger; Sebastian P\"olsterl

arxiv: 1907.04102 · v1 · pith:TUNRE4CAnew · submitted 2019-07-09 · 💻 cs.LG · cs.CV· eess.IV· stat.ML

Quantifying Confounding Bias in Neuroimaging Datasets with Causal Inference

Christian Wachinger , Benjamin Gutierrez Becker , Anna Rieckmann , Sebastian P\"olsterl This is my paper

Pith reviewed 2026-05-25 00:23 UTC · model grok-4.3

classification 💻 cs.LG cs.CVeess.IVstat.ML

keywords causal inferenceconfounding biasneuroimagingMRIminimum description lengthgraphical modelsdataset poolingKolmogorov complexity

0 comments

The pith

Finding the simplest causal graphical model via minimum description length separates confounding biases from true causal effects in pooled neuroimaging datasets.

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

The paper shows that combining MRI scans from multiple studies to train larger models often creates confounding biases that models can exploit instead of learning real medical signals. Scans from 15 different studies totaling over 12,000 images can still be correctly assigned back to their source dataset at 73 percent accuracy, proving the biases are detectable. To separate confounding factors from genuine causal relationships, the authors select the graphical model with the lowest Kolmogorov complexity, approximated by the minimum description length principle. This produces a data-driven estimate of how much confounding is present and what the plausible causal links are. A reader would care because it offers a concrete way to make pooled medical imaging data safer for machine learning without relying on external labels or assumptions about the studies.

Core claim

By approximating Kolmogorov complexity with the minimum description length principle, the simplest graphical model can be identified in a dataset of 12,207 MRI scans from 15 studies, enabling the quantification of confounding bias and the estimation of plausible causal relationships between variables in neuroimaging data.

What carries the argument

The minimum description length principle as an approximation to Kolmogorov complexity for selecting the causal graphical model with the lowest complexity from pooled scans.

If this is right

Pooling without correction allows models to learn dataset-specific artifacts instead of biological signals.
The recovered graphs can quantify the extent of confounding present in any single combined dataset.
Empirical tests on real data produce plausible causal estimates that distinguish study-specific biases from true effects.
This supplies a fully data-driven procedure for identifying which variables act as confounders versus causes.

Where Pith is reading between the lines

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

The same selection procedure could be tested on simulated data with fully known ground-truth graphs to measure recovery accuracy directly.
If the approach works, it suggests a general preprocessing step for any multi-site medical dataset where site effects might masquerade as signals.
The method might be extended to longitudinal or multi-modal imaging collections where confounding structures are even more complex.
One could check whether the identified causal subgraphs improve downstream prediction performance on held-out tasks compared with uncorrected pooling.

Load-bearing premise

The minimum description length provides a sufficiently accurate approximation to Kolmogorov complexity to recover the true causal graphical model separating confounding from causal factors in pooled neuroimaging data.

What would settle it

Apply the method to a pooled dataset where known confounding factors have been deliberately injected and check whether the recovered graph correctly isolates those confounding edges rather than attributing them to causal links.

Figures

Figures reproduced from arXiv: 1907.04102 by Anna Rieckmann, Benjamin Gutierrez Becker, Christian Wachinger, Sebastian P\"olsterl.

**Figure 1.** Figure 1: Left: Dataset classification accuracy for age and sex, volume, thickness, and their combination. The percentage of the data used for training is shown in log-scale. Lines show the average score over 50 repetitions, error bars show the standard deviation. Right: Confusion matrix for volume and thickness with 70% training data. posed in [25]. In contrast to prior work, note that our proposed approach aims to… view at source ↗

**Figure 2.** Figure 2: Probabilistic graphical models for observed variables X, Y and unobserved confounders Z. The statistical relationship between X and Y is due to confounder Z and due to the influence of X on Y (left). Limiting cases are pure confounding (middle) and pure causality (right). While this has yielded useful insights, it is flawed: (i) it cannot be used with MRI scans from a single dataset only, and (ii) it only … view at source ↗

**Figure 3.** Figure 3: Left: Mean difference ∆ across brain structures for all datasets. Higher values indicate datasets where age and sex have a stronger causal effect on volume. Right: Differences ∆ for all brain structures on the ADNI dataset. The complexity of the confounded model can be estimated by Lco(X, Yj ) = − log Z P(X, Yj |Z,W)P(Z)P(W)dWdZ, Zi ∼ N (0, σ2 z I), Wi ∼ N (0, σ2 wI), X|Z,W ∼ N (W>Z, σ2 x I), (2) where the… view at source ↗

read the original abstract

Neuroimaging datasets keep growing in size to address increasingly complex medical questions. However, even the largest datasets today alone are too small for training complex machine learning models. A potential solution is to increase sample size by pooling scans from several datasets. In this work, we combine 12,207 MRI scans from 15 studies and show that simple pooling is often ill-advised due to introducing various types of biases in the training data. First, we systematically define these biases. Second, we detect bias by experimentally showing that scans can be correctly assigned to their respective dataset with 73.3% accuracy. Finally, we propose to tell causal from confounding factors by quantifying the extent of confounding and causality in a single dataset using causal inference. We achieve this by finding the simplest graphical model in terms of Kolmogorov complexity. As Kolmogorov complexity is not directly computable, we employ the minimum description length to approximate it. We empirically show that our approach is able to estimate plausible causal relationships from real neuroimaging data.

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

The paper flags real pooling bias in MRI data via a 73% classification test and sketches an MDL causal-graph approach, but supplies no synthetic validation that the procedure recovers known causal structure rather than just a parsimonious fit.

read the letter

The core observation is useful: combining 12k scans from 15 studies lets a classifier recover dataset identity at 73.3 percent accuracy, which demonstrates that naive pooling mixes in unwanted structure. That part is straightforward and worth noting for anyone who pools imaging cohorts. The proposed fix applies minimum description length to search for the simplest graphical model as a proxy for Kolmogorov complexity, then claims this separates causal from confounding factors. The abstract presents this as new for the neuroimaging setting. On the positive side, the authors are explicit about the practical motivation and they run the method on real pooled data rather than staying purely theoretical. The soft spot is that the central claim rests on an untested link. The stress-test note is right: without benchmarks on data whose true DAG is known, it is impossible to tell whether the MDL minimum recovers the generating causal graph or simply returns a compact factorization of the observed correlations. The abstract only reports “plausible” relationships, and the circularity concern (selecting the model on the same data whose structure is being recovered) is not addressed in the provided summary. Implementation details for the MDL encoding on graphs and variables are also missing. This is the kind of paper that could interest a reading group focused on causal methods in medical imaging, but only after the authors add controlled experiments that measure recovery accuracy against injected confounders. I would not cite the causal-recovery claim in its current form. A serious editor could send it to review if the full manuscript supplies those controls and a clearer description of the MDL procedure; otherwise the empirical support is too thin for the strength of the conclusion.

Referee Report

2 major / 0 minor

Summary. The paper claims that pooling neuroimaging datasets from multiple studies introduces confounding biases, which can be detected by a classifier assigning scans to their source datasets at 73.3% accuracy. It proposes quantifying causal versus confounding factors via the minimum description length (MDL) principle as a proxy for Kolmogorov complexity to recover the simplest graphical model, and reports that this yields plausible causal relationships on a pooled set of 12,207 MRI scans from 15 studies.

Significance. If the MDL-based procedure can be shown to recover ground-truth causal structure, the work would offer a practical information-theoretic tool for diagnosing dataset biases in pooled neuroimaging data and improving downstream machine-learning reliability. The emphasis on Kolmogorov complexity and MDL for causal discovery is a conceptually interesting direction, though its empirical grounding remains limited to real-data plausibility checks.

major comments (2)

[Abstract] Abstract: the central claim that MDL minimization recovers the true causal graphical model separating confounding from causal factors rests on an untested assumption that the chosen encoding yields a description length whose minimum coincides with the generating DAG; no synthetic benchmarks with injected confounders and known ground-truth structure are described, so it is impossible to distinguish recovery of causality from selection of a parsimonious but non-causal factorization.
[Abstract] Abstract: model selection is performed by minimizing description length on the identical dataset whose causal structure is being recovered, without mention of held-out validation, external benchmarks, or statistical controls; this circularity risks selecting models that merely fit observed correlations rather than independent causal mechanisms.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for the detailed review and constructive criticism. The points raised regarding the validation of our MDL-based causal inference method are well-taken. We provide point-by-point responses below.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that MDL minimization recovers the true causal graphical model separating confounding from causal factors rests on an untested assumption that the chosen encoding yields a description length whose minimum coincides with the generating DAG; no synthetic benchmarks with injected confounders and known ground-truth structure are described, so it is impossible to distinguish recovery of causality from selection of a parsimonious but non-causal factorization.

Authors: The referee correctly identifies that our manuscript lacks synthetic benchmarks with known ground-truth causal structures. While the MDL principle provides a theoretical basis for preferring causal models through simplicity, we agree that empirical validation on synthetic data would be necessary to confirm that the minimum description length corresponds to the true generating DAG rather than an alternative parsimonious model. This represents a gap in the current presentation. We will incorporate synthetic experiments with injected confounders in the revised version of the manuscript. revision: yes
Referee: [Abstract] Abstract: model selection is performed by minimizing description length on the identical dataset whose causal structure is being recovered, without mention of held-out validation, external benchmarks, or statistical controls; this circularity risks selecting models that merely fit observed correlations rather than independent causal mechanisms.

Authors: We acknowledge that the model selection via MDL is conducted on the same dataset used for inference, which is standard practice in many causal discovery algorithms but does introduce the risk highlighted by the referee. Our encodings are designed to capture domain knowledge from neuroimaging, but to address the concern of circularity, we will add held-out validation procedures and additional controls in the revised manuscript to demonstrate that the selected models capture causal mechanisms beyond mere correlations. revision: yes

Circularity Check

0 steps flagged

No circularity; method is a direct MDL application without reduction to inputs

full rationale

The paper proposes selecting the simplest graphical model via minimum description length as a proxy for Kolmogorov complexity to separate causal from confounding factors in pooled neuroimaging data. This is a methodological choice grounded in the MDL principle, with the claim that the resulting model yields plausible causal relationships demonstrated empirically on real data. No derivation chain reduces a claimed prediction or result to its own fitted inputs by construction, no self-citation is load-bearing for the central premise, and no ansatz or uniqueness theorem is imported from prior author work. The approach is self-contained as an application of existing information-theoretic model selection; concerns about validation on synthetic ground-truth data pertain to empirical correctness rather than circularity in the stated procedure.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the unproven adequacy of the MDL approximation for causal discovery in this domain and on the assumption that the recovered graphical model corresponds to real causal relationships rather than data artifacts.

axioms (1)

domain assumption Minimum description length approximates Kolmogorov complexity sufficiently well to identify the true causal graphical model
Explicitly invoked in the abstract as the mechanism for finding the simplest graphical model.

pith-pipeline@v0.9.0 · 5717 in / 1223 out tokens · 26920 ms · 2026-05-25T00:23:11.794857+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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Neuroinformatics 11(3), 367–388 (2013)

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Han, X., Fischl, B.: Atlas renormalization for improved brain mr image segmenta- tion across scanner platforms. IEEE TMI 26(4), 479–486 (2007)

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Journal of magnetic resonance imaging 27(4), 685–691 (2008)

Jack, C.R., Bernstein, M.A., Fox, N.C., Thompson, P., et al.: The alzheimer’s disease neuroimaging initiative (adni): Mri methods. Journal of magnetic resonance imaging 27(4), 685–691 (2008)

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In: SIAM International Conference on Data Mining (2019)

Kaltenpoth, D., Vreeken, J.: We are not your real parents: Telling causal from confounded by mdl. In: SIAM International Conference on Data Mining (2019)

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Neuroimage 49(3), 2123–2133 (2010)

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Human brain mapping 34(9), 2302–2312 (2013) Quantifying Confounding Bias in Neuroimaging Datasets 9

Mayer, A., Ruhl, D., Merideth, F., Ling, J., Hanlon, F., Bustillo, J., Ca˜ nive, J.: Functional imaging of the hemodynamic sensory gating response in schizophrenia. Human brain mapping 34(9), 2302–2312 (2013) Quantifying Confounding Bias in Neuroimaging Datasets 9

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Frontiers in systems neuroscience 6, 62 (2012)

Milham, M.P., Fair, D., Mennes, M., Mostofsky, S.H., et al.: The adhd-200 con- sortium: a model to advance the translational potential of neuroimaging in clinical neuroscience. Frontiers in systems neuroscience 6, 62 (2012)

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Nooner, K.B., et al.: The nki-rockland sample: a model for accelerating the pace of discovery science in psychiatry. Frontiers in neuroscience 6 (2012)

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NeuroImage 150, 23–49 (2017)

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In: Computer Vision and Pattern Recognition (CVPR)

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Scientiﬁc data 1, 140049 (2014)

Zuo, X.N., Anderson, J.S., Bellec, P., et al.: An open science resource for estab- lishing reliability and reproducibility in functional connectomics. Scientiﬁc data 1, 140049 (2014)

work page 2014