Counterfactual Explanations in Medical Imaging: Exploring SPN-Guided Latent Space Manipulation

Julia Siekiera; Stefan Kramer

REVIEW 3 major objections 6 minor 30 references

Counterfactual Explanations in Medical Imaging: Exploring SPN-Guided Latent Space Manipulation

T0 review · 3 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read A sum-product network in the VAE latent space keeps chest X-ray counterfactuals valid when regularization is weak.

desk verdict New SPN-in-VAE combination for chest X-ray counterfactuals, but the robustness claim rests on a self-referential validity metric that tracks classifier entropy more than counterfactual quality. read the letter →

arxiv 2507.19368 v1 pith:VRIXD5AP submitted 2025-07-25 cs.LG cs.AI

Julia Siekiera , Stefan Kramer This is my paper · ORCID

classification cs.LGcs.AI

keywords counterfactualexplanationssum-productnetworksvariationalautoencoderlatentspacemanipulationchestX-rayclassificationexplainableAIKLDregularization

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

This paper tries to make counterfactual explanations for a chest X-ray classifier more reliable by describing the VAE's latent space with a sum-product network (SPN). The SPN doubles as the density model of the latent codes and as the classifier, so the search for a counterfactual code can maximize the target-class probability while discouraging large or unlikely moves. On a balanced cardiomegaly-versus-no-finding task, the authors report that when the latent-space regularization is weak, SPN-guided edits flip the prediction in 43-89% of test cases, whereas an MLP baseline flips only 3-9%. The practical interest is that weakly regularized VAEs reconstruct images more faithfully, and the SPN appears to preserve counterfactual validity exactly in the regime where the standard neural classifier fails.

What carries the argument

The central mechanism is a class-conditional Gaussian sum-product network: a rooted directed acyclic graph whose leaves are univariate Gaussian densities and whose internal nodes are weighted sums and products, learned from latent codes by a recursive structure-learning algorithm. Because the network is complete and decomposable, it gives exact, tractable values of $p_{\mathrm{SPN}}(z)$ and $p_{\mathrm{SPN}}(y|z)$, so one model supplies the classifier term, the density term, and the class-conditioned likelihood used in the latent-space objective. The learned network is converted into a differentiable neural-network form so that the counterfactual code $z_{\mathrm{cf}}$ can be optimized by gradient descent and then decoded into an image.

What would settle it

Recompute validity with a single fixed referee classifier, such as the original MLP or a third independently trained model, labeling both SPN-generated and MLP-generated counterfactuals; if the SPN's validity advantage disappears or reverses, the robustness claim fails. A supporting check is to temperature-scale both classifiers to matching entropy and see whether the validity gap vanishes.

Watch

Extended reading notes

Core claim

The authors claim that a structure-learned sum-product network placed over the latent space of a semi-supervised VAE (a VAE trained so its latent codes also predict the class) can serve as both the latent-space density descriptor and the classifier for counterfactual generation. Starting from a sampled latent code $z$ for an image, they search for $z_{\mathrm{cf}}$ by gradient descent to maximize $\log p_{\mathrm{SPN}}(y_{\mathrm{cf}}|z')$, with optional penalties $\beta\|z'-z\|^2$ and $\gamma|\log p_{\mathrm{SPN}}(z')-\log p_{\mathrm{SPN}}(z)|$, then decode $z_{\mathrm{cf}}$ into a counterfactual image. Their empirical claim is that this SPN-guided manipulation maintains validity, the fraction of counterfactuals whose predicted class changes, under weak Kullback-Leibler divergence (KLD) regularization ($\beta_1$ from 0.01 down to 0.0001), while the MLP baseline's validity collapses to near zero. The auxiliary $\beta$ and $\gamma$ weights have little effect, and the visualized counterfactual changes concentrate around the heart region.

Load-bearing premise

The load-bearing premise is that validity measured by each method's own classifier is a fair comparison; if the SPN merely has less confidence in its predictions, its higher flip rate would not mean better counterfactuals.

Editorial extensions

If this is right

If the SPN robustness holds, weakly regularized VAEs, which reconstruct finer image detail, can still support counterfactual explanation without losing the ability to flip predictions.
The small effect of $\beta$ and $\gamma$ implies that the target-class probability term, not the proximity or likelihood penalties, is the main driver of the optimized latent shift.
Absolute $\ell^2$ and FID scores track reconstruction quality more than counterfactual quality, so comparisons across VAE regularizations need relative or class-conditioned versions of these metrics.
SPN-guided explanations localize changes around the heart across regularization settings, while MLP-guided explanations do so only under strong regularization, which matters if explanations are meant to point clinicians to disease-relevant regions.

Reading between the lines

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

Editorial: the validity comparison is not controlled for classifier confidence; the SPN's higher predictive entropy at low $\beta_1$ means its flip rate may reflect softer decisions, so a fixed referee classifier should be used before concluding the SPN produces better counterfactuals.
Editorial: because the $\beta$ and $\gamma$ penalties barely changed outcomes, a natural next step is to use the SPN log-likelihood itself as the distance penalty, replacing the Euclidean term with a distribution-aware measure.
Editorial: the result suggests a cheap diagnostic for any latent-space counterfactual method: report predictive entropy alongside validity, since confident classifiers can make otherwise identical edits look invalid.
Editorial: transferring the approach to other pathologies or multiclass labels would require class-specific FID and $\ell^2$ metrics, because absolute reconstruction metrics are dominated by VAE quality.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Worth a look if you work at the SPN/XAI intersection. The paper's new bit is a genuine combination: train a semi-supervised VAE on chest X-rays, replace the latent classifier with a structure-learned SPN, then use the SPN as both density model and classifier to guide latent-space counterfactuals. The method is clearly described, the code is linked, and the authors are upfront about limitations.

The headline robustness claim, however, is not yet supported. Table 3 shows SPN validity holding at 0.43–0.89 under weak VAE regularization while the MLP falls to 0.03–0.09. But validity (Eq. 3) uses the same classifier that generated the counterfactual: for SPN counterfactuals, f is the SPN; for MLP counterfactuals, f is the MLP. Since the objective (Eq. 2) maximizes log p(y_cf|z') with that same f, the metric mostly tells you how often each method crosses its own decision boundary. Table 2 shows the SPN has much higher predictive entropy in exactly the weak-regularization regimes where the gap appears (0.756–2.233 vs 0.359–0.365 for beta_1 = 0.01, 0.001, 0.0001). A softer boundary flips more easily. The authors even note this mechanism in Section 4.4 ('the MLP's low entropy... is more challenging to modify') but do not control for it. So the claim that the SPN demonstrates 'larger robustness' is not a stable statement about counterfactual quality yet.

This is fixable and not fatal. Use a fixed external classifier to define validity, or match entropy/confidence between the two models. Error bars would help; their absence is secondary. A comparison with an existing counterfactual method (latent shift, GDVAE) would strengthen the empirical case, though this is a workshop paper and the authors already do a careful ablation of beta and gamma.

The paper deserves a serious referee because the combination is new and the evaluation can be repaired. As it stands, I would not accept it without a reworked validity analysis. Who gets value: the SPN community and anyone building probabilistic latent-space XAI for medical images.

Send it to review, but expect heavy revision.

Referee Report

3 major / 6 minor

Summary. The paper proposes a counterfactual explanation pipeline for medical images in which a sum-product network (SPN) is trained on the latent space of a semi-supervised VAE and then used both as a class-posterior model and as a likelihood descriptor for latent-space counterfactual search. After VAE training, the MLP classifier is replaced by a structure-learned Gaussian SPN, and counterfactual latent codes are obtained by maximizing the SPN's target-class log-posterior while penalizing squared distance and log-likelihood deviation (Eq. 2). Experiments on a balanced binary CheXpert subset (cardiomegaly vs. no finding) compare the SPN with the MLP baseline under four KLD strengths beta_1 and with different combinations of beta and gamma. The headline result is that under weak regularization the MLP validity drops to 0.03-0.09 while the SPN remains at 0.43-0.89, which the paper interprets as greater robustness of SPN-guided manipulation; the paper also reports L2 proximity, FID plausibility, and alteration visualizations.

Significance. The proposed integration of tractable SPN inference with VAE latent space manipulation is a sensible and potentially useful direction for probabilistic counterfactual explanations, and the released code and detailed experimental setup are assets. If the robustness claim were established, the paper would provide a practical demonstration that probabilistic classifiers can support counterfactual search under weak latent regularization. However, the current evidence does not establish the claimed cross-method advantage, because the validity metric is evaluated with the same classifier that generates the counterfactual and the comparison is not controlled for classifier confidence; the absence of uncertainty estimates further weakens the empirical claims.

major comments (3)

[Section 4.4, Eq. (3); Tables 2-3] The central robustness claim is confounded by the self-referential validity measure. In Eq. (3), f is the SPN for SPN counterfactuals and the MLP for MLP counterfactuals, and Eq. (2) maximizes log p(y_cf|z') under the same f. Validity therefore measures how often each method's own optimization pushes latent codes across its own decision boundary, not an independent property of the generated counterfactuals. Table 2 shows that in the weak-regularization regimes where the validity gap appears, the SPN has much higher predictive entropy than the MLP (0.756-2.233 vs. 0.359-0.365), and Section 4.4 explicitly attributes the MLP's difficulty to 'the MLP's low entropy... more challenging to modify'. Hence the higher SPN validity may reflect a softer, less confident classifier rather than better counterfactuals. To support the claim that SPN-guided manipulation is more robust, the authors should evaluate both sets of counterfactuals with a fixed independent classifier, and/or report validity under each classifier in both directions, and/or control for predictive entropy or calibration. This is the main load-bearing issue for the paper's headline conclusion.
[Section 4.2, Eq. (4)] The FID formula is not the standard Frechet Inception Distance. The correct expression is ||mu_org - mu_cf||^2 + Tr(Sigma_org + Sigma_cf - 2(Sigma_org Sigma_cf)^{1/2}); the manuscript writes the cross-term as -2Tr(Sigma_org Sigma_cf), which is the trace of a matrix product and not a valid distance statistic. The reported FID values should be recomputed with the correct formula before they are used to support any claims about plausibility.
[Section 4.1, Table 3] All counterfactual statistics are reported as means over the three cross-validation splits without standard deviations, confidence intervals, or significance tests. For the paper's central comparison, the reader cannot tell whether gaps such as 0.55 vs. 0.09 are stable across splits or driven by a single fold; please report per-split results and appropriate uncertainty measures, and test the validity differences when the confound in the first comment is addressed.

minor comments (6)

[Section 4.3] The text says 'Only for beta_1 = 0.1, the SPN achieves an improvement... However, for smaller beta_1 = 0.1, the MLP outperforms the SPN.' The phrase 'smaller beta_1 = 0.1' should be corrected to 'beta_1 < 0.1' or 'smaller values of beta_1.'
[Section 4.1, Table 3] The text states that the MLP baseline is run with gamma in {0,1}, but Table 3 lists MLP only for gamma = 0.0; please specify which configurations were actually run and why gamma = 1.0 is omitted for the MLP.
[Section 4.3] The text mentions 'for both datasets,' but the experiments use only the CheXpert dataset; please remove or correct this phrase.
[Section 4.2, Eq. (3)] The validity indicator 1[f(x) != f(x_cf)] counts any prediction change, not necessarily a flip to the targeted counterfactual class y_cf; please use 1[f(x_cf) = y_cf] or report both quantities.
[Section 4.2, Table 3] The 'switch epoch' metric is reported in Table 3 but is not defined in the metrics section; please define how it is computed.
[Table 2] The reported entropy values exceed 1.0 for binary classification, which suggests a particular logarithm base or averaging convention; please specify the base and clarify whether this is per-class averaged entropy.

Circularity Check

1 steps flagged · score 4.0 of 10

SPN validity is self-referential: the same fitted SPN is both the optimization target (Eq. 2) and the evaluation function (Eq. 3), so the headline robustness gap largely reflects classifier softness; independent content remains in FID/L2 and the raw MLP comparison.

self definitional [Section 3.3 Eq. (2), Section 4.2 Eq. (3), Table 3, Section 4.4]
"z_{cf} = arg max_{z'} log(p(y_{cf}|z')) − β||z'−z||^2 − γ|log(p(z'))−log(p(z))| (2) ... Validity = 1/|X| ∑_{x∈X} 1[f(x)≠f(x_{cf})] (3) ... under weaker regularization, validity significantly declines for the MLP (0.09-0.03), while the SPN retains moderate validity (0.43-0.89)."

Eq. (2)'s first term maximizes the fitted SPN posterior p_spn(y_cf|z'), and Eq. (3)'s validity for SPN rows is the flip rate of that same SPN (f=SPN). Thus SPN validity measures only whether the optimizer pushed the SPN's own posterior over threshold, not objective counterfactual quality. The MLP rows use f=MLP, so the Table 3 gap (0.43–0.89 vs 0.03–0.09) compares the ease of flipping two different decision surfaces; Table 2 shows SPN entropy (0.756–2.233) far above MLP (0.359–0.365) in those regimes. The paper concedes the mechanism: 'the MLP's low entropy ... is more challenging to modify in the latent space.' Hence the headline robustness conclusion is self-referential: the SPN is both generator and judge.

full rationale

The paper's central empirical claim—that SPN-guided counterfactuals retain moderate validity under weak VAE regularization while the MLP baseline collapses—is partially circular because the validity metric (Eq. 3) uses the very classifier that the counterfactual objective (Eq. 2) optimizes. For SPN counterfactuals, f in Eq. 3 is the SPN, and Eq. 2 maximizes the SPN's own class posterior; the reported validity therefore tracks how easily the SPN's soft decision boundary is crossed, not an independent measure of counterfactual quality. This is confirmed by Table 2, where the SPN has substantially higher entropy than the MLP in the weak-regularization regimes where the validity gap appears, and by the paper's own admission in Section 4.4 that the MLP's low entropy is more challenging to modify. However, this is not a full circularity: the comparison with the MLP is an independent empirical observation, the FID and L2 metrics use the external Inception V3 feature extractor and input-space distances, and no self-citation or imported uniqueness theorem is load-bearing. The core methodology (SPN as latent descriptor and classifier) has content beyond the metric definition, but the headline robustness conclusion is weakened by the self-referential validity evaluation.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The method relies on standard VAE and SPN machinery, plus several domain assumptions about the latent space and evaluation metrics. The free parameters listed above are the numbers chosen by hand that the central empirical results depend on; notably, three of them (beta_0, beta_2, R) are unreported. No new physical or theoretical entities are introduced.

free parameters (5)

beta_1 (KLD regularization weight) = {0.1, 0.01, 0.001, 0.0001}
Central trade-off axis in Eq. 1; all results are stratified by this value and the paper's main conclusions depend on the comparison across these settings.
beta and gamma (counterfactual objective weights) = {0, 1}
Weights in Eq. 2 controlling minimality and plausibility; swept over a small grid, and the paper observes their impact is 'unexpectedly small'.
beta_0 and beta_2 (reconstruction and classification weights) = not reported
The VAE loss in Eq. 1 requires three weights, but only beta_1 is reported. This leaves the trained model incompletely specified.
Latent dimension = 62
Architecture choice for the VAE latent space; no sensitivity analysis or justification is given.
R (number of replicate samples) = not reported
Algorithm 1 samples z from the encoder R times and averages decoded counterfactuals, but the value of R is never given, affecting the exact counterfactual outputs.

assumptions (6)

standard math The VAE ELBO with reparameterization provides a valid training objective for the latent space (Section 3.1).
Standard VAE theory; the paper relies on this to produce the latent representation and the semi-supervised extension.
standard math SPN completeness and decomposability ensure exact and tractable probabilistic inference (Section 3.2).
Cited from Poon and Domingos; the paper depends on this property to use the SPN likelihood in the optimization objective.
domain assumption LearnSPN learns a structure that accurately models the VAE latent distribution from finite samples (Section 3.2).
The SPN structure is learned from the training latents; if the learned structure is a poor approximation, the likelihood term in Eq. 2 is not meaningful.
domain assumption The latent space of the VAE is smooth enough that gradient ascent on p(y_cf|z) yields images that are plausible and recognizable (Section 3.3).
This is an implicit assumption of all latent-space counterfactual methods; the paper does not probe it beyond reporting FID and visual examples.
domain assumption FID computed with Inception V3 embeddings is a valid measure of counterfactual plausibility (Section 4.2).
The paper uses FID between original and counterfactual sets, but acknowledges that this metric is influenced by reconstruction quality rather than counterfactual-specific properties.
domain assumption CheXpert labels for cardiomegaly and no finding are treated as ground truth (Section 4.1).
The binary task is defined by these labels; label noise in CheXpert is known, though not discussed in the paper.

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Cite this review

Pith. "Pith review of Counterfactual Explanations in Medical Imaging: Exploring SPN-Guided Latent Space Manipulation." pith.science (2026). https://pith.science/paper/VRIXD5AP

@misc{pith2026250719368,
  author       = {Pith},
  title        = {Pith review of: Counterfactual Explanations in Medical Imaging: Exploring SPN-Guided Latent Space Manipulation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VRIXD5AP}},
  note         = {Machine review of arXiv:2507.19368}
}

read the original abstract

Artificial intelligence is increasingly leveraged across various domains to automate decision-making processes that significantly impact human lives. In medical image analysis, deep learning models have demonstrated remarkable performance. However, their inherent complexity makes them black box systems, raising concerns about reliability and interpretability. Counterfactual explanations provide comprehensible insights into decision processes by presenting hypothetical "what-if" scenarios that alter model classifications. By examining input alterations, counterfactual explanations provide patterns that influence the decision-making process. Despite their potential, generating plausible counterfactuals that adhere to similarity constraints providing human-interpretable explanations remains a challenge. In this paper, we investigate this challenge by a model-specific optimization approach. While deep generative models such as variational autoencoders (VAEs) exhibit significant generative power, probabilistic models like sum-product networks (SPNs) efficiently represent complex joint probability distributions. By modeling the likelihood of a semi-supervised VAE's latent space with an SPN, we leverage its dual role as both a latent space descriptor and a classifier for a given discrimination task. This formulation enables the optimization of latent space counterfactuals that are both close to the original data distribution and aligned with the target class distribution. We conduct experimental evaluation on the cheXpert dataset. To evaluate the effectiveness of the integration of SPNs, our SPN-guided latent space manipulation is compared against a neural network baseline. Additionally, the trade-off between latent variable regularization and counterfactual quality is analyzed.

Figures

Figures reproduced from arXiv: 2507.19368 by the authors.

**Figure 2.** Model architecture for SPN-guided counter [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Example visualization of input alterations in the generated counterfactuals for the different VAE regular [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

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Matan Atad, Vitalii Dmytrenko, Yitong Li, Xinyue Zhang, Matthias Keicher, Jan Kirschke, Bene Wiestler, Ashkan Khakzar, and Nassir Navab. 2022. CheXplaining in Style: Counterfactual Explanations for Chest X-rays using StyleGAN. arXiv:2207.07553 [eess.IV] https: //arxiv.org/abs/2207.07553

arXiv 2022

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Butz, Jhonatan S

Cory J. Butz, Jhonatan S. Oliveira, André E. dos Santos, and André L. Teixeira. 2019. Deep Convolutional Sum-Product Networks. Proceed- ings of the AAAI Conference on Artificial Intelligence 33, 01 (Jul. 2019), Counterfactual Explanations in Medical Imaging BIOKDD 2025, August 03, 2025, Toronto, Canada 3248–3255. doi:10.1609/aaai.v33i01.33013248

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Lungren, and Akshay Chaudhari

Joseph Paul Cohen, Rupert Brooks, Sovann En, Evan Zucker, Anuj Pa- reek, Matthew P. Lungren, and Akshay Chaudhari. 2021. Gifsplanation via Latent Shift: A Simple Autoencoder Approach to Counterfactual Generation for Chest X-rays. InProceedings of the Fourth Conference on Medical Imaging with Deep Learning (Proceedings of Machine Learning Research, Vol. 14...

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