Pith. sign in

REVIEW 3 major objections 4 minor 62 references

Generative Intervention Models for Causal Perturbation Modeling

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read One model learns to map perturbation features to atomic interventions in a causal model, predicting effects of unseen perturbations and identifying their targets.

desk verdict GIMs close a real gap by amortizing the mapping from perturbation features to atomic interventions in a jointly learned causal model, but the fully OOD benchmark is partly circular because the features encode the true mechanisms. read the letter →

arxiv 2411.14003 v2 pith:WKUEKNRO submitted 2024-11-21 cs.LG stat.ML

Nora Schneider , Lars Lorch , Niki Kilbertus , Bernhard Schölkopf , Andreas Krause This is my paper · ORCID
classification cs.LGstat.ML
keywords generativeinterventionmodelcausalperturbationmodelingout-of-distributionpredictiontargetidentificationdiscoverystructuralsingle-cellresponse
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 tries to establish that a causal model can predict the distribution shift caused by a never-seen perturbation, provided the perturbation is described by observable features. The proposed generative intervention model (GIM) learns a map from those features to a distribution over atomic interventions — which variables are targeted and with what parameters — inside a causal model that is itself learned from data. If correct, this gives practitioners both prediction and mechanism: for a new drug, the model outputs a shifted gene-expression distribution and an explanation in terms of the regulatory mechanisms it hits. On synthetic structural causal models and on scRNA-seq drug-perturbation data, the authors report that GIMs match unstructured black-box predictors on out-of-distribution accuracy while recovering intervention targets and causal graphs at least as well as dedicated causal-inference methods.

What carries the argument

The central object is the generative intervention model, defined by equations (4)–(5): a learnable conditional distribution over atomic interventions, p(I;γ,φ) = p(I;gφ(γ)) p(ψ;hφ(I,γ)), where gφ and hφ are neural networks outputting Bernoulli target probabilities and Gaussian intervention parameters. It turns the unobserved atomic intervention into an amortized latent variable: instead of inferring I separately for each observed perturbation, the model learns a shared map from features to interventions and integrates I out when computing the likelihood. This is what lets the same causal model predict p(x|D;γ*) for arbitrary unseen features γ*.

What would settle it

Hold out perturbations whose feature vectors γ are constructed from randomly permuted or heavily PCA-truncated versions of the true intervention targets; if GIM predictions remain above the observational baseline for such uninformative features, the claimed dependence on γ's informativeness is not real.

Watch

Extended reading notes

Core claim

GIMs treat the atomic intervention I (target set and parameters) underlying each perturbation as a latent variable generated from the perturbation features γ by a shared, learned function, and marginalize it out in the likelihood. Concretely, the intervention prior factorizes as p(I;γ,φ) = p(I;gφ(γ)) p(ψ;hφ(I,γ)), and the perturbed density is p(x;M,γ,φ) = ∫ p(x|I;M) p(I;γ,φ) dI. Model M (causal graph and mechanisms) and the generator φ are estimated jointly by MAP, using a continuous relaxation of the graph and Gumbel-sigmoid reparameterization of the discrete targets. The result is that, unlike earlier causal approaches that infer one intervention per training context, a GIM can evaluate any γ, including unseen ones, by sampling its intervention and propagating it through the causal model. The paper's empirical claim is that this yields out-of-distribution predictions on par with the best unstructured baselines while providing mechanistic interpretations that are often more accurate than those of the causal baselines.

Load-bearing premise

The load-bearing premise is that every perturbation's effect can be captured by a sparse atomic intervention on one fixed structural causal model, and that the features describing the perturbation are informative enough for the learned map to generalize to perturbations never seen in training.

Editorial extensions

If this is right

  • For a new drug or dosage never seen in training, GIM produces a full predictive distribution over system variables, because sampling an intervention and propagating it through the causal model generates samples from p(x|D;γ*).
  • The same learned causal model answers mechanistic questions: the inferred intervention targets and parameters indicate which genes or pathways a perturbation acts on, giving interpretability that black-box predictors lack.
  • Multiple perturbations specified by different feature vectors can be combined in silico by generating each atomic intervention and applying them jointly in the causal model, enabling predictions for combination treatments.
  • When the causal model is misspecified, as in the scRNA-seq analysis with a zero-inflated log-normal mechanism, the predictive distribution can still be accurate, suggesting the framework degrades gracefully under model mismatch.
  • Identifiability of unseen perturbations is bounded by the information content of γ: as the paper's PCA analysis shows, predictive accuracy degrades monotonically as γ is made less informative.

Reading between the lines

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

  • A practical consequence the authors leave implicit: GIM's posterior over interventions for a candidate γ makes it a natural component in active experiment design — pick the next perturbation to maximize information about the causal model and its intervention generator, then predict its effect before running it.
  • The atomic-intervention assumption suggests a boundary condition for deployment: perturbations that act by rewiring the graph itself, or by introducing interactions between mechanisms, fall outside the model class; detecting such cases would require a model-selection or residual check on held-out perturbations.
  • The same 'features → latent interventions → distribution' template could transfer to other domains where interventions are described by context variables — policy changes, device failures, environmental interventions — with the caveat that atomicity and feature informativeness must hold.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper proposes generative intervention models (GIMs), a causal perturbation modeling framework that maps observed perturbation features gamma to distributions over atomic interventions I=(I,psi) in a jointly estimated structural causal model. Predictions for unseen perturbations are obtained by marginalizing over the intervention distribution in the causal model (Eqs. 4-6). The authors derive a MAP objective with Monte Carlo gradient estimators, evaluate on synthetic linear/nonlinear SCMs and SciPlex3 scRNA-seq drug perturbation data, and report that GIMs match unstructured baselines on distributional prediction while recovering intervention targets better than other causal inference methods.

Significance. If the central claim holds, the framework fills a real gap: existing causal discovery methods with unknown interventions (BaCaDI, UT-IGSP, GnIES, JCI-PC) cannot make predictions for unseen perturbation features, while unstructured black-box models provide no mechanistic insight. The core modeling contribution is clearly specified: Equations (4)-(6) define a coherent generative process, Appendix B gives explicit gradient derivations, and the experiments on synthetic data use known ground truth, which is a genuine strength. The paper additionally studies the dependence on the information content of gamma in Figure 4 rather than hiding it, and it ships code. However, the central two-part claim is currently supported under favorable evaluation choices: the synthetic perturbation features are constructed by PCA over the true intervention targets and parameters, and the real-data OOD evaluation holds out only dosages of seen drugs, not unseen drugs. These issues are load-bearing for the headline claims about mechanism inference and generalization to novel perturbations.

major comments (3)
  1. [Section 5.1, Appendix D.1] The synthetic perturbation features are created by standardizing and PCA-compressing the concatenation of the true intervention target mask I and intervention parameters psi across training environments (Section 5.1 and Appendix D.1). In the fully OOD setting, the test features are constructed from the very quantities the model is asked to infer. Consequently, the Target-F1 comparisons in Figure 2 and the information-content analysis in Figure 4 largely measure whether g_phi can invert a PCA-compressed code of the true mechanism, rather than whether the model discovers mechanisms from perturbed samples alone. The causal baselines (BaCaDi*, UT-IGSP, GnIES, JCI-PC) never receive gamma, so the comparison is not an equal test of mechanism inference. This does not invalidate the framework under the stated assumption that gamma is informative, but the abstract's claim of 'effectively inferring the underlying perturbation mechanisms, often better than other causal inference methods' is overstated. I recommend either constructing gamma from observable proxies independent of the true I and psi, or restricting the mechanism-inference claim explicitly to the setting where gamma is informative by construction and acknowledging that Target-F1 then includes a decoding component.
  2. [Section 5.1, Figure 5] The only real-data out-of-distribution evaluation holds out the highest dosage (10 uM) of each of the four drugs; all test perturbations share drugs seen in training. The perturbation features include one-hot drug identity and dosage encodings (Appendix D.2), so the model can use drug identity as a strong conditioning signal. This does not demonstrate generalization to unseen drugs, which is the motivating scenario in the introduction ('predicting how cells react to novel molecules'). The abstract's 'unseen perturbation features' should be qualified in the real-data experiments as 'unseen dosages of seen drugs', and the paper should either add a truly held-out drug evaluation or explicitly scope the generalization claim.
  3. [Section 6, Figures 2 and 3] The text states that GIMs 'significantly outperform' the baselines in nonlinear systems (Section 6, Figure 2B) and 'tend to yield better results for fully OOD interventions' (Section 6, Figure 3). The reported boxplots show medians and IQRs over perturbations/contexts, but no repeated-seed variance, confidence intervals, or hypothesis tests are provided. Without these, the word 'significantly' is not supported, and some apparent differences (e.g., GIM versus MLP on fully OOD W2 in Figure 3) may be within noise. Please add repeated-seed error bars and appropriate statistical tests, or soften the significance language.
minor comments (4)
  1. [Section 3.2, Eq. (4)] The notation p(I; gamma, phi) = p(I; g_phi(gamma)) p(psi; h_phi(I, gamma)) uses the same symbol p for distributions over different spaces and conditions psi on I while also treating I as the target set; a brief notational clarification would help readers distinguish the target mask from the full atomic intervention.
  2. [Section 4.2, last paragraph] The sentence 'Identifiability for unseen perturbations depends on the informativeness of the features gamma, which we evaluate empirically Section 6' is missing a preposition ('in Section 6') and should also cite Figure 4 explicitly, as that figure is the direct empirical study of this dependence.
  3. [Section 6, SciPlex3 paragraph] The claim that GIMs achieve robust predictions 'on par with unstructured approaches' is stronger than what Figure 3 shows for in-distribution and partially OOD settings, where the MLP baseline consistently has the lowest Mean Distance; the wording should be adjusted to 'competitive' or the comparison should be qualified.
  4. [Appendix D.4] The initialization statement 'with lambda_0 = 0 and mu_0 = 1-9' appears to contain a typo (presumably 1e-9); please correct the exponent notation.

Circularity Check

1 steps flagged · score 6.0 of 10

Synthetic fully-OOD mechanism inference reduces to decoding PCA features built from the true interventions; the distribution-prediction part is not circular.

  1. self definitional [Section 5.1 (Synthetic data) and Figure 2 (Fully OOD Target-F1), with acknowledgment in Section 6 ('Generalization requires...')]
    "We create the features γ by standardizing the concatenation of I and ψ, applying principal component analysis (PCA) across all training environments of a system, and keeping the top 15 principal components. ... In the fully OOD task, we sample 20 new target and Hill function pairs distinct from the training set and perform perturbations at the training dosages c ∈ {0.5, 1, 1.5, 2}."

    By the paper's own construction, the input features γ are a standardized concatenation of the ground-truth intervention targets I and parameters ψ, projected onto 15 principal components. For the fully-OOD test perturbations, γ* is therefore a lossy linear code of the exact (I*, ψ*) that GIM is claimed to 'infer' in the Target-F1 evaluation. The learned map g_φ: γ → I is trained on data whose input already contains the label in compressed form, so the fully-OOD Target-F1 results in Figure 2 and the information-content analysis in Figure 4 measure how well GIM inverts this PCA encoding, not how well it discovers unknown mechanisms from perturbation responses alone.

full rationale

The mathematical framework itself is not circular: Equations (4)-(5) define a generative model p(x; M, γ, φ) by marginalizing over latent interventions, and the MAP objective in Equation (9) is a self-contained likelihood-based training procedure. The identifiability argument is imported from Brouillard et al. (2020), not from the present authors, and is not a self-citation chain. The self-citations that do appear (DiBS graph representation, BaCaDI baseline, Ormaniec et al. standardization) are methodological and not load-bearing for the central claim. The significant circularity is confined to the synthetic mechanism-inference evaluation: γ is defined as a function of the very I and ψ that the method is then said to infer, so the fully-OOD Target-F1 scores reduce by construction to decoding the PCA-encoded intervention. This does not invalidate the end-to-end distribution predictions, which are evaluated against p(x | G, θ, I, ψ) and are meaningful even when γ is derived from the true mechanism, nor does it affect the real-data dosage-holdout results. However, because the 'effectively inferring the underlying perturbation mechanisms' claim is central to the abstract and is only benchmarked on synthetic data where the features are built from the mechanisms, the partial circularity warrants a score of 6 rather than a lower score. The real-data OOD limitation (holding out only dosages of seen drugs, not whole unseen drugs) is a generalization-scope concern, not a circularity, and should be assessed as correctness risk rather than as additional circularity.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The ledger shows that the central claim rests on domain assumptions about atomicity and feature informativeness rather than on new physical entities. The GIM (gφ, hφ) is a neural-network modeling component, not an invented entity. The main free parameters are sparsity penalties and temperatures tuned on held-out data, plus the PCA dimension of the synthetic features, which is the most consequential design choice for the OOD benchmark. No new particles, forces, mediators, dimensions, or conserved quantities are introduced.

free parameters (7)
  • Intervention target sparsity penalty βI = tuned in {1, 10, 50, 100}
    Controls the L1 penalty on predicted intervention targets; selected per experiment on held-out data (Appendix D.6, Table 1).
  • Graph sparsity penalty βM = tuned in {50, 100, 500}
    Controls the sparsity of the learned causal graph; chosen by held-out KDE-NLL.
  • Gumbel-sigmoid inverse temperature τ = tuned in {0.01, 0.1, 1, 10}
    Temperature of the continuous relaxation for samples of I and G; set by hyperparameter search.
  • Number of PCA components for synthetic features γ = 15
    Determines how much information about the true atomic intervention is present in γ; OOD performance degrades with fewer components (Figure 4), so this choice directly shapes the favorable fully OOD results.
  • Hard-coded dosage mapping for SciPlex3 = 10nM→0.2, 100nM→0.4, 1μM→0.6, 10μM→0.8
    Manual scaling of dosage values into [0,1] used in the perturbation feature vector; arbitrary and affects feature geometry.
  • Intervention parameter noise scale η_h = hyperparameter, not reported numerically
    Standard deviation of the Gaussian over ψ in Eq. (4); fixed by the authors.
  • Monte Carlo sample size M = 128
    Number of MC samples for the graph and intervention distributions; an implementation choice that trades bias against cost.
assumptions (5)
  • domain assumption The system is generated by a fixed acyclic SCM, and every perturbation is a sparse atomic intervention on that SCM.
    Core modeling assumption behind Eq. (2)-(3); if environments differ by changing graphs or non-atomic shifts (e.g., cell-state transitions), the representation p(x;M,γ)=∫p(x|I;M)p(I;γ,ϕ)dI is misspecified.
  • domain assumption Perturbation features γ are informative enough that a learnable function can predict the intervention distribution.
    Explicitly stated in Section 4.2: 'Identifiability for unseen perturbations depends on the informativeness of the features γ.' The fully OOD synthetic test guarantees this by setting γ = PCA(I,ψ); the real-data test only holds out dosages of known drugs.
  • standard math Continuous relaxation optimization (Gumbel-sigmoid, NO-BEARS augmented Lagrangian) finds adequate MAP solutions of the nonconvex objective.
    Relies on prior methods (Maddison et al. 2017, Lee et al. 2019, Zheng et al. 2018); there is no guarantee of reaching a global optimum.
  • domain assumption Identifiability of interventional Markov equivalence classes carries over to the GIM MAP estimate.
    Used in Section 4.2; requires the true interventional equivalence class to intersect the prior support and the regularity conditions of Yang et al. 2018 and Brouillard et al. 2020.
  • domain assumption Zero-inflated log-normal conditional distributions adequately model scRNA-seq gene expression.
    Modeling choice for SciPlex3 (Eq. 15, Appendix D.4); the paper acknowledges model mismatch, and its qualitative evaluation is based on histograms.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Generative Intervention Models for Causal Perturbation Modeling." pith.science (2026). https://pith.science/paper/WKUEKNRO

@misc{pith2026241114003,
  author       = {Pith},
  title        = {Pith review of: Generative Intervention Models for Causal Perturbation Modeling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WKUEKNRO}},
  note         = {Machine review of arXiv:2411.14003}
}
read the original abstract

We consider the problem of predicting perturbation effects via causal models. In many applications, it is a priori unknown which mechanisms of a system are modified by an external perturbation, even though the features of the perturbation are available. For example, in genomics, some properties of a drug may be known, but not their causal effects on the regulatory pathways of cells. We propose a generative intervention model (GIM) that learns to map these perturbation features to distributions over atomic interventions in a jointly-estimated causal model. Contrary to prior approaches, this enables us to predict the distribution shifts of unseen perturbation features while gaining insights about their mechanistic effects in the underlying data-generating process. On synthetic data and scRNA-seq drug perturbation data, GIMs achieve robust out-of-distribution predictions on par with unstructured approaches, while effectively inferring the underlying perturbation mechanisms, often better than other causal inference methods.

Figures

Figures reproduced from arXiv: 2411.14003 by the authors.

Figure 1
Figure 1. Graphical model for the MAP estimation of the causal model M and GIM parameters ϕ. The atomic interventions I are marginalized out during inference. The dataset D consists of K pairs of observed perturbation features γ (k) and data matrices X(k) . For clarity, we depict γ (k) as an observed random variable, but there is no prior over γ, and we treat the perturbation features as a constant throughout. Gray labels ind… view at source ↗
Figure 2
Figure 2. Evaluating the learned causal structure and interventions. A & B: For linear and nonlinear SCMs, SID and Edge-F1 scores of inferred causal graphs (top) and Target-F1 scores (bottom) for in- and out-of-distribution perturbation features γ. GIMs outperform all baselines at inferring the causal structure and intervention targets in nonlinear systems, while also generalizing to OOD perturbation features. C: Example inte… view at source ↗
Figure 3
Figure 3. Benchmarking the predicted distribution shifts on nonlinear Gaussian SCMs. W2 and Mean Distance for SCMs under perturbations with: seen dosages and targets (left, in distribution), novel dosages with seen targets (center, partially OOD), and novel targets with seen dosages (right, fully OOD). Metrics are medians over all perturbations for a given dataset. GIMs demonstrate robust predictive performance, matching the … view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Predictive accuracy (W2) of GIMs relative to infor￾mation contained in γ. Fully OOD perturbations in nonlinear systems with hard atomic interventions. GIMs’ predictive perfor￾mance improves monotonically with the information content in γ. tion on a variable in this sce…
Figure 5
Figure 5. Figure 5: Generalization to heldout drug-dosage combinations on the SciPlex3 scRNA-seq drug perturbation data (Srivatsan et al., 2020). Mean Distance and Pearson Correlation between predicted and true data (left). Examples of true and predicted marginal distributions on the 2 to…
Figure 6
Figure 6. Figure 6: Benchmarking the predicted distribution shifts on Gaussian SCMs with ER graphs and hard interventions. (a) KDE-NLL for SCMs with nonlinear mechanisms. (b) W2, Mean Distance and KDE-NLL for SCMs with linear mechanisms. We show perturbations with training dosages and tar…
Figure 7
Figure 7. Figure 7: Evaluating the learned causal structure, interventions and distribution shifts on Gaussian SCMs with ER graphs and shift interventions. (a) SID and Edge-F1 scores of inferred causal graphs for linear (left) and nonlinear (right) Gaussian SCMs. (b) Target-F1 scores for …
Figure 8
Figure 8. Figure 8: Evaluating the learned causal structure, interventions and distribution shifts on Gaussian SCMs with SF graphs and hard interventions. (a) SID and Edge-F1 scores of inferred causal graphs for linear (left) and nonlinear (right) Gaussian SCMs. (b) Target-F1 scores for i…
Figure 9
Figure 9. Figure 9: Evaluating the learned causal structure, interventions and distribution shifts on Gaussian SCMs with SF graphs and shift interventions. (a) SID and Edge-F1 scores of inferred causal graphs for linear (left) and nonlinear (right) Gaussian SCMs. (b) Target-F1 scores for …
Figure 10
Figure 10. Figure 10: Causal Discovery when Selecting Hyperparameters based on Edge-F1. SID and Edge-F1 scores of the inferred causal graphs for linear (left) and nonlinear (right) Gaussian SCMs with hard, atomic interventions. Boxplots show medians and interquartile ranges (IQR). Whiskers…
Figure 11
Figure 11. Figure 11: Target Identification (Target-F1) of GIMs relative to information contained in γ. Target-F1 scores for in-distribution (left) and fully OOD perturbations (right) in nonlinear systems with hard atomic interventions. Boxplots show medians and interquartile ranges (IQR).…
Figure 12
Figure 12. Figure 12: KDE-NLL for heldout drug-dosage combinations on SciPlex3 scRNA-seq drug perturbation data (Srivatsan et al., 2020). 0 2 CA12 0 2 TFPI2 0 2 HNF1A-AS1 0 2 IGFL2-AS1 0 2 ALDH3A1 0 2 KRT81 0 2 COL26A1 0 2 RBFOX3 0 2 GAPDH 0 2 AKR1B1 0 2 AC010197.1 0 2 CEACAM22P 0 2 ACSL3 …
Figure 13
Figure 13. Figure 13: True and predicted marginal distributions on SciPlex3 data. 50 top-ranked marker genes for the Givinostat perturbation on A549-cells. 25 [PITH_FULL_IMAGE:figures/full_fig_p025_13.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

62 extracted references · 45 canonical work pages

  1. [1]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION format.date year duplicate empty "emp...

  2. [2]

    ABCD - Strategy : Budgeted experimental design for targeted causal structure discovery

    Agrawal, R., Squires, C., Yang, K., Shanmugam, K., and Uhler, C. ABCD - Strategy : Budgeted experimental design for targeted causal structure discovery. In The 22nd International Conference on Artificial Intelligence and Statistics, pp.\ 3400--3409. PMLR, 2019

    work page 2019

  3. [3]

    S., and Kilbertus, N

    Ailer, E., Dern, N., Hartford, J. S., and Kilbertus, N. Targeted sequential indirect experiment design. Advances in Neural Information Processing Systems, 38: 0 122029--122053, 2024

    work page 2024

  4. [4]

    and Albert, R

    Barab \'a si, A.-L. and Albert, R. Emergence of scaling in random networks. Science, 286 0 (5439): 0 509--512, 1999

    work page 1999

  5. [5]

    Differentiable causal discovery from interventional data

    Brouillard, P., Lachapelle, S., Lacoste, A., Lacoste-Julien, S., and Drouin, A. Differentiable causal discovery from interventional data. Advances in Neural Information Processing Systems, 33: 0 21865--21877, 2020

    work page 2020

  6. [6]

    Supervised training of conditional Monge maps

    Bunne, C., Krause, A., and Cuturi, M. Supervised training of conditional Monge maps. Advances in Neural Information Processing Systems, 35: 0 6859--6872, 2022

    work page 2022

  7. [7]

    G., Gut, G., Del Castillo, J

    Bunne, C., Stark, S. G., Gut, G., Del Castillo, J. S., Levesque, M., Lehmann, K.-V., Pelkmans, L., Krause, A., and R \"a tsch, G. Learning single-cell perturbation responses using neural optimal transport. Nature Methods, 20 0 (11): 0 1759--1768, 2023

    work page 2023

  8. [8]

    Chickering, D. M. Optimal structure identification with greedy search. Journal of Machine Learning Research, 3 0 (Nov): 0 507--554, 2002

    2002

Show all 62 references
  1. [9]

    R., and Mitavskiy, B

    Chu, D., Zabet, N. R., and Mitavskiy, B. Models of transcription factor binding: sensitivity of activation functions to model assumptions. Journal of Theoretical Biology, 257 0 (3): 0 419--429, 2009

    2009

  2. [10]

    Scgpt: toward building a foundation model for single-cell multi-omics using generative ai

    Cui, H., Wang, C., Maan, H., Pang, K., Luo, F., Duan, N., and Wang, B. Scgpt: toward building a foundation model for single-cell multi-omics using generative ai. Nature Methods, pp.\ 1--11, 2024

    2024

  3. [11]

    Sinkhorn distances: Lightspeed computation of optimal transport

    Cuturi, M. Sinkhorn distances: Lightspeed computation of optimal transport. Advances in Neural Information Processing Systems, 26, 2013

    2013

  4. [12]

    Optimal transport tools (ott): A jax toolbox for all things wasserstein

    Cuturi, M., Meng-Papaxanthos, L., Tian, Y., Bunne, C., Davis, G., and Teboul, O. Optimal transport tools (ott): A jax toolbox for all things wasserstein. arXiv preprint arXiv:2201.12324, 2022

    2022 arXiv

  5. [13]

    and Sinha, S

    Dibaeinia, P. and Sinha, S. SERGIO : a single-cell expression simulator guided by gene regulatory networks. Cell Systems, 11 0 (3): 0 252--271, 2020

    2020

  6. [14]

    On the number of experiments sufficient and in the worst case necessary to identify all causal relations among n variables

    Eberhardt, F., Glymour, C., and Scheines, R. On the number of experiments sufficient and in the worst case necessary to identify all causal relations among n variables. In Conference on Uncertainty in Artificial Intelligence, 2005

    2005

  7. [15]

    On the evolution of random graphs

    Erd o s, P., R \'e nyi, A., et al. On the evolution of random graphs. Publication of the Mathematical Institute of the Hungarian Academy of Sciences, 5 0 (1): 0 17--60, 1960

    1960

  8. [16]

    L., Taeb, A., Heinze-Deml, C., and B \"u hlmann, P

    Gamella, J. L., Taeb, A., Heinze-Deml, C., and B \"u hlmann, P. Characterization and greedy learning of Gaussian structural causal models under unknown interventions. arXiv preprint arXiv:2211.14897, 2022

    2022 arXiv

  9. [17]

    The Hill equation and the origin of quantitative pharmacology

    Gesztelyi, R., Zsuga, J., Kemeny-Beke, A., Varga, B., Juhasz, B., and Tosaki, A. The Hill equation and the origin of quantitative pharmacology. Archive for History of Exact Sciences, 66: 0 427--438, 2012

    2012

  10. [18]

    and Bengio, Y

    Glorot, X. and Bengio, Y. Understanding the difficulty of training deep feedforward neural networks. In Proceedings of the thirteenth International Conference on Artificial Intelligence and Statistics, pp.\ 249--256. JMLR Workshop and Conference Proceedings, 2010

    2010

  11. [19]

    Combinatorial prediction of therapeutic perturbations using causally-inspired neural networks

    Gonzalez, G., Herath, I., Veselkov, K., Bronstein, M., and Zitnik, M. Combinatorial prediction of therapeutic perturbations using causally-inspired neural networks. bioRxiv, 2024

    2024

  12. [20]

    a gele, A., Rothfuss, J., Lorch, L., Somnath, V. R., Sch \

    H \"a gele, A., Rothfuss, J., Lorch, L., Somnath, V. R., Sch \"o lkopf, B., and Krause, A. BaCaDI : Bayesian causal discovery with unknown interventions. In International Conference on Artificial Intelligence and Statistics, pp.\ 1411--1436. PMLR, 2023

    2023

  13. [21]

    Large-scale foundation model on single-cell transcriptomics

    Hao, M., Gong, J., Zeng, X., Liu, C., Guo, Y., Cheng, X., Wang, T., Ma, J., Zhang, X., and Song, L. Large-scale foundation model on single-cell transcriptomics. Nature Methods, pp.\ 1--11, 2024

    2024

  14. [22]

    and B \"u hlmann, P

    Hauser, A. and B \"u hlmann, P. Characterization and greedy learning of interventional Markov equivalence classes of directed acyclic graphs. Journal of Machine Learning Research, 13 0 (79): 0 2409--2464, 2012

    2012

  15. [23]

    Predicting cellular responses to novel drug perturbations at a single-cell resolution

    Hetzel, L., Boehm, S., Kilbertus, N., G \"u nnemann, S., Theis, F., et al. Predicting cellular responses to novel drug perturbations at a single-cell resolution. Advances in Neural Information Processing Systems, 35: 0 26711--26722, 2022

    2022

  16. [24]

    Ibragimov, I. A. and Has'minskii, R. Z. Statistical Estimation --- Asymptotic Theory. Springer-Verlag, New York, 1981

    1981

  17. [25]

    Categorical reparameterization with gumbel-softmax

    Jang, E., Gu, S., and Poole, B. Categorical reparameterization with gumbel-softmax. In International Conference on Learning Representations, 2017

    2017

  18. [26]

    M., Jindal, K., Solnica-Krezel, L., and Morris, S

    Kamimoto, K., Stringa, B., Hoffmann, C. M., Jindal, K., Solnica-Krezel, L., and Morris, S. A. Dissecting cell identity via network inference and in silico gene perturbation. Nature, 614 0 (7949): 0 742--751, 2023

    2023

  19. [27]

    Kingma, D. P. and Ba, J. Adam: A method for stochastic optimization. In International Conference on Learning Representations, 2015

    2015

  20. [28]

    T., and Dudley, J

    Lee, H.-C., Danieletto, M., Miotto, R., Cherng, S. T., and Dudley, J. T. Scaling structural learning with NO-BEARS to infer causal transcriptome networks. In Pacific Symposium on Biocomputing 2020, pp.\ 391--402. World Scientific, 2019

    2020

  21. [29]

    B., Jordan, M

    Lopez, R., Regier, J., Cole, M. B., Jordan, M. I., and Yosef, N. Deep generative modeling for single-cell transcriptomics. Nature Methods, 15 0 (12): 0 1053--1058, 2018

    2018

  22. [30]

    Large-scale differentiable causal discovery of factor graphs

    Lopez, R., H \"u tter, J.-C., Pritchard, J., and Regev, A. Large-scale differentiable causal discovery of factor graphs. Advances in Neural Information Processing Systems, 35: 0 19290--19303, 2022

    2022

  23. [31]

    DiBS : Differentiable Bayesian structure learning

    Lorch, L., Rothfuss, J., Sch \"o lkopf, B., and Krause, A. DiBS : Differentiable Bayesian structure learning. Advances in Neural Information Processing Systems, 34: 0 24111--24123, 2021

    2021

  24. [32]

    A., and Theis, F

    Lotfollahi, M., Wolf, F. A., and Theis, F. J. scgen predicts single-cell perturbation responses. Nature Methods, 16 0 (8): 0 715--721, 2019

    2019

  25. [33]

    L., Srivatsan, S

    Lotfollahi, M., Klimovskaia Susmelj, A., De Donno, C., Hetzel, L., Ji, Y., Ibarra, I. L., Srivatsan, S. R., Naghipourfar, M., Daza, R. M., Martin, B., et al. Predicting cellular responses to complex perturbations in high-throughput screens. Molecular Systems Biology, 19 0 (6):...

    2023

  26. [34]

    H., Colombo, D., Kalisch, M., and B \"u hlmann, P

    Maathuis, M. H., Colombo, D., Kalisch, M., and B \"u hlmann, P. Predicting causal effects in large-scale systems from observational data. Nature Methods, 7 0 (4): 0 247--248, 2010

    2010

  27. [35]

    The concrete distribution: A continuous relaxation of discrete random variables

    Maddison, C., Mnih, A., and Teh, Y. The concrete distribution: A continuous relaxation of discrete random variables. In Proceedings of the International Conference on Learning Representations, 2017

    2017

  28. [36]

    M., Magliacane, S., and Claassen, T

    Mooij, J. M., Magliacane, S., and Claassen, T. Joint causal inference from multiple contexts. The Journal of Machine Learning Research, 21 0 (1): 0 3919--4026, 2020

    2020

  29. [37]

    Standardizing structural causal models

    Ormaniec, W., Sussex, S., Lorch, L., Sch \"o lkopf, B., and Krause, A. Standardizing structural causal models. In The Thirteenth International Conference on Learning Representations, 2025

    2025

  30. [38]

    Learning independent causal mechanisms

    Parascandolo, G., Kilbertus, N., Rojas-Carulla, M., and Sch \"o lkopf, B. Learning independent causal mechanisms. In International Conference on Machine Learning, pp.\ 4036--4044. PMLR, 2018

    2018

  31. [39]

    Causality

    Pearl, J. Causality. Cambridge university press, 2009

    2009

  32. [40]

    Mechanistic neural networks for scientific machine learning

    Pervez, A., Locatello, F., and Gavves, S. Mechanistic neural networks for scientific machine learning. In Salakhutdinov, R., Kolter, Z., Heller, K., Weller, A., Oliver, N., Scarlett, J., and Berkenkamp, F. (eds.), Proceedings of the 41st International Conference on Machine Lea...

    2024

  33. [41]

    and B \"u hlmann, P

    Peters, J. and B \"u hlmann, P. Structural intervention distance for evaluating causal graphs. Neural Computation, 27 0 (3): 0 771--799, 2015

    2015

  34. [42]

    Elements of causal inference: foundations and learning algorithms

    Peters, J., Janzing, D., and Sch \"o lkopf, B. Elements of causal inference: foundations and learning algorithms. The MIT Press, 2017

    2017

  35. [43]

    Beware of the simulated DAG ! Causal discovery benchmarks may be easy to game

    Reisach, A., Seiler, C., and Weichwald, S. Beware of the simulated DAG ! Causal discovery benchmarks may be easy to game. Advances in Neural Information Processing Systems, 34: 0 27772--27784, 2021

    2021

  36. [44]

    Predicting transcriptional outcomes of novel multigene perturbations with GEARS

    Roohani, Y., Huang, K., and Leskovec, J. Predicting transcriptional outcomes of novel multigene perturbations with GEARS . Nature Biotechnology, 42 0 (6): 0 927--935, 2024

    2024

  37. [45]

    BACKSHIFT : Learning causal cyclic graphs from unknown shift interventions

    Rothenh \"a usler, D., Heinze, C., Peters, J., and Meinshausen, N. BACKSHIFT : Learning causal cyclic graphs from unknown shift interventions. Advances in Neural Information Processing Systems, 28, 2015

    2015

  38. [46]

    Sadybekov, A. V. and Katritch, V. Computational approaches streamlining drug discovery. Nature, 616 0 (7958): 0 673--685, 2023

    2023

  39. [47]

    Causality for Machine Learning, pp.\ 765–804

    Sch\" o lkopf, B. Causality for Machine Learning, pp.\ 765–804. Association for Computing Machinery, New York, NY, USA, 1 edition, 2022. ISBN 9781450395861

    2022

  40. [48]

    R., Kalchbrenner, N., Goyal, A., and Bengio, Y

    Sch \"o lkopf, B., Locatello, F., Bauer, S., Ke, N. R., Kalchbrenner, N., Goyal, A., and Bengio, Y. Toward causal representation learning. Proceedings of the IEEE, 109 0 (5): 0 612--634, 2021

    2021

  41. [49]

    Scott, D. W. Multivariate density estimation: theory, practice, and visualization. John Wiley & Sons, 2015

    2015

  42. [50]

    Causation, prediction, and search

    Spirtes, P., Glymour, C., and Scheines, R. Causation, prediction, and search. MIT press, 2000

    2000

  43. [51]

    Permutation-based causal structure learning with unknown intervention targets

    Squires, C., Wang, Y., and Uhler, C. Permutation-based causal structure learning with unknown intervention targets. In Peters, J. and Sontag, D. (eds.), Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), volume 124 of Proceedings of Machine Lea...

    2020

  44. [52]

    R., McFaline-Figueroa, J

    Srivatsan, S. R., McFaline-Figueroa, J. L., Ramani, V., Saunders, L., Cao, J., Packer, J., Pliner, H. A., Jackson, D. L., Daza, R. M., Christiansen, L., et al. Massively multiplex chemical transcriptomics at single-cell resolution. Science, 367 0 (6473): 0 45--51, 2020

    2020

  45. [53]

    Tejada-Lapuerta, A., Bertin, P., Bauer, S., Aliee, H., Bengio, Y., and Theis, F. J. Causal machine learning for single-cell genomics. Nature Genetics, pp.\ 1--12, 2025

    2025

  46. [54]

    Active Bayesian causal inference

    Toth, C., Lorch, L., Knoll, C., Krause, A., Pernkopf, F., Peharz, R., and Von K \"u gelgen, J. Active Bayesian causal inference. Advances in Neural Information Processing Systems, 35: 0 16261--16275, 2022

    2022

  47. [55]

    J., Camgoz, N

    Vowels, M. J., Camgoz, N. C., and Bowden, R. D’ya like DAG s? A survey on structure learning and causal discovery. ACM Computing Surveys, 55 0 (4): 0 1--36, 2022

    2022

  48. [56]

    Permutation-based causal inference algorithms with interventions

    Wang, Y., Solus, L., Yang, K., and Uhler, C. Permutation-based causal inference algorithms with interventions. Advances in Neural Information Processing Systems, 30, 2017

    2017

  49. [57]

    Characterizing and learning equivalence classes of causal DAG s under interventions

    Yang, K., Katcoff, A., and Uhler, C. Characterizing and learning equivalence classes of causal DAG s under interventions. In International Conference on Machine Learning, pp.\ 5541--5550. PMLR, 2018

    2018

  50. [58]

    and Welch, J

    Yu, H. and Welch, J. D. Perturbnet predicts single-cell responses to unseen chemical and genetic perturbations. BioRxiv, pp.\ 2022--07, 2022

    2022

  51. [59]

    K., and Xing, E

    Zheng, X., Aragam, B., Ravikumar, P. K., and Xing, E. P. DAG s with NO TEARS : Continuous optimization for structure learning. Advances in Neural Information Processing Systems, 31, 2018

    2018

  52. [60]

    @esa (Ref

    \@ifxundefined[1] #1\@undefined \@firstoftwo \@secondoftwo \@ifnum[1] #1 \@firstoftwo \@secondoftwo \@ifx[1] #1 \@firstoftwo \@secondoftwo [2] @ #1 \@temptokena #2 #1 @ \@temptokena \@ifclassloaded agu2001 natbib The agu2001 class already includes natbib coding, so you should ...

  53. [61]

    \@lbibitem[] @bibitem@first@sw\@secondoftwo \@lbibitem[#1]#2 \@extra@b@citeb \@ifundefined br@#2\@extra@b@citeb \@namedef br@#2 \@nameuse br@#2\@extra@b@citeb \@ifundefined b@#2\@extra@b@citeb @num @parse #2 @tmp #1 NAT@b@open@#2 NAT@b@shut@#2 \@ifnum @merge>\@ne @bibitem@firs...

  54. [62]

    @open @close @open @close and [1] URL: #1 \@ifundefined chapter * \@mkboth \@ifxundefined @sectionbib * \@mkboth * \@mkboth\@gobbletwo \@ifclassloaded amsart * \@ifclassloaded amsbook * \@ifxundefined @heading @heading NAT@ctr thebibliography [1] @ \@biblabel @NAT@ctr \@bibset...

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.