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Conditional Diffusion Models Based Conditional Independence Testing

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Conditional diffusion models can supply the unknown X given Z distribution that conditional randomization tests need, giving asymptotic type I error control.

desk verdict A useful empirical CRT variant with a real, fixable gap between the stated type I error guarantee and the discretized sampler actually implemented. read the letter →

arxiv 2412.11744 v2 pith:K62GXDHI submitted 2024-12-16 stat.ML cs.LG

Yanfeng Yang , Shuai Li , Yingjie Zhang , Zhuoran Sun , Hai Shu , Ziqi Chen , Renming Zhang This is my paper · ORCID
classification stat.MLcs.LG MSC 62G1062H1562G20
keywords conditionalindependencetestingrandomizationtestdiffusionmodelsscore-basedgenerativemutualinformationtypeIerrorcontrolhigh-dimensionalmixeddatamodelapproximation
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 proposes CDCIT, a conditional independence test for $X \perp\!\!\!\perp Y \mid Z$ that does not require the conditional distribution of $X$ given $Z$ to be known. A conditional diffusion model trained on unlabeled data produces pseudo-copies of $X$, and a classifier-based conditional mutual information estimate provides the test statistic. The central claim is that the generated distribution converges to the true conditional distribution in total variation at a polynomial rate, which makes the conditional randomization test p-value satisfy $P(p \le \alpha \mid H_0) \le \alpha + o(1)$ under mild smoothness assumptions. If correct, the test controls type I error asymptotically in high-dimensional settings with mixed continuous and discrete conditioning variables, and it does so without assuming a specific distributional form or dependency structure.

What carries the argument

The load-bearing machinery is the score-based conditional diffusion model: an Ornstein-Uhlenbeck forward process corrupts $X$ into noise, a ReLU neural network is trained by conditional score matching to approximate $\nabla \log p_t(x|z)$, and a reverse stochastic differential equation started at $N(0, I)$ generates pseudo-samples from $\hat{P}(\cdot|Z)$. What carries the statistical argument is the total-variation guarantee of Theorem 1, the product-space inequality $d_{\mathrm{TV}}(p^{(n)}(\cdot|Z), \hat{p}^{(n)}(\cdot|Z)) \le n\, d_{\mathrm{TV}}(p(\cdot|Z), \hat{p}(\cdot|Z))$, and the exchangeability of the null triples in the CRT p-value. The test statistic is the classifier-based conditional mutual information estimator, which estimates the likelihood ratio $p(x,y,z)/(p(x,z)p(y|z))$ from a binary classifier's predicted probabilities, with 1-nearest-neighbor resampling used to build the negative samples.

What would settle it

Under a null model with known Gaussian $X|Z$ satisfying the paper's smoothness assumptions, run Algorithm 3 with large $N$ and $n$ chosen so the corollary's rate applies, and record the rejection frequency at $\alpha=0.05$; if the empirical type I error stays above $\alpha$ by a nonvanishing amount when the number of diffusion steps $K$ is fixed, the discretization gap is a genuine break in the argument.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is a transfer theorem for conditional randomization tests: when the true conditional law $P(\cdot|Z)$ is replaced by an estimated law $\hat{P}(\cdot|Z)$, the excess type I error is no larger than the total-variation distance between the product laws. Theorem 2 states $P(p \le \alpha \mid Y,Z) \le \alpha + d_{\mathrm{TV}}(p^{(n)}(\cdot|Z), \hat{p}^{(n)}(\cdot|Z))$, and Theorem 1 gives the sampler a rate $O(N^{-\Gamma_1(k,\alpha)}(\log N)^{\Gamma_2(k,\alpha)})$ for that distance. Corollary 1 then concludes that the p-value from Algorithm 3 controls type I error at level $\alpha$ asymptotically whenever $n \cdot N^{-\Gamma_1(k,\alpha)}(\log N)^{\Gamma_2(k,\alpha)} \to 0$.

Load-bearing premise

The whole validity argument rests on the assumption that the finite-step discretized sampler used in Algorithm 2 inherits the total-variation convergence proven for the continuous-time reverse diffusion process, so the generated pseudo-samples really are close to $P(X|Z)$.

Editorial extensions

If this is right

  • CDCIT removes the main practical obstacle to conditional randomization tests: the conditional distribution $X|Z$ no longer has to be known, because the diffusion sampler supplies the pseudo-copies.
  • The test controls type I error asymptotically even when $Z$ is high-dimensional and mixes continuous and discrete variables, provided the smoothness and sub-Gaussian assumptions hold.
  • Because the diffusion model is trained only on unlabeled pairs $(X,Z)$, the method can exploit large unlabeled databases and keep the labeled sample size $n$ small relative to $N$.
  • The excess type I error is controlled by the total-variation rate of the sampler, so improving the diffusion approximation directly tightens the validity guarantee.
  • The classifier-based CMI statistic makes power available under complex, nonparametric dependence structures between $X$ and $Y$ given $Z$.

Reading between the lines

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

  • The proof chain is sampler-agnostic: any generative model with a total-variation guarantee could be substituted for the diffusion model in the CRT validity argument, so the contribution is a template as well as a specific test.
  • A concrete open gap is the Euler-Maruyama discretization in Algorithm 2: the stated TV rate is proven for the continuous-time reverse process, and the implemented finite-step sampler would need a matching discretization bound to close the argument.
  • In finite samples, experiments show that a small unlabeled sample $N$ inflates type I error, so the rate in Corollary 1 is not merely a formality; it predicts when the test becomes usable.
  • In constraint-based causal discovery, a high-dimensional mixed-data CI test with valid error rates could serve as the oracle in algorithms that build graphs from conditional independence decisions.
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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 CDCIT, a conditional randomization test in which the conditional distribution X|Z is learned with a score-based conditional diffusion model trained on unlabeled data. Pseudo-replicates of X are generated from the learned conditional distribution by a K-step Euler-Maruyama discretization of the reverse SDE, the test statistic is a classifier-based conditional mutual information estimator, and the p-value is computed by the CRT formula. The main theoretical claims are Theorem 1, a total-variation bound between the true and generated conditional distributions; Theorem 2, an excess type I error bound in terms of that total-variation distance; and Corollary 1, stating asymptotic type I error control for Algorithm 3. The paper also reports quantile-based comparisons of generated samples, synthetic experiments against seven baselines, and two real-data studies.

Significance. If the stated guarantees hold, this is a practically valuable combination: conditional diffusion models provide a more stable and higher-quality sampler for the CRT than the GAN-based and nearest-neighbor alternatives, and the classifier-based CMI statistic is well suited to high-dimensional and mixed-type conditioning sets. Theorem 2's exchangeability argument is clean, the empirical comparison is broad and includes public code, and the computational cost is reported. The main caveat is that the headline asymptotic guarantee is currently a theorem about a continuous-time process rather than the implemented Euler-Maruyama sampler, and the mixed-type setting is outside the stated assumptions; these gaps affect the central claim as stated.

major comments (3)
  1. [Theorem 1 and Algorithm 2] Theorem 1 is stated for the density bp(·|Z) of bX sampled from Algorithm 2, but the proof in Supplementary S2 bounds the continuous-time reverse SDE in Eq. (3), not the K-step Euler-Maruyama recursion in Algorithm 2 (lines 3-7). The three terms in the bound, C2 sqrt(tmin)(log(1/tmin))^{(dx+1)/2}, C3 exp(-T), and C4 sqrt(T R(bs)), come from Proposition 4.5 of Fu et al. (2024) and contain no discretization error term. With the implementation settings T=10, tmin=0.01, K=1000, the step size is Delta t = 0.00999, and the gap between the continuous-time process and the discretized chain is not controlled. Moreover, Theorem 1 specifies tmin = N^{-4Γ1(k,α)-1} and T = 2Γ1(k,α) log N, whereas Algorithm 2 uses fixed values of tmin and T, so the theorem's scaling is not matched by the implemented algorithm. Since Corollary 1 rests on Theorem 1, the claim P(p ≤ α | H0) ≤ α + o(1) is not currently established for Algorithm 3 as implemented. The authors should either add a discretization error bound to Theorem 1 or state Theorem 1 for the continuous-time sampler and clearly separate the guarantee for the implemented algorithm.
  2. [Theorem 2 and Algorithm 3] Theorem 2 states P(p ≤ α | Y, Z) ≤ α + dTV(p(n)(·|Z), bp(n)(·|Z)). In Algorithm 3, bp is random because it is determined by the trained score network bs, which depends on the unlabeled data DU. As written, the left-hand side conditions only on Y and Z while the right-hand side is a random variable, so the inequality is not on a common conditioning. The proof works if the statement is read conditional on DU, or equivalently on bs: then \dot X and cX(b) are i.i.d. draws from bp(n) and the exchangeability argument is valid; taking expectations afterward gives the unconditional bound. Please restate Theorem 2 with this conditioning made explicit.
  3. [Supplementary S1, Assumption 2 and mixed-type claims] The paper repeatedly claims that the method handles conditioning sets that mix continuous and discrete variables (Abstract, Model M3, Scenario II, and the real-data clinical covariates). However, Assumption 2 in Supplementary S1 assumes that pZ has a density with respect to Lebesgue measure and is sub-Gaussian, which fails when any coordinate of Z is discrete. Consequently Theorem 1 and Corollary 1 do not cover the mixed-type simulations and real-data analyses. The empirical results may stand on their own, but the theoretical type I error guarantee should be either restricted to continuous Z or extended to distributions with atomic components.
minor comments (4)
  1. [Theoretical Guarantee for Sampling Quality] The quantities k and α appearing in Γ1(k,α) and Γ2(k,α) are defined only in the Supplementary Material; they should be defined in the main text where Theorem 1 is stated.
  2. [Introduction] There are typos, for example 'Moerever' in the Introduction; a careful proofreading pass is needed.
  3. [Methodology for Sampling] In Eq. (2), the coefficient of ϵ should read sqrt(1 - exp(-t)); the current typesetting with 'p 1 - exp(-t)' is easy to misread.
  4. [Table 1] The caption says the smallest MSEs and SDs are bolded, but this is not consistently implemented across all rows (for example, the M2 0.05 row); the caption should also state whether boldface indicates best MSE, best SD, or both.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation: the type I error guarantee rests on an external TV-convergence theorem and standard CRT exchangeability, not on the test's own fitted outputs; the Euler-Maruyama discretization gap in the proof of Theorem 1 is a correctness concern, not circularity.

full rationale

The central derivation chain is: (i) CRT p-value validity when P(·|Z) is known is the standard exchangeability argument from Candès et al. (2018); (ii) Theorem 2 converts the error from replacing P with the diffusion-generated bp into an additive total-variation term, and holds for any test statistic; (iii) Theorem 1 bounds that TV distance by importing Lemma D.7 and Proposition 4.5 from Fu et al. (2024), an external source with no author overlap with the present paper; (iv) Corollary 1 combines these. None of these steps defines the desired type I error bound into an assumption: the TV rate is an external benchmark, and the p-value is not fitted to the data. The self-citations to Li et al. (2023, 2024) supply the 1-NN negative-sampling gadget for the CCMI statistic and a comparison baseline, but Theorem 2 does not depend on that choice, and CCMI consistency is cited to Mukherjee et al. (2020), so the self-citations are not load-bearing for the central claim. The notable defect is an omitted proof, not circularity: Theorem 1 is stated for Algorithm 2's finite-step Euler-Maruyama sampler, while the proof in Supplementary S2 bounds only the continuous-time reverse process via Fu et al.'s Proposition 4.5 and contains no discretization-error term; this threatens Corollary 1's applicability to the implemented algorithm but is a correctness gap, not a reduction of the result to its own inputs. Overall circularity score is low.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the regularity of p(x|z) and pZ, an imported score approximation bound, and a data-distribution match between the unlabeled training set and the labeled test set. The experiments also use several hand-chosen hyperparameters whose values do not follow the theoretical scaling.

free parameters (4)
  • Early stopping time t_min = 0.01 in experiments; theory requires N^{-4Gamma1-1}
    Hand-chosen; the constant value does not match the theoretical scaling with N, creating a gap between theory and experiment.
  • Terminal time T = 10 in experiments; theory requires 2Gamma1 log N
    Hand-chosen; larger than the theoretical minimum for the simulated N, so likely benign but not justified formally.
  • Reverse-process steps K = 1000
    Euler-Maruyama step count; the theoretical error bound does not explicitly include discretization error.
  • Network architecture (depth/width) = 3 hidden layers, 16 or 128 units; 3 Res-blocks for real data
    Chosen by hand to fit the problem scale; affects sampling quality and is not derived from theory.
assumptions (5)
  • domain assumption Assumption 1: p(x|z) = exp(-B1||x||^2/2) v(x,z) with v bounded above and below and Holder smooth.
    Supplementary S1; required for the score approximation bound from Fu et al. (2024).
  • domain assumption Assumption 2: pZ has sub-Gaussian tails.
    Supplementary S1; needed for the diffusion model error analysis.
  • domain assumption Score approximation bound (Lemma D.7 of Fu et al. 2024).
    The paper directly uses this external lemma to bound the score estimation error; no proof is included here.
  • domain assumption DU and DT are drawn from the same joint distribution p(x,z).
    Needed for the conditional sampler to reflect the test data; not stated explicitly as an assumption.
  • domain assumption Class-based CMI estimator is consistent (Mukherjee et al. 2020).
    Used to justify power; not needed for type I error control but needed for the claim of power under alternatives.

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Pith. "Pith review of Conditional Diffusion Models Based Conditional Independence Testing." pith.science (2026). https://pith.science/paper/K62GXDHI

@misc{pith2026241211744,
  author       = {Pith},
  title        = {Pith review of: Conditional Diffusion Models Based Conditional Independence Testing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K62GXDHI}},
  note         = {Machine review of arXiv:2412.11744}
}
abstract

Conditional independence (CI) testing is a fundamental task in modern statistics and machine learning. The conditional randomization test (CRT) was recently introduced to test whether two random variables, $X$ and $Y$, are conditionally independent given a potentially high-dimensional set of random variables, $Z$. The CRT operates exceptionally well under the assumption that the conditional distribution $X|Z$ is known. However, since this distribution is typically unknown in practice, accurately approximating it becomes crucial. In this paper, we propose using conditional diffusion models (CDMs) to learn the distribution of $X|Z$. Theoretically and empirically, it is shown that CDMs closely approximate the true conditional distribution. Furthermore, CDMs offer a more accurate approximation of $X|Z$ compared to GANs, potentially leading to a CRT that performs better than those based on GANs. To accommodate complex dependency structures, we utilize a computationally efficient classifier-based conditional mutual information (CMI) estimator as our test statistic. The proposed testing procedure performs effectively without requiring assumptions about specific distribution forms or feature dependencies, and is capable of handling mixed-type conditioning sets that include both continuous and discrete variables. Theoretical analysis shows that our proposed test achieves a valid control of the type I error. A series of experiments on synthetic data demonstrates that our new test effectively controls both type-I and type-II errors, even in high dimensional scenarios.

Figures

Figures reproduced from arXiv: 2412.11744 by the authors.

Figure 1
Figure 1. Comparison of conditional density estimators on [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. More results regarding N and n are provided in Figures 4 and 5 in Supplementary Materials. We have the following observations. First, in both post￾nonlinear and mixed models, our test controls type I error very well and achieves high power under H1 as dz increases. Second, NNSCIT has satisfactory performance in control￾ling type I error, but it loses power under H1, especially when dz exceeds 40 in the mixed model. … view at source ↗
Figure 2
Figure 2. Comparison of the type I error (lower is better) and power (higher is better) of our method with seven SOTA methods [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figures from the paper (5 more)
Figure 3
Figure 3. Figure 3: Comparisons of conditional density estimators on [PITH_FULL_IMAGE:figures/full_fig_p012_3.png]
Figure 4
Figure 4. Figure 4: Performance of various methods in terms of type I error and power under [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]
Figure 5
Figure 5. Figure 5: CDCIT’s performance in terms of type I error and power under [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 6
Figure 6. Figure 6: Venn diagram of CD genes detected by 7 algo [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 7
Figure 7. Figure 7: Average running times in seconds as a function of [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]

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Works this paper leans on

66 extracted references · 60 canonical work pages

  1. [1]

    Arjovsky, M.; Chintala, S.; and Bottou, L. 2017. Wasserstein generative adversarial networks. In International Conference on Machine Learning, 214--223

    work page 2017

  2. [2]

    T.; Cameselle-Teijeiro, J

    Beca, F.; Pereira, M. T.; Cameselle-Teijeiro, J. F.; et al. 2015. Altered PPP2R2A and Cyclin D1 expression defines a subgroup of aggressive luminal-like breast cancer. BMC Cancer, 15(1): 285

    work page 2015

  3. [3]

    I.; Baratin, A.; Rajeshwar, S.; Ozair, S.; Bengio, Y.; Courville, A.; et al

    Belghazi, M. I.; Baratin, A.; Rajeshwar, S.; Ozair, S.; Bengio, Y.; Courville, A.; et al. 2018. Mutual information neural estimation. In International Conference on Machine Learning, 531--540

    work page 2018

  4. [4]

    Bellot, A.; and van der Schaar, M. 2019. Conditional independence testing using generative adversarial networks. In Advances in Neural Information Processing Systems, volume 32

    work page 2019

  5. [5]

    B.; Wang, Y.; Barber, R

    Berrett, T. B.; Wang, Y.; Barber, R. F.; and Samworth, R. J. 2020. The conditional permutation test for independence while controlling for confounders. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 82(1): 175--197

    work page 2020

  6. [6]

    B rresen-Dale, A.-L. 2003. TP53 and breast cancer. Human Mutation, 21(3): 292--300

    work page 2003

  7. [7]

    Cand \`e s, E.; Fan, Y.; Janson, L.; and Lv, J. 2018. Panning for gold:`model-X' knockoffs for high dimensional controlled variable selection. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 80(3): 551--577

    work page 2018

  8. [8]

    Chen, T.; and Guestrin, C. 2016. Xgboost: A scalable tree boosting system. In ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 785--794

    work page 2016

Show all 66 references
  1. [9]

    M.; and Thomas, J

    Cover, T. M.; and Thomas, J. A. 2012. Elements of Information Theory. John Wiley & Sons

    2012

  2. [10]

    Curtis, C.; Shah, S.; Chin, S.-F.; Turashvili, G.; Rueda, O.; Dunning, M.; et al. 2012. The genomic and transcriptomic architecture of 2,000 breast tumors reveals novel subgroups. Nature, 486: 346–352

    2012

  3. [11]

    Dai, B.; Shen, X.; and Pan, W. 2022. Significance tests of feature relevance for a black-box learner. IEEE Transactions on Neural Networks and Learning Systems

    2022

  4. [12]

    Dai, H.; Ng, I.; Luo, G.; Spirtes, P.; Stojanov, P.; and Zhang, K. 2024. Gene Regulatory Network Inference in the Presence of Dropouts: a Causal View. arXiv:2403.15500

    2024 arXiv

  5. [13]

    Dhariwal, P.; and Nichol, A. 2021. Diffusion models beat gans on image synthesis. In Advances in Neural Information Processing Systems, volume 34

    2021

  6. [14]

    Doran, G.; Muandet, K.; Zhang, K.; and Sch \"o lkopf, B. 2014. A permutation-based kernel conditional independence test. In Conference on Uncertainty in Artificial Intelligence, 132--141

    2014

  7. [15]

    Efron, B. 2004. Selection and estimation for large-scale simultaneous inference . Technical Report 2005-18B/232, Division of Biostatistics, Stanford University

    2004

  8. [16]

    Fu, H.; Yang, Z.; Wang, M.; and Chen, M. 2024. Unveil conditional diffusion models with classifier-free guidance: A sharp statistical theory. arXiv:2403.11968

    2024 arXiv

  9. [17]

    Fukumizu, K.; Gretton, A.; Sun, X.; and Sch \"o lkopf, B. 2007. Kernel measures of conditional dependence. In Advances in Neural Information Processing Systems, volume 20

    2007

  10. [18]

    Genevay, A.; Peyr \'e , G.; and Cuturi, M. 2018. Learning generative models with sinkhorn divergences. In International Conference on Artificial Intelligence and Statistics, 1608--1617

    2018

  11. [19]

    Goodfellow, I.; Bengio, Y.; and Courville, A. 2016. Deep learning. MIT Press

    2016

  12. [20]

    Hall, P.; Racine, J.; and Li, Q. 2004. Cross-validation and the estimation of conditional probability densities. Journal of the American Statistical Association, 99(468): 1015--1026

    2004

  13. [21]

    Hall, P.; and Yao, Q. 2005. Approximating conditional distribution functions using dimension reduction. The Annals of Statistics, 1404--1421

    2005

  14. [22]

    Han, X.; Zheng, H.; and Zhou, M. 2022. Card: Classification and regression diffusion models. In Advances in Neural Information Processing Systems, volume 35

    2022

  15. [23]

    He, K.; Zhang, L.; and Long, X. 2016. Quantitative assessment of the association between APC promoter methylation and breast cancer. Oncotarget, 7(25): 37920--37930

    2016

  16. [24]

    Ho, J.; Jain, A.; and Abbeel, P. 2020. Denoising diffusion probabilistic models. In Advances in Neural Information Processing Systems, volume 33

    2020

  17. [25]

    Ho, J.; Salimans, T.; Gritsenko, A.; et al. 2022. Video diffusion models. In Advances in Neural Information Processing Systems, volume 35

    2022

  18. [26]

    Izbicki, R.; and Lee, A. B. 2017. Converting high-dimensional regression to high-dimensional conditional density estimation. Electronic Journal of Statistics, 11: 2800--2831

    2017

  19. [27]

    V.; and Kathiresan, S

    Khera, A. V.; and Kathiresan, S. 2017. Genetics of coronary artery disease: discovery, biology and clinical translation. Nature Reviews Genetics, 18(6): 331--344

    2017

  20. [28]

    Koller, D.; and Friedman, N. 2009. Probabilistic graphical models: principles and techniques. MIT Press

    2009

  21. [29]

    Kuchibhotla, A. K. 2020. Exchangeability, conformal prediction, and rank tests. arXiv:2005.06095

    2020 arXiv

  22. [30]

    Lauritzen, S. L. 1996. Graphical models, volume 17. Clarendon Press

    1996

  23. [31]

    Li, C.; and Fan, X. 2020. On nonparametric conditional independence tests for continuous variables. Wiley Interdisciplinary Reviews: Computational Statistics, 12(3): e1489

    2020

  24. [32]

    Li, S.; Chen, Z.; Zhu, H.; Wang, C.; and Wen, W. 2023. Nearest-neighbor sampling based conditional independence testing. In AAAI Conference on Artificial Intelligence, volume 37, 8631--8639

    2023

  25. [33]

    Li, S.; Zhang, Y.; Zhu, H.; Wang, C.; Shu, H.; Chen, Z.; et al. 2024. K-nearest-neighbor local sampling based conditional independence testing. In Advances in Neural Information Processing Systems, volume 36

    2024

  26. [34]

    Liu, M.; Katsevich, E.; Janson, L.; and Ramdas, A. 2022. Fast and powerful conditional randomization testing via distillation. Biometrika, 109(2): 277--293

    2022

  27. [35]

    Maguire, S.; Leonidou, A.; Wai, P.; Marchiò, C.; Ng, C.; Sapino, A.; et al. 2015. SF3B1 mutations constitute a novel therapeutic target in breast cancer. The Journal of Pathology, 235(4): 571--580

    2015

  28. [36]

    Mei, W.; Mei, B.; Chang, J.; Liu, Y.; Zhou, Y.; Zhu, N.; et al. 2024. Role and regulation of FOXO3a: new insights into breast cancer therapy. Frontiers in Pharmacology, 15

    2024

  29. [37]

    C.; and Shalizi, C

    Mesner, O. C.; and Shalizi, C. R. 2020. Conditional mutual information estimation for mixed, discrete and continuous data. IEEE Transactions on Information Theory, 67(1): 464--484

    2020

  30. [38]

    M.; and Heskes, T

    Mooij, J. M.; and Heskes, T. 2013. Cyclic causal discovery from continuous equilibrium data. In Conference on Uncertainty in Artificial Intelligence, 431--439

    2013

  31. [39]

    Mukherjee, S.; Asnani, H.; and Kannan, S. 2020. CCMI: Classifier based conditional mutual information estimation. In Conference on Uncertainty in Artificial Intelligence, 1083--1093

    2020

  32. [40]

    Ng, I.; Ghassami, A.; and Zhang, K. 2020. On the role of sparsity and dag constraints for learning linear dags. In Advances in Neural Information Processing Systems, volume 33

    2020

  33. [41]

    Pearl, J. 1988. Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan kaufmann

    1988

  34. [42]

    Pereira, B.; Chin, S.-F.; Rueda, O.; et al. 2016. Erratum: The somatic mutation profiles of 2,433 breast cancers refine their genomic and transcriptomic landscapes. Nature Communications, 7(11479): 11908

    2016

  35. [43]

    Runge, J. 2018. Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information. In International Conference on Artificial Intelligence and Statistics, 938--947

    2018

  36. [44]

    A.; and Nolan, G

    Sachs, K.; Perez, O.; Pe'er, D.; Lauffenburger, D. A.; and Nolan, G. P. 2005. Causal protein-signaling networks derived from multiparameter single-cell data. Science, 308(5721): 523--529

    2005

  37. [45]

    Scetbon, M.; Meunier, L.; and Romano, Y. 2022. An asymptotic test for conditional independence using analytic kernel embeddings. In International Conference on Machine Learning, 19328--19346

    2022

  38. [46]

    T.; Shanmugam, K.; Dimakis, A

    Sen, R.; Suresh, A. T.; Shanmugam, K.; Dimakis, A. G.; and Shakkottai, S. 2017. Model-powered conditional independence test. In Advances in Neural Information Processing Systems, volume 30

    2017

  39. [47]

    Shi, C.; Xu, T.; Bergsma, W.; and Li, L. 2021. Double generative adversarial networks for conditional independence testing. Journal of Machine Learning Research, 22(285): 1--32

    2021

  40. [48]

    Shigekawa, T.; Ijichi, N.; Ikeda, K.; et al. 2011. FOXP1, an Estrogen-Inducible Transcription Factor, Modulates Cell Proliferation in Breast Cancer Cells and 5-Year Recurrence-Free Survival of Patients with Tamoxifen-Treated Breast Cancer. Hormones & Cancer, 2(5): 286--297

    2011

  41. [49]

    Song, J.; Meng, C.; and Ermon, S. 2021. Denoising diffusion implicit models. In International Conference on Learning Representations

    2021

  42. [50]

    P.; Kumar, A.; Ermon, S.; and Poole, B

    Song, Y.; Sohl-Dickstein, J.; Kingma, D. P.; Kumar, A.; Ermon, S.; and Poole, B. 2021. Score-based generative modeling through stochastic differential equations. In International Conference on Learning Representations

    2021

  43. [51]

    N.; and Scheines, R

    Spirtes, P.; Glymour, C. N.; and Scheines, R. 2000. Causation, prediction, and search. MIT Press

    2000

  44. [52]

    Su, L.; and White, H. 2008. A nonparametric Hellinger metric test for conditional independence. Econometric Theory, 24(4): 829--864

    2008

  45. [53]

    Su, L.; and White, H. 2014. Testing conditional independence via empirical likelihood. Journal of Econometrics, 182(1): 27--44

    2014

  46. [54]

    Sun, W.; and Cai, T. T. 2007. Oracle and adaptive compound decision rules for false discovery rate control. Journal of the American Statistical Association, 102(479): 901--912

    2007

  47. [55]

    Tsybakov, A. B. 2009. Introduction to Nonparametric Estimation. New York: Springer

    2009

  48. [56]

    Verma, S.; Bakshi, D.; Sharma, V.; Sharma, I.; Shah, R.; Bhat, A.; et al. 2020. Genetic variants of 11 and 2 genes and their association with ovarian and breast cancer. International Journal of Gynecology & Obstetrics, 148(1): 118--122

    2020

  49. [57]

    Wang, X.; Pan, W.; Hu, W.; Tian, Y.; and Zhang, H. 2015. Conditional distance correlation. Journal of the American Statistical Association, 110(512): 1726--1734

    2015

  50. [58]

    Weglarczyk, S. 2018. Kernel density estimation and its application. ITM Web of Conferences, 23: 00037

    2018

  51. [59]

    Xiong, H.; Chen, Z.; Lin, B.; et al. 2022. Naringenin Regulates FKBP4/NR3C1/NRF2 Axis in Autophagy and Proliferation of Breast Cancer and Differentiation and Maturation of Dendritic Cell. Frontiers in Immunology, 12

    2022

  52. [60]

    Yang, L.; Zhang, Z.; Song, Y.; et al. 2023. Diffusion models: A comprehensive survey of methods and applications. ACM Computing Surveys, 56(4): 1--39

    2023

  53. [61]

    K.; et al

    Zan, L.; Meynaoui, A.; Assaad, C. K.; et al. 2022. A conditional mutual information estimator for mixed data and an associated conditional independence test. Entropy, 24(9): 1234

    2022

  54. [62]

    Zhang, K.; Peters, J.; Janzing, D.; and Sch \"o lkopf, B. 2011. Kernel-based conditional independence test and application in causal discovery. In Conference on Uncertainty in Artificial Intelligence, 804--813

    2011

  55. [63]

    Zhu, S.; Ng, I.; and Chen, Z. 2020. Causal Discovery with Reinforcement Learning. In International Conference on Learning Representations

    2020

  56. [64]

    Zhu, Z.; Zheng, Z.; Zhang, F.; et al. 2018. Causal associations between risk factors and common diseases inferred from GWAS summary data. Nature Communications, 9(1): 1--12

    2018

  57. [65]

    , " * write output.state after.block = add.period write newline

    ENTRY address archivePrefix author booktitle chapter edition editor eid eprint howpublished institution isbn journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all...

  58. [66]

    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 gl...

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.