A new method tests conditional independence by transforming it into an unconditional problem using transport maps.
problem Testing conditional independence between two random vectors given a third.
method Constructing transport maps to transform conditional independence into unconditional independence, estimating these maps from data using conditional continuous normalizing flow models.
result The proposed method is validated through simulations and real-data analysis, demonstrating practical effectiveness.
Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly challenging. We propose a Kernel-based Conditional Independence test (KCI-test), by con…
Paper introduces a new test for conditional independence using weighted partial copulas.
problem Testing conditional independence between variables.
method The approach uses a weighted partial copula function and a bootstrap procedure to compute regions of rejection.
result The proposed test has competitive power compared to existing methods.
New test for conditional independence using kernel embeddings.
problem Testing conditional independence in high-dimensional settings.
method Analytic kernel embeddings, asymptotic distribution.
result New test outperforms existing methods in high-dimensional settings.
A new test for conditional independence in discretized data.
problem Testing conditional independence when only discretized observations are available.
method Proposes a conditional independence test designed for discretized observations, using bridge equations to recover latent variables' information.
result Demonstrates the effectiveness of the proposed test through theoretical and empirical validation.
LCIT tests conditional independence using latent representations.
problem Detecting conditional independencies in statistical and machine learning tasks.
method Generative framework for learning latent representations of target variables X and Y, then testing for remaining dependencies.
result LCIT outperforms state-of-the-art baselines consistently under different metrics and settings.
Sequential Kernel-based Conditional Independence Testing via Adaptive Betting
problem Testing conditional independence
method Testing-by-betting on an adaptively optimized Kernel Conditional Independence statistic
result Significantly reduces Type I error inflation while preserving high power
DIET tests conditional independence using marginal dependence measures of residual information.
problem Computational intractability of conditional randomization tests (CRTs).
method DIET avoids fitting large models by leveraging marginal independence statistics of information residuals.
result DIET achieves higher power than other tractable CRTs on synthetic and real benchmarks.
New algorithm reduces conditional independence tests needed for causal discovery.
problem Efficiently infer causal relations from observational data.
method Established an algorithm with complexity pO(s) tests. result Achieves exponent-optimality up to a logarithmic factor in terms of conditional independence tests.
Fast nonparametric conditional independence testing via two-stage regression
problem Fast nonparametric conditional independence testing
method BLITZ (Broad-to-Local Independence Testing via residualiZation)
result Better null calibration than fast kernel, random-feature, and regression-based competitors
Unified framework for structure learning via conditional independence testing.
problem Optimal structure learning and conditional independence testing.
method Established a fundamental connection and reduction between structure learning and conditional independence testing.
result Optimal rates for structure learning are determined by conditional independence testing rates.
This work identifies redundant tests in conditional-independence-based discovery that can improve graphical model accuracy.
problem Reliability and sensitivity of conditional-independence-based discovery algorithms.
method Analysis of redundant tests and their impact on error detection and correction.
result Redundant tests can improve graphical model accuracy but not all are beneficial.
Model-X test detects conditional independence in streaming data.
problem Detecting conditional independence in data streams with arbitrary dependency.
method Sequential testing inspired by model-X and testing by betting.
result Significantly reduces type-I error rate and enhances data efficiency.
Constraint-based causal discovery (CCD) algorithms require fast and accurate conditional independence (CI) testing. The Kernel Conditional Independence Test (KCIT) is currently one of the most popular CI tests in the non-parametric setting, but many investigators cannot use KCIT with large datasets because the test sca…
FastKCI speeds up KCI tests for causal inference on large datasets.
problem Cubic computational complexity of kernel-based conditional independence tests.
method Mixture-of-experts approach with parallel Gaussian process inference.
result Substantial computational speedups with maintained statistical power.
ACID neural network tests conditional independence efficiently.
problem Testing conditional independence in data.
method Amortized conditional independence testing using transformer-based neural networks.
result ACID achieves state-of-the-art performance and robust generalization.
Private CI tests for continuous Z with privacy constraints.
problem Testing conditional independence under differential privacy constraints.
method Developed two private CI testing procedures based on generalized covariance and conditional randomization tests.
result First private CI tests with rigorous theoretical guarantees for continuous Z.
Testing (conditional) independence of multivariate random variables is a task central to statistical inference and modelling in general - though unfortunately one for which to date there does not exist a practicable workflow. State-of-art workflows suffer from the need for heuristic or subjective manual choices, high c…
Unified CI test for categorical and ordinal data maintains power in high dimensions.
problem Rapid degradation of statistical power in existing CI tests for high-dimensional conditioning variables.
method Unified CI test for categorical and ordinal data, maintaining reasonable calibration and power in high dimensions.
result Our test outperforms existing baselines in model testing and structure learning for dense directed graphical models.
Conditional independence tests (CI tests) have received special attention lately in Machine Learning and Computational Intelligence related literature as an important indicator of the relationship among the variables used by their models. In the field of Probabilistic Graphical Models (PGM)--which includes Bayesian Net…
New insights into CI tests reveal key factors for practical performance.
problem Understanding and improving CI tests in practical applications.
method Investigation of the Kernel-based Conditional Independence (KCI) test and analysis of its practical behavior.
result Errors in conditional mean embedding estimates and appropriate conditioning kernel selection are crucial for CI tests.
ECCIT improves conditional independence tests by calibrating for miscalibration.
problem Inaccurate frequentist guarantees in CITs, especially in small samples and misspecified models.
method Empirically Calibrated Conditional Independence Tests (ECCIT) that optimize and correct for miscalibration.
result ECCIT achieves valid FDR with higher power than existing calibration strategies.
We study 'meta-dependence' in conditional independence tests across different empirical distributions.
problem Understanding the breakdown of conditional independence properties in finite data.
method Geometric intuition and information projections to measure meta-dependence between conditional independences.
result We provide a measure of meta-dependence that consolidates findings across synthetic and real-world data.
New method tests independence with single nonstationary time series.
problem Testing independence in nonstationary nonlinear time series.
method Time-varying nonlinear regression, local long-run covariance estimation, strong Gaussian approximation.
result First framework for conditional independence testing with a single realization of a nonstationary nonlinear process.
Testing for conditional independence is a core aspect of constraint-based causal discovery. Although commonly used tests are perfect in theory, they often fail to reject independence in practice, especially when conditioning on multiple variables. We focus on discrete data and propose a new test based on the notion of …
New test for conditional independence using GNNs avoids estimating conditional distributions.
problem Testing conditional independence of X and Y given Z. method Proposes a non-parametric testing procedure using GNNs to sample from marginal conditional distributions.
result Test statistic is doubly robust against GNN approximation errors.
New method uses CDMs to improve CI testing without distributional assumptions.
problem Testing conditional independence when the conditional distribution is unknown.
method Uses conditional diffusion models (CDMs) to approximate X∣Z and a classifier-based CMI estimator. result Proposed method performs better than GAN-based CI tests and controls type I and II errors.
New method tests conditional independence using spectral representations.
problem Untestable conditional independence in many settings.
method Spectral representations of partial covariance operators, bi-level contrastive learning.
result Asymptotic validity and power guarantees for CI testing.
FMCIT accelerates CI tests for causal discovery, maintaining power and efficiency.
problem High computational complexity in CI tests limits practical applicability of causal discovery methods.
method Flow Matching-based Conditional Independence Test (FMCIT) that leverages flow matching for fast CI tests.
result FMCIT effectively controls type-I error and maintains high testing power under the alternative hypothesis.
We present and evaluate the Fast (conditional) Independence Test (FIT) -- a nonparametric conditional independence test. The test is based on the idea that when P(X∣Y,Z)=P(X∣Y), Z is not useful as a feature to predict X, as long as Y is also a regressor. On the contrary, if $P(X \mid Y, Z) \neq P(X…
Develops a test for conditional local independence of counting processes.
problem Testing the hypothesis of conditional local independence among continuous time stochastic processes.
method Introduces a new functional parameter, the Local Covariance Measure (LCM), and proposes a test called (X)-LCT using nonparametric estimators and sample splitting or cross-fitting.
result The (X)-LCT test can be controlled uniformly with modest rates, and it works well without restrictive parametric assumptions.
New method tests CMI using deep neural networks for high-dimensional data.
problem Testing conditional mean independence in high-dimensional settings.
method Population CMI measure and bootstrap-based testing with deep generative neural networks.
result Strong empirical performance and versatility in various scenarios.
Conditional independence testing is a key problem required by many machine learning and statistics tools. In particular, it is one way of evaluating the usefulness of some features on a supervised prediction problem. We propose a novel conditional independence test in a predictive setting, and show that it achieves bet…
MixCIT tests conditional independence for mixed data types efficiently and reliably.
problem Testing conditional independence for mixed data types, especially when at least one is continuous.
method Graph-based test statistic comparing kernel similarities, debiased local-polynomial approach for continuous variables.
result Unified, efficient, and statistically guaranteed solution across heterogeneous data types.
As a crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known effect Z, i.e., E(Y|X, Z) = E(Y|Z). Assuming that E(Y|Z) and Z are linearly related, …
E-CIT framework reduces CITs' computational burden and improves causal discovery performance.
problem High computational cost of traditional CITs in causal discovery.
method E-CIT framework using divide-and-aggregate strategy with stable distribution p-value combination.
result Significant reduction in computational burden and competitive performance in causal discovery.
A new kernel-based CI test improves on existing methods.
problem Testing conditional independence (CI) in a broad range of dependencies.
method Regression-model-agnostic kernel-based CI test using reproducing kernel Hilbert spaces.
result GKCM outperforms state-of-the-art CI tests in simulations.
Proposes a new method using GANs for testing conditional independence.
problem High-dimensional conditional independence testing in statistics and machine learning.
method Double GANs framework to learn conditional distributions, then construct a test statistic.
result The test statistic is doubly robust and has asymptotic power approaching one.
Deep CITs test conditional independence in images, improving brain MRI scan analysis.
problem Testing conditional independence in complex, high-dimensional variables like images.
method Combines embedding maps and nonparametric CITs for feature representations.
result Valid DNCITs for brain MRI scans and behavioral traits, confirming null results.
This work develops a non-parametric test for relational independence in non-i.i.d. data.
problem Testing independence in relational systems where data samples are not i.i.d.
method Kernel mean embedding for relational variables, consistent non-parametric scalable kernel test.
result Empirically validated effectiveness compared to state-of-the-art tests.
New method identifies causal structure in exchangeable data.
problem Existing causal discovery methods struggle with i.i.d. data.
method Exchangeable data provides richer conditional independence structure.
result Exchangeable data allows for unique causal structure identification.
New methods for CI testing under model misspecification.
problem Challenges in CI testing with misspecified models.
method Proposes new approximations and upper bounds for testing errors of regression-based CI tests.
result Introduces the Rao-Blackwellized Predictor Test (RBPT) robust against misspecified inductive biases.
It is often stated in papers tackling the task of inferring Bayesian network structures from data that there are these two distinct approaches: (i) Apply conditional independence tests when testing for the presence or otherwise of edges; (ii) Search the model space using a scoring metric. Here I argue that for complete…
We show how to estimate a model's test error from unlabeled data, on distributions very different from the training distribution, while assuming only that certain conditional independencies are preserved between train and test. We do not need to assume that the optimal predictor is the same between train and test, or t…
A new algorithm for robust causal discovery in small sample sizes.
problem Limited data leads to weak conditional independence tests in causal discovery.
method Proposes a k-PC algorithm that bounds conditioning set size for robust causal discovery. result The k-PC algorithm enables more robust causal discovery in small sample sizes. Develops non-parametric tests for group symmetry in data.
problem Lack of statistical tests for group symmetry in data.
method Formulates and implements non-parametric tests for distributional symmetry under specified groups.
result Develops tests for conditional invariance/equivariance and applies them to real-world data.
Study on testing two populations with confounders.
problem Determining if two populations have the same distribution after accounting for confounding factors.
method Introduce two general frameworks for conditional two-sample testing.
result Demonstrated the power and validity of the proposed frameworks.
We consider the problem of learning causal relationships from relational data. Existing approaches rely on queries to a relational conditional independence (RCI) oracle to establish and orient causal relations in such a setting. In practice, queries to a RCI oracle have to be replaced by reliable tests for RCI against …