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.
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.
Develops a new framework for conditional independence.
problem Generalizing previous notions of conditional independence.
method Introduces transition probability spaces and transitional random variables.
result Satisfies all desired relevance relations except symmetry.
In an independence model, the triplets that represent conditional independences between singletons are called elementary. It is known that the elementary triplets represent the independence model unambiguously under some conditions. In this paper, we show how this representation helps performing some operations with in…
Determinantal point process have recently been used as models in machine learning and this has raised questions regarding the characterizations of conditional independence. In this paper we investigate characterizations of conditional independence. We describe some conditional independencies through the conditions on t…
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…
Measuring conditional independence is one of the important tasks in statistical inference and is fundamental in causal discovery, feature selection, dimensionality reduction, Bayesian network learning, and others. In this work, we explore the connection between conditional independence measures induced by distances on …
TCRI improves domain generalization by enforcing conditional independence constraints.
problem Limitations of existing domain generalization methods due to incomplete constraints.
method TCRI implements regularizers motivated by conditional independence constraints.
result TCRI achieves cross-domain stability and outperforms baselines in worst-domain accuracy.
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.
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.
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.
A new graphical model for discrete data without parametric restrictions.
problem Discrete data modeling with restrictions.
method Additive conditional independence and penalized estimation of precision operator.
result Consistency of the estimator in ultrahigh-dimensional 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
Forré introduces a new conditional independence notion for mixed variables.
problem Unified framework for random and non-stochastic variables.
method Unified framework of transitional conditional independence and causal calculus for iDMGs.
result Unified framework connects conditional independencies to graphical separation criteria.
The paper analyzes counterfactual invariance and its relation to conditional independence.
problem Understanding the relationship between counterfactual invariance and conditional independence.
method Theoretical analysis of existing definitions, graphical implications, and mathematical proofs.
result Counterfactual invariance implies conditional independence, but not the other way around.
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.
This work investigates the intersection property of conditional independence. It states that for random variables A,B,C and X we have that X independent of A given B,C and X independent of B given A,C implies X independent of (A,B) given C. Under the assumption that the joint distribution has a co…
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.
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
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.
Algorithm learns causal structures from low-order conditional independencies.
problem Estimating high-order conditional independencies from data is challenging.
method Proposes an algorithm to compute a faithful graphical representation from low-order conditional independencies.
result Algorithm successfully learns causal structures from zero- and first-order conditional independencies.
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.
The paper shows how to infer conditional independence from non-Gaussian data.
problem Inferring conditional independence from non-Gaussian distributions.
method Developed a method to recover conditional independence structure from the precision matrix of generalized nonparanormal data.
result The conditional independence structure can be inferred from the precision matrix of generalized nonparanormal data.
Method discovers local independence in systems with continuous variables.
problem Applying Context-Specific Independence (CSI) to continuous variables is impractical.
method Neural contextual decomposition (NCD) learns partition of joint outcome space.
result NCD successfully discovers local independence in synthetic and real-world systems.
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.
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.
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.
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. Revisits information metric as pseudo metric on observables, with applications to conditional independence.
problem Clarifying the nature of information metric on manifolds of observables.
method Characterizes geodesics and applies Pythagorean theorem to conditional independence.
result Illustrates computation of information metric on Diabetes dataset.
GTMs model complex multivariate data with varying conditional independencies.
problem Modeling multivariate data with intricate marginals and complex dependency structures.
method Semiparametric approach using penalized splines and lasso regularization.
result GTMs accurately learn complex dependencies and identify conditional independencies.
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.
This article introduces a Bayesian nonparametric method for quantifying the relative evidence in a dataset in favour of the dependence or independence of two variables conditional on a third. The approach uses Polya tree priors on spaces of conditional probability densities, accounting for uncertainty in the form of th…
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.
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…
Constraint-based structure learning algorithms infer the causal structure of multivariate systems from observational data by determining an equivalent class of causal structures compatible with the conditional independencies in the data. Methods based on additive-noise (AN) models have been proposed to further discrimi…
New algorithms learn simple staged trees from data, improving model fit.
problem Complex conditional independences in categorical data vectors.
method Structural learning algorithms for simple staged trees, coalescing the underlying tree.
result Data-learned simple staged trees often outperform Bayesian networks in model fit.
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…
Develops a nonparametric graphical model for conditional independence.
problem Evaluation of conditional independence without distributional assumptions.
method Nonlinear sufficient dimension reduction techniques applied to a nonparametric graphical model.
result Method outperforms existing methods in non-Gaussian settings and high-dimensional data.
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…
Bayesian networks are simplified for categorical variables using staged trees and asymmetry-labeled DAGs.
problem Representing non-symmetric conditional independences in Bayesian networks.
method Formalized relationship between Bayesian networks and staged trees, introduced asymmetry-labeled DAGs, and developed an algorithm to learn staged trees.
result A novel algorithm for learning staged trees that captures non-symmetric independences.
A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full conditional independence between these two variables given all the other variables. In…
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.
CIRCE measures conditional independence for learning invariant features.
problem Learning invariant features while being conditionally independent of a distractor.
method CIRCE is a measure of conditional independence applied as a regularizer in feature learning.
result CIRCE provides a zero value if and only if features are conditionally independent of the distractor given the target.
The paper uses distance covariance to improve fairness in machine learning models.
problem Improving fairness in machine learning models.
method Using conditional and distance covariance statistics to assess independence and add a penalty for fairness.
result The method effectively reduces the fairness gap in machine learning models.
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 …
Learning the Markov network structure from data is a problem that has received considerable attention in machine learning, and in many other application fields. This work focuses on a particular approach for this purpose called independence-based learning. Such approach guarantees the learning of the correct structure …
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.
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.