Testing conditional independence for continuous random variables

By Wicher P. Bergsma. 2004

67 citations recorded by the source corpus.

Subfields: Statistics and Probability, Causal Inference & Discovery

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “Testing for conditional independence is generally a challenging problem due to the “curse of dimensionality” in terms of the dimensionality of the conditioning variable Z (Bergsma 2004).”
Identifiability of Causal Graphs using Functional Models (2011, background): “Such tests are difficult to perform in practice [e.g. Bergsma, 2004].”
Kernel-based Conditional Independence Test and Application in Causal Discovery (2011, background): “Testing for CI is much more diﬃcult than that for unconditional independence (Bergsma, 2004).”
The conditional permutation test (2018, methodology): “The use of partial copulas was studied by Bergsma [3] and Song [18].”
Comparing Probabilistic Forecasting Systems with the Brier Score (2007, background): “This assumption is difficult to test empirically for ensemble forecasts with a distribution that changes through time and requires further investigation (cf. Bergsma 2004) so we appeal to the long lead time of our rainfall forecasts for justification.”
Causal Inference on Time Series using Structural Equation Models (2012, methodology): “(3) Bad model assumptions: The methods share a similar problem: Performing general conditional independence tests is desirable, but not feasible, partially because the conditioning sets are too large [e.g. Bergsma, 2004].”
On Azadkia–Chatterjee’s conditional dependence coefficient (2021, methodology): “been explored in studies of rank- and graph-based tests in related statistical problems (Bhattacharya, 2019; Cao and Bickel, 2020; Shi et al., 2020). The critical detection boundary in such cases is known to be at root-n; (b) the conditional distribution of (Y,Z) given X is assumed to be Hölder smoo”
A Permutation-Based Kernel Conditional Independence Test (2014, background): “Generally, conditional independence testing is a challenging problem (Bergsma, 2004).”
Identiﬁability of Causal Graphs using Functional Models (unknown): “Such tests are diﬃcult to perform in practice [e.g. Bergsma, 2004].”
Minimax optimal conditional independence testing (2020, methodology): “The works [7, 8] propose a partial copula approach, which needs estimators of the conditional distributions of X|Z and Y |Z.”
The conditional permutation test for independence while controlling for confounders (2018, methodology): “When is the total variation distance small? For theorem 4 to have practical implications, we need to verify that there are settings where, although the true distribution QÅ of X|Z is unknown, it can be estimated to high accuracy, with dTV { QÅ.·|Z/, Q.·|Z/}=op.1/ (so that excess type I error is guar”