A Permutation-Based Kernel Conditional Independence Test

By Gary Doran, Krikamol Muandet, Kun Zhang, Bernhard Schölkopf. 2014

137 citations recorded by the source corpus.

Subfields: Statistics and Probability, Causal Inference & Discovery

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Citations in the corpus

Toward Causal Representation Learning (2021, background): “Recent progress in (conditional) independence testing heavily relies on kernel function classes to represent probability distributions in reproducing kernel Hilbert spaces [43], [61], [74], [91], [92], [193], [280].”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “More recent applications of the covariance operator include independence and conditional independence measures (Gretton et al. 2005b, Zhang et al. 2008; 2011, Doran et al. 2014).”
Towards Causal Representation Learning (2021, positive): “progress in (conditional) independence testing heavily relies on kernel function classes to represent probability distributions in reproducing kernel Hilbert spaces [90, 91, 73, 278, 60, 191, 42].”
Fast Conditional Independence Test for Vector Variables with Large Sample Sizes (2018, methodology): “As Doran et al. [2014] point out however, Type I and Type II errors can bias the results.”
Disentangling by Factorising (2018, methodology): “This is a standard trick used in the independence testing literature [1, 6].”
The conditional permutation test for independence while controlling for confounders (2018, methodology): “ta into reproducing kernel Hilbert spaces are studied in, for example, Fukumizu et al. [12], Zhang et al. [33] and Strobl et al. [25]. Other works use permutations of the data, including Doran et al. [10] and Sen et al. [21], where the methods have the avor of binning Z and then permuting within gro”
Minimax optimality of permutation tests (2020, methodology): “When the conditional variable is continuous, however, this strategy does not work and this has led several authors to use “local permutation” heuristics (see for instance Doran et al., 2014; Fukumizu et al., 2008; Neykov et al., 2019).”
High-dimensional consistency in score-based and hybrid structure learning (2015, background): “Analogously, one can define scoring criteria based on more general conditional independence tests, leading to score-based (or hybrid) competitors of the PC algorithms based on such conditional independence tests [e.g., Zhang et al. (2011), Doran et al. (2014)].”
On Azadkia–Chatterjee’s conditional dependence coefficient (2021, methodology): “This (asymptotic) distribution-freeness is in line with similar observations made earlier for related problems such as two-sample goodness-of-fit tests, where Friedman and Rafsky (1979) extended Wald and Wolfowitz (1940)’s rank-based run test to multivariate spaces via minimum spanning trees; see, a”
The conditional permutation test (2018, methodology): “Other works use permutations of the data, including Doran et al. [8] and Sen et al. [16], where the methods have the ﬂavor of binning Z and then permuting within groups.”
Approximate Kernel-Based Conditional Independence Tests for Fast Non-Parametric Causal Discovery (2017, methodology): “, 2011), and PCIT takes too long to solve for its required permutation (Doran et al., 2014).”
Panning for gold: ‘model‐X’ knockoffs for high dimensional controlled variable selection (2016, background): “Doran et al. (2014) also rely on the data containing repeated observations of X - j so that certain observations can be permuted nonparametrically while maintaining the null distribution.”
Panning for Gold: Model-free Knockoffs for High-dimensional Controlled Variable Selection (2016, background): “Doran et al. (2014) also rely on the data containing repeated observations of X-j so that certain observations can be permuted nonparametrically while maintaining the null distribution.”
Minimax optimal conditional independence testing (2020, background): “[13] Gary Doran, Krikamol Muandet, Kun Zhang, and Bernhard Schölkopf.”
Gaussian Processes for Independence Tests with Non-iid Data in Causal Inference (2015, methodology): “…[Fukumizu et al. 2007], Kernel-based Conditional Independence (KCI) [Zhang et al. 2011], a scale-invariant measure [Reddi and P´oczos 2013], a scalable method called Conditional Correlation Independence (CCI) [Ramsey 2014], and a permutation-based conditional independence test [Doran et al. 2014].”