On nonparametric conditional independence tests for continuous variables

Li, Chun; Fan, Xiaodan

doi:10.1002/wics.1489

Cited by 30 publications

(16 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The above methods are mainly for continuous data, whereas there are numerous CI tests available for discrete data as well (Agresti, 1992;Balakrishnan and Wasserman, 2018;Canonne et al, 2018;Kim and Agresti, 1997;Marx and Vreeken, 2019;Neykov et al, 2021;Yao and Tritchler, 1993). A more extensive review of CI tests can be found in Li and Fan (2020).…”

Section: Related Workmentioning

confidence: 99%

Local permutation tests for conditional independence

Kim¹,

Neykov²,

Balakrishnan³

et al. 2021

Preprint

View full text Add to dashboard Cite

In this paper, we investigate local permutation tests for testing conditional independence between two random vectors X and Y given Z. The local permutation test determines the significance of a test statistic by locally shuffling samples which share similar values of the conditioning variables Z, and it forms a natural extension of the usual permutation approach for unconditional independence testing. Despite its simplicity and empirical support, the theoretical underpinnings of the local permutation test remain unclear. Motivated by this gap, this paper aims to establish theoretical foundations of local permutation tests with a particular focus on binning-based statistics. We start by revisiting the hardness of conditional independence testing and provide an upper bound for the power of any valid conditional independence test, which holds when the probability of observing "collisions" in Z is small. This negative result naturally motivates us to impose additional restrictions on the possible distributions under the null and alternate. To this end, we focus our attention on certain classes of smooth distributions and identify provably tight conditions under which the local permutation method is universally valid, i.e. it is valid when applied to any (binning-based) test statistic. To complement this result on type I error control, we also show that in some cases, a binning-based statistic calibrated via the local permutation method can achieve minimax optimal power. We also introduce a double-binning permutation strategy, which yields a valid test over less smooth null distributions than the typical single-binning method without compromising much power. Finally, we present simulation results to support our theoretical findings.

show abstract

Section: Related Workmentioning

confidence: 99%

Local permutation tests for conditional independence

Kim¹,

Neykov²,

Balakrishnan³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The review over nonparametric conditional independence tests for continuous variables by Li and Fan [2020] groups the tests into the following categories.…”

Section: Introductionmentioning

confidence: 99%

The Weighted Generalised Covariance Measure

Scheidegger¹,

Hörrmann²,

Bühlmann³

2021

Preprint

View full text Add to dashboard Cite

We introduce a new test for conditional independence which is based on what we call the weighted generalised covariance measure (WGCM). It is an extension of the recently introduced generalised covariance measure (GCM). To test the null hypothesis of X and Y being conditionally independent given Z, our test statistic is a weighted form of the sample covariance between the residuals of nonlinearly regressing X and Y on Z. We propose different variants of the test for both univariate and multivariate X and Y . We give conditions under which the tests yield the correct type I error rate. Finally, we compare our novel tests to the original GCM using simulation and on real data sets. Typically, our tests have power against a wider class of alternatives compared to the GCM. This comes at the cost of having less power against alternatives for which the GCM already works well.

show abstract

“…Those limitations make these tests impractical in our context of scRNA-seq DEA and thus require adaptation. (Li and Fan, 2020) Performing DEA necessarily involves performing as many independent tests as there are genes.…”

Section: Introductionmentioning

confidence: 99%

“…Two random variables X and Y are conditionally independent given a third variable Z if, and only if, P ( X, Y | Z ) = P ( X | Z ) P ( Y | Z ). As described in Li and Fan (2020), many CIT have been developed previously and are readily available such as discretization-based tests (Margaritis (2005), Huang and others (2010)), metric-based tests (Runge (2018), Su and White (2007), Huang and others (2016)), permutation-based two-sample tests (Doran and others (2014), Gretton and others (2012), Sen and others (2017)), kernel-based tests (Muandet and others (2017), Li and others (2009)) and regression-based tests (see Li and Fan (2020) for a short review). Yet, these CIT either suffer from the curse of dimensionality or are hardly applicable to a large number of observations (Muandet and others (2017), Zhang and others (2011)).…”

Section: Introductionmentioning

confidence: 99%

“…A CIT broadens the classical independence test by testing for independence between two variables given a third one, or a set of additional variables (see Figure 8). Two random variables X and Y are conditionally independent given a third variable Z if, and only Li and Fan (2020), many CIT have been developed previously and are readily available such as discretization-based tests (Huang and others, 2010), metric-based tests (Runge, 2018;Su and White, 2007;Huang and others, 2016), permutation-based two-sample tests (Doran and others, 2014;Sen and others, 2017), kernel-based tests (Muandet and others, 2017;Li and others, 2009) and regression-based tests (see Li and Fan (2020) for a short review). Yet, these CIT either suffer from the curse of dimensionality or are hardly applicable to a large number of observations (Muandet and others, 2017).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Distribution-free complex hypothesis testing for single-cell RNA-seq differential expression analysis

Gauthier

Agniel

Thiébaut

et al. 2021

Preprint

View full text Add to dashboard Cite

State-of-the-art methods for single-cell RNA-seq (scRNA-seq) Differential Expression Analysis (DEA) often rely on strong distributional assumptions that are difficult to verify in practice. Furthermore, while the increasing complexity of clinical and biological single-cell studies calls for greater tool versatility, the majority of existing methods only tackle the comparison between two conditions. We propose a novel, distribution-free, and flexible approach to DEA for single-cell RNA-seq data. This new method, called ccdf, tests the association of each gene expression with one or many variables of interest (that can be either continuous or discrete), while potentially adjusting for additional covariates. To test such complex hypotheses, ccdf uses a conditional independence test relying on the conditional cumulative distribution function, estimated through multiple regressions. We provide the asymptotic distribution of the ccdf test statistic as well as a permutation test (when the number of observed cells is not sufficiently large). ccdf substantially expands the possibilities for scRNA-seq DEA studies: it obtains good statistical performance in various simulation scenarios considering complex experimental designs i.e. beyond the two condition comparison), while retaining competitive performance with state-of-the-art methods in a two-condition benchmark.

show abstract

On nonparametric conditional independence tests for continuous variables

Cited by 30 publications

References 39 publications

Local permutation tests for conditional independence

Local permutation tests for conditional independence

The Weighted Generalised Covariance Measure

Distribution-free complex hypothesis testing for single-cell RNA-seq differential expression analysis

Contact Info

Product

Resources

About