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Tests of conditional independence (CI) of ran- dom variables play an important role in ma- chine learning and causal inference. Of partic- ular interest are kernel-based CI tests which allow us to test for independence among ran- dom variables with complex distribution func- tions. The efficacy of a CI test is measured in terms of its power and its calibratedness. We show that the Kernel CI Permutation Test (KCIPT) suffers from a loss of calibratedness as its power is increased by increasing the number of bootstraps. To address this limita- tion, we propose a novel CI test, called Self- Discrepancy Conditional Independence Test (SDCIT). SDCIT uses a test statistic that is a modified unbiased estimate of maximum mean discrepancy (MMD), the largest difference in the means of features of the given sample and its permuted counterpart in the kernel-induced Hilbert space. We present results of experi- ments that demonstrate SDCIT is, relative to the other methods: (i) competitive in terms of its power and calibratedness, outperforming other methods when the number of condition- ing variables is large; (ii) more robust with re- spect to the choice of the kernel function; and (iii) competitive in run time.
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A general framework for powerful confounder adjustment in omics association studies
Abstract MotivationGenomic data are subject to various sources of confounding, such as demographic variables, biological heterogeneity, and batch effects. To identify genomic features associated with a variable of interest in the presence of confounders, the traditional approach involves fitting a confounder-adjusted regression model to each genomic feature, followed by multiplicity correction. ResultsThis study shows that the traditional approach is suboptimal and proposes a new two-dimensional false discovery rate control framework (2DFDR+) that provides significant power improvement over the conventional method and applies to a wide range of settings. 2DFDR+ uses marginal independence test statistics as auxiliary information to filter out less promising features, and FDR control is performed based on conditional independence test statistics in the remaining features. 2DFDR+ provides (asymptotically) valid inference from samples in settings where the conditional distribution of the genomic variables given the covariate of interest and the confounders is arbitrary and completely unknown. Promising finite sample performance is demonstrated via extensive simulations and real data applications. Availability and implementationR codes and vignettes are available at https://github.com/asmita112358/tdfdr.np.
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- Award ID(s):
- 2113359
- PAR ID:
- 10552297
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Bioinformatics
- Volume:
- 39
- Issue:
- 9
- ISSN:
- 1367-4811
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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