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RANK: Large-Scale Inference with Graphical Nonlinear Knockoffs.

ABSTRACT: Power and reproducibility are key to enabling refined scientific discoveries in contemporary big data applications with general high-dimensional nonlinear models. In this paper, we provide theoretical foundations on the power and robustness for the model-X knockoffs procedure introduced recently in Candès, Fan, Janson and Lv (2018) in high-dimensional setting when the covariate distribution is characterized by Gaussian graphical model. We establish that under mild regularity conditions, the power of the oracle knockoffs procedure with known covariate distribution in high-dimensional linear models is asymptotically one as sample size goes to infinity. When moving away from the ideal case, we suggest the modified model-X knockoffs method called graphical nonlin-ear knockoffs (RANK) to accommodate the unknown covariate distribution. We provide theoretical justifications on the robustness of our modified procedure by showing that the false discovery rate (FDR) is asymptotically controlled at the target level and the power is asymptotically one with the estimated covariate distribution. To the best of our knowledge, this is the first formal theoretical result on the power for the knockoffs procedure. Simulation results demonstrate that compared to existing approaches, our method performs competitively in both FDR control and power. A real data set is analyzed to further assess the performance of the suggested knockoffs procedure.

SUBMITTER: Fan Y

PROVIDER: S-EPMC7394464 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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RANK: Large-Scale Inference with Graphical Nonlinear Knockoffs.

Fan Yingying Y Demirkaya Emre E Li Gaorong G Lv Jinchi J

Journal of the American Statistical Association 20190411 529

Power and reproducibility are key to enabling refined scientific discoveries in contemporary big data applications with general high-dimensional nonlinear models. In this paper, we provide theoretical foundations on the power and robustness for the model-X knockoffs procedure introduced recently in Candès, Fan, Janson and Lv (2018) in high-dimensional setting when the covariate distribution is characterized by Gaussian graphical model. We establish that under mild regularity conditions, the powe ...[more]

PMID: 32742045

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Project description:BackgroundRecently we developed a gene orthology inference tool based on genome rearrangements (Journal of Bioinformatics and Computational Biology 19:6, 2021). Given a set of genomes our method first computes all pairwise gene similarities. Then it runs pairwise ILP comparisons to compute optimal gene matchings, which minimize, by taking the similarities into account, the weighted rearrangement distance between the analyzed genomes (a problem that is NP-hard). The gene matchings are then integrated into gene families in the final step. The mentioned ILP includes an optimal capping that connects each end of a linear segment of one genome to an end of a linear segment in the other genome, producing an exponential increase of the search space.ResultsIn this work, we design and implement a heuristic capping algorithm that replaces the optimal capping by clustering (based on their gene content intersections) the linear segments into [Formula: see text] subsets, whose ends are capped independently. Furthermore, in each subset, instead of allowing all possible connections, we let only the ends of content-related segments be connected. Although there is no guarantee that m is much bigger than one, and with the possible side effect of resulting in sub-optimal instead of optimal gene matchings, the heuristic works very well in practice, from both the speed performance and the quality of computed solutions. Our experiments on primate and fruit fly genomes show two positive results. First, for complete assemblies of five primates the version with heuristic capping reports orthologies that are very similar to the orthologies computed by the version of our tool with optimal capping. Second, we were able to efficiently analyze fruit fly genomes with incomplete assemblies distributed in hundreds or even thousands of contigs, obtaining gene families that are very similar to [Formula: see text] families. Indeed, our tool inferred a higher number of complete cliques, with a higher intersection with [Formula: see text], when compared to gene families computed by other inference tools. We added a post-processing for refining, with the aid of the [Formula: see text] algorithm, our ambiguous families (those with more than one gene per genome), improving even more the accuracy of our results. Our approach is implemented into a pipeline incorporating the pre-computation of gene similarities and the post-processing refinement of ambiguous families with [Formula: see text]. Both the original version with optimal capping and the new modified version with heuristic capping can be downloaded, together with their detailed documentations, at https://gitlab.ub.uni-bielefeld.de/gi/FFGC or as a Conda package at https://anaconda.org/bioconda/ffgc .

Project description:BackgroundGraphical Gaussian models are popular tools for the estimation of (undirected) gene association networks from microarray data. A key issue when the number of variables greatly exceeds the number of samples is the estimation of the matrix of partial correlations. Since the (Moore-Penrose) inverse of the sample covariance matrix leads to poor estimates in this scenario, standard methods are inappropriate and adequate regularization techniques are needed. Popular approaches include biased estimates of the covariance matrix and high-dimensional regression schemes, such as the Lasso and Partial Least Squares.ResultsIn this article, we investigate a general framework for combining regularized regression methods with the estimation of Graphical Gaussian models. This framework includes various existing methods as well as two new approaches based on ridge regression and adaptive lasso, respectively. These methods are extensively compared both qualitatively and quantitatively within a simulation study and through an application to six diverse real data sets. In addition, all proposed algorithms are implemented in the R package "parcor", available from the R repository CRAN.ConclusionIn our simulation studies, the investigated non-sparse regression methods, i.e. Ridge Regression and Partial Least Squares, exhibit rather conservative behavior when combined with (local) false discovery rate multiple testing in order to decide whether or not an edge is present in the network. For networks with higher densities, the difference in performance of the methods decreases. For sparse networks, we confirm the Lasso's well known tendency towards selecting too many edges, whereas the two-stage adaptive Lasso is an interesting alternative that provides sparser solutions. In our simulations, both sparse and non-sparse methods are able to reconstruct networks with cluster structures. On six real data sets, we also clearly distinguish the results obtained using the non-sparse methods and those obtained using the sparse methods where specification of the regularization parameter automatically means model selection. In five out of six data sets, Partial Least Squares selects very dense networks. Furthermore, for data that violate the assumption of uncorrelated observations (due to replications), the Lasso and the adaptive Lasso yield very complex structures, indicating that they might not be suited under these conditions. The shrinkage approach is more stable than the regression based approaches when using subsampling.

Dataset Information

RANK: Large-Scale Inference with Graphical Nonlinear Knockoffs.

Publications

RANK: Large-Scale Inference with Graphical Nonlinear Knockoffs.

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