Cross-covariance matrix estimation for directional integration of dual-omics data

초록

Cross-covariance matrix ${\mathbf{\Sigma }}_{\mathbf{XY}}$ Sigma XY refers to the off-diagonal submatrix of the covariance matrix of $\mathbf{Z}=\left(\mathbf{X}{<}^{>}\top ,\mathbf{Y}{<}^{>}\top \right){<}^{>}\top$ Z=(X inverted perpendicular,Y inverted perpendicular)inverted perpendicular, which is an important statistical summary in integrative data analysis. In this work, we propose a two-stage estimator of ${\mathbf{\Sigma }}_{\mathbf{XY}}$ Sigma XY when prior knowledge informs that elements of $\mathbf{X}$ X are members of overlapping groups, and each element of $\mathbf{Y}$ Y is correlated with groups of variables in $\mathbf{X}$ X, a common scenario in multi-omics molecular data. The proposed estimator has consistency in Frobenius norm at a sharp convergence rate like other sparse covariance matrix estimators. Simulation studies confirm the advantage of the method in comparison to existing estimators. We also demonstrate that the non-zero cross-covariance elements successfully recaptured previously annotated regulatory relationships between the protein abundance of transcription factor genes and the mRNA expression of their target genes in two dual-omics cancer data sets, where an alternative approach did not attain the same success.

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