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. 2014 Jun;101(2):253-268.
doi: 10.1093/biomet/asu009.

Direct estimation of differential networks

Sihai Dave Zhao  1 , T Tony Cai  2 , Hongzhe Li  1
Affiliations

Direct estimation of differential networks

Sihai Dave Zhao et al. Biometrika. 2014 Jun.

Abstract

It is often of interest to understand how the structure of a genetic network differs between two conditions. In this paper, each condition-specific network is modeled using the precision matrix of a multivariate normal random vector, and a method is proposed to directly estimate the difference of the precision matrices. In contrast to other approaches, such as separate or joint estimation of the individual matrices, direct estimation does not require those matrices to be sparse, and thus can allow the individual networks to contain hub nodes. Under the assumption that the true differential network is sparse, the direct estimator is shown to be consistent in support recovery and estimation. It is also shown to outperform existing methods in simulations, and its properties are illustrated on gene expression data from late-stage ovarian cancer patients.

Keywords: Differential network; Graphical model; High dimensionality; Precision matrix.

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Figures

Figure 1
Figure 1
Receiver operating characteristic curves for support recovery of Δ0=ΣY−1−ΣX−1; solid line: thresholded direct estimator; dashed line: thresholded fused graphical lasso estimator with λ1 = 0; dotted line: fused graphical lasso estimator with λ1 = 0 · 1
Figure 2
Figure 2
Estimates of the differential networks between ovarian cancer subtypes. The direct and fused graphical lasso estimators were thresholded and the separate estimator was further sparsified; see text. Black edges show increase in conditional dependency from ovarian cancer subtype C1 to subtypes C2–C6, gray edges show decrease. (a)–(c): KEGG 04350, TGF-β pathway, (d)–(f): KEGG 04210, Apoptosis pathway. (a)–(e) tuned using L∞ with (5), (f) tuned with λ1 = 0 and λ2 to give the same number of edges as (d); see text. Separate estimator not shown for apoptosis pathway.
See this image and copyright information in PMC

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