Abstract
Detecting the change of biological interaction networks is of great importance in biological and medical research. We proposed a simple loss function, named as CrossFDTL, to identify the network change or differential network by estimating the difference between two precision matrices under Gaussian assumption. The CrossFDTL is a natural fusion of the D-trace loss for the considered two networks by imposing the $\ell _{1}$ penalty to the differential matrix to ensure sparsity. The key point of our method is to utilize the cross variables, which correspond to the sum and difference of two precision matrices instead of using their original forms. Moreover, we developed an efficient minimization algorithm for the proposed loss function and further rigorously proved its convergence. Numerical results showed that our method outperforms the existing methods in both accuracy and convergence speed for the simulated and real data.
Highlights
Network inference based on the observed biological data is a fundamental topic in network biology along with the rapid developments of high-throughput technologies
Under the Gaussian assumption, the network inference problem is equivalent to determinng the sparsity pattern of the precision matrix, which is consistent with the covariance selection problem [4]
We remark that the D-trace loss function considered in Yuan et al [31] is not suitable for coordinate descent method since the sparsity is not preserved during the updates
Summary
Network inference based on the observed biological data is a fundamental topic in network biology along with the rapid developments of high-throughput technologies. A typical approach in gene regulatory network inference is to utilize the Gaussian graphical model [18]. D-trace loss function for differential network to directly estimate Δ with lasso penalty Their computation time is usually in the order of hours or days even when p ∼ O(103). The key novelty of our method is to utilize a transformed formulation of the loss through cross variables, which correspond to the sum and difference of two precision matrices instead of using their original form. We call it CrossFDTL formulation for the differential network inference.
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