network deconvolution as a general method to distinguish direct dependencies in networks

network deconvolution as a general method to distinguish direct dependencies in networks

MIT group; Accepted Jun. 2013; Nature Biotechnology

Presented by Haicang ZhangFeb.24 2013

Outline• Motivation• Basic idea of Method• Applications and results

– gene regulatory networks– protein structural constrains – co-authorship collaboration relationships

• Methods in detail – framework – convergence – computational complexity

• Discussion

Motivation

• Networks are usually to represent the interdependencies among variables.

• Indirect dependencies occurs owing to transitive effects of correlations.

• It is necessary to separate the direct dependence from the indirect ones.

Motivation

• Current method– partial correlations method– graphical models– other methods

Basic idea of method

• i

Basic idea of method

• i

Applications and results- protein structural constraints

• i

Applications and results- protein structural constraints

• i

Methods in detail-framework

• s

Methods in detail-intuition

• The intuition of this method– Network de-convolution can be viewed as a

nonlinear filter that is applied to eigenvalues of the observed dependency matrix.

– In general, ND decreases magnitudes of large positive eigenvalues of the observed matrix since transitivity inflate these positive eigenvalues.

Methods in detail-intuition

• i

Methods in detail-convergences

• converges iff the largest absolute value of eigenvalues of G_dir < 1.

• scale G_obs

• if beta < 1 , the largest absolute value of eigenvalues < 1

• Then,

Methods in detail-convergences

• i

Discussion

• Network de-convolution provides a general framework for computing direct dependencies in a network by use of observed similarities.

• It can recognize and remove spurious transitive edges due to indirect effects, decrease edge weights that are overestimated owing to indirect relationships, and assign edge weights corresponding to direct dependencies to the remaining edges