Consistent community detection in inter-layer dependent multi-layer networks

Community detection in multi-layer networks, which aims at finding groups of nodes with similar connective patterns among all layers, has attracted tremendous interests in multi-layer network analysis. Most existing methods are extended from those for single-layer networks, which assume that different layers are independent. In this paper, we propose a novel community detection method in multi-layer networks with inter-layer dependence, which integrates the stochastic block model (SBM) and the Ising model. The community structure is modeled by the SBM model and the inter-layer dependence is incorporated via the Ising model. An efficient alternative updating algorithm is developed to tackle the resultant optimization task. Moreover, the asymptotic consistencies of the proposed method in terms of both parameter estimation and community detection are established, which are supported by extensive simulated examples and a real example on a multi-layer malaria parasite gene network.</p

A Generic Sure Independence Screening Procedure

<p>Extracting important features from ultra-high dimensional data is one of the primary tasks in statistical learning, information theory, precision medicine, and biological discovery. Many of the sure independent screening methods developed to meet these needs are suitable for special models under some assumptions. With the availability of more data types and possible models, a model-free generic screening procedure with fewer and less restrictive assumptions is desirable. In this article, we propose a generic nonparametric sure independence screening procedure, called BCor-SIS, on the basis of a recently developed universal dependence measure: Ball correlation. We show that the proposed procedure has strong screening consistency even when the dimensionality is an exponential order of the sample size without imposing sub-exponential moment assumptions on the data. We investigate the flexibility of this procedure by considering three commonly encountered challenging settings in biological discovery or precision medicine: iterative BCor-SIS, interaction pursuit, and survival outcomes. We use simulation studies and real data analyses to illustrate the versatility and practicability of our BCor-SIS method. Supplementary materials for this article are available online.</p

Interferogram From SLC data without coherence optimization.

<p>Interferogram From SLC data without coherence optimization.</p

Range and azimuth frequency distribution of level 0 data before processing.

<p>Range and azimuth frequency distribution of level 0 data before processing.</p

Robust Estimation Using Modified Huber’s Functions With New Tails

<p>It is traditionally believed that robustness is obtained by sacrificing efficiency. Estimators with high breakdown point and high efficiency are therefore highly desirable. We investigate a new estimation procedure based on Huber’s robust approach, but with tail functions replaced by the exponential squared loss. The tuning parameters are data-dependent to achieve high efficiency even in nonnormal cases. In the regression framework, we show that our hybrid estimator is of high efficiency, reaching the highest asymptotic breakdown point of 50%. We have also established the <math><msqrt><mi>n</mi></msqrt></math>-consistency and asymptotic normality of our estimator under regularity conditions. Extensive numerical studies are carried out to compare the performances of our method and other existing methods in terms of the standard errors and relative efficiency, and the results reveal that the newly proposed method has smaller standard errors and higher relative efficiency than its competitors when the sample size is sufficiently large. Finally, we present three real examples for demonstration. Supplementary materials for the article are available online.</p

Doppler difference for flat ground and mountain area.

<p>Doppler difference for flat ground and mountain area.</p

Statistical values of coherence in the experiment results.

<p>Statistical values of coherence in the experiment results.</p

Interferogram From Level 0 Data with coherence optimization.

<p>Interferogram From Level 0 Data with coherence optimization.</p

Coherence map from level 0 data with consistent doppler parameters.

<p>Coherence map from level 0 data with consistent doppler parameters.</p

Decorrelation by baseline.

<p>Decorrelation by baseline.</p