Estimating networks with jumps.
Estimating networks with jumps.
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DOI：
10.1214/12-ejs739
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发表时间：
2012
影响因子：
1.1
通讯作者：
Xing EP
中科院分区：
文献类型：
--
作者：
Kolar M;Xing EP
我们研究了在一段时间内收集的数据（如相互作用的个体的社会状态或基因网络的微阵列表达谱）基础上估计时变系数和变结构（VCVS）图形模型的问题，而不是当前结构估计文献中广泛考虑的不变模型的i.i.d.数据。特别地，我们考虑模型以分段恒定方式发展的场景。我们提出了一种通过最小化时间平滑L1惩罚回归来估计图形模型结构的方法，该方法允许联合估计VCVS模型的分区边界和分区每个块上的稀疏精度矩阵的系数。针对合成凸优化问题，提出了一种高度可伸缩的近端梯度方法；首次建立了这种估计器的稀疏估计条件以及分区边界和网络结构的收敛速度。
We study the problem of estimating a temporally varying coefficient and varying structure (VCVS) graphical model underlying data collected over a period of time, such as social states of interacting individuals or microarray expression profiles of gene networks, as opposed to i.i.d. data from an invariant model widely considered in current literature of structural estimation. In particular, we consider the scenario in which the model evolves in a piece-wise constant fashion. We propose a procedure that estimates the structure of a graphical model by minimizing the temporally smoothed L1 penalized regression, which allows jointly estimating the partition boundaries of the VCVS model and the coefficient of the sparse precision matrix on each block of the partition. A highly scalable proximal gradient method is proposed to solve the resultant convex optimization problem; and the conditions for sparsistent estimation and the convergence rate of both the partition boundaries and the network structure are established for the first time for such estimators.