时变离散马尔可夫随机场的稀疏估计
Sparsistent Estimation of Time-Varying Discrete Markov Random Fields
摘要：
网络模型已经流行用于建模和表示观察变量之间的复杂关系和依赖关系。当数据来自动态随机过程时，单个静态网络模型不能充分捕获瞬时依赖性，例如生物体整个发育周期的基因调控依赖性。Kolar et al（2010 b）提出了一种基于核平滑l1惩罚逻辑斯谛回归的方法，用于从时间序列观测数据中收集的节点观测估计时变网络。在本文中，我们建立的条件下，所提出的方法一致地恢复时变网络的结构。这项工作补充了以往的经验研究结果，提供了良好的理论保证，建议的估计程序。为了完整性，我们在本文中包括数值模拟。
英文摘要：
Network models have been popular for modeling and representing complex relationships and dependencies between observed variables. When data comes from a dynamic stochastic process, a single static network model cannot adequately capture transient dependencies, such as, gene regulatory dependencies throughout a developmental cycle of an organism. Kolar et al (2010b) proposed a method based on kernel-smoothing l1-penalized logistic regression for estimating time-varying networks from nodal observations collected from a time-series of observational data. In this paper, we establish conditions under which the proposed method consistently recovers the structure of a time-varying network. This work complements previous empirical findings by providing sound theoretical guarantees for the proposed estimation procedure. For completeness, we include numerical simulations in the paper.
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