Network estimation from multi-variate point process or time series data is a problem of fundamental importance. Prior work has focused on parametric approaches that require a known parametric model, which makes estimation procedures less robust to model mis-specification, non-linearities and heterogeneities. In this paper, we develop a semi-parametric approach based on the monotone single-index multi-variate autoregressive model (SIMAM) which addresses these challenges. We provide theoretical guarantees for dependent data and an alternating projected gradient descent algorithm. Significantly we do not explicitly assume mixing conditions on the process (although we do require conditions analogous to restricted strong convexity) and we achieve rates of the form $O(T^{-\frac{1}{3}} \sqrt{s\log(TM)})$ (optimal in the independent design case) where $s$ is the threshold for the maximum in-degree of the network that indicates the sparsity level, $M$ is the number of actors and $T$ is the number of time points. In addition, we demonstrate the superior performance both on simulated data and two real data examples where our SIMAM approach out-performs state-of-the-art parametric methods both in terms of prediction and network estimation.
翻译:从多变点进程或时间序列数据得出的网络估计是一个根本性的问题。先前的工作侧重于需要已知的参数模型的参数学方法,这使得估计程序不那么健全,无法模拟错误的特性、非线性和异质性。在本文中,我们根据单体单体单指数多变性自动递减模型(SIMAM)制定了半参数法,以应对这些挑战。我们为依赖数据和交替预测梯度下降算法提供理论保证。我们没有明确假定该过程的混合条件(尽管我们确实需要类似于限制强烈共性的条件),并且我们达到了表格$(O-\\\frac{1\%3\\\\\\\\\\\\ \ \ qrt{s\log}}(在独立设计案例中是最佳的)的半参数。我们为显示宽度水平的网络的最大度的门槛是$, $是行为者的数量,$T$是时间点。此外,我们还在模拟模型数据和两个模型中展示了S-AM预测方法的优劣性业绩,在S-marg-al as-al asim a y y y y work y at at at ex at at suggid ex ex ex subild ex ex ex ex ex ide subit at at at at subit sublement at sublement sublement sublement at sublement at sublement at subild thes.