基于 Graphical LASSO 的时间序列模型选择
Graphical LASSO Based Model Selection for Time Series
AI总结：
提出面向高维平稳时间序列的非参数 gLASSO 图模型选择方法，用 ADMM 求解 l1 正则化近似似然，并给出高斯过程下错误识别 CIG 的概率界与实验验证。
摘要：
我们提出了一种新颖的图模型选择（GMS）方案，用于处理高维平稳时间序列或离散时间过程。该方法基于 graphical LASSO（gLASSO）的自然推广；gLASSO 最初是为基于独立同分布（i.i.d.）样本的 GMS 而提出的，而本文方法从有限长度观测中估计时间序列的条件独立图（CIG）。用于时间序列的 gLASSO 被定义为一个 l1 正则化最大（近似）似然问题的解。我们使用交替方向乘子法（ADMM）求解这一优化问题。我们的方法是非参数的，因为我们不为观测过程假设有限维参数模型（例如自回归模型）。相反，我们要求该过程在谱域中具有充分的光滑性。对于高斯过程，我们通过推导算法未能正确识别 CIG 的概率上界，从理论上刻画了方法的性能。数值实验证明，我们的方法能够利用有限数量的样本恢复正确的 CIG。
英文摘要：
We propose a novel graphical model selection (GMS) scheme for high-dimensional stationary time series or discrete time process. The method is based on a natural generalization of the graphical LASSO (gLASSO), introduced originally for GMS based on i.i.d. samples, and estimates the conditional independence graph (CIG) of a time series from a finite length observation. The gLASSO for time series is defined as the solution of an l1-regularized maximum (approximate) likelihood problem. We solve this optimization problem using the alternating direction method of multipliers (ADMM). Our approach is nonparametric as we do not assume a finite dimensional (e.g., an autoregressive) parametric model for the observed process. Instead, we require the process to be sufficiently smooth in the spectral domain. For Gaussian processes, we characterize the performance of our method theoretically by deriving an upper bound on the probability that our algorithm fails to correctly identify the CIG. Numerical experiments demonstrate the ability of our method to recover the correct CIG from a limited amount of samples.
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