论文标题
具有平稳结构变化的图形模型的有效变分贝叶斯学习
Efficient Variational Bayes Learning of Graphical Models with Smooth Structural Changes
论文作者
论文摘要
在各种社会，金融，生物学和工程系统中，估算时变图形模型至关重要，因为可以使用此类网络的发展来发现趋势，检测异常，预测脆弱性并评估干预措施的影响。现有方法需要广泛调整控制图形稀疏性和时间平滑度的参数。此外，这些方法在计算上是繁重的，$ p $变量的时间复杂性$ O（NP^3）$和$ n $时间点。作为一种补救措施，我们提出了一种低复杂性的无调贝叶斯方法，名为Bass。具体而言，我们将时间依赖性的尖峰和斜纹先验施加在图表上，使它们在时间上稀疏且变化平稳。然后，得出一种变分推理算法以自动从数据中学习图形结构。拥有伪样和平均场近似值，低音的时间复杂性仅为$ o（np^2）$。此外，通过识别与时变图形模型的频域相似之处，我们表明鲈鱼可以扩展到学习频率变化的逆光谱密度矩阵，并产生用于多元固定时间序列的图形模型。合成数据和实际数据的数值结果表明，低音可以更好地恢复潜在的真实图，同时比现有方法更有效，尤其是对于高维情况。
Estimating time-varying graphical models are of paramount importance in various social, financial, biological, and engineering systems, since the evolution of such networks can be utilized for example to spot trends, detect anomalies, predict vulnerability, and evaluate the impact of interventions. Existing methods require extensive tuning of parameters that control the graph sparsity and temporal smoothness. Furthermore, these methods are computationally burdensome with time complexity $O(NP^3)$ for $P$ variables and $N$ time points. As a remedy, we propose a low-complexity tuning-free Bayesian approach, named BASS. Specifically, we impose temporally-dependent spike-and-slab priors on the graphs such that they are sparse and varying smoothly across time. A variational inference algorithm is then derived to learn the graph structures from the data automatically. Owning to the pseudo-likelihood and the mean-field approximation, the time complexity of BASS is only $O(NP^2)$. Additionally, by identifying the frequency-domain resemblance to the time-varying graphical models, we show that BASS can be extended to learning frequency-varying inverse spectral density matrices, and yields graphical models for multivariate stationary time series. Numerical results on both synthetic and real data show that that BASS can better recover the underlying true graphs, while being more efficient than the existing methods, especially for high-dimensional cases.
