arXiv 1909.008532019-09-02cs.LGstat.ML

多尺度网络结构回归的进一步结果

Further results on structured regression for multi-scale networks

University of Niš（尼什大学）；University of Kragujevac（克拉古耶瓦茨大学）；Temple University（天普大学）

Milan Bašić, Branko Arsić, Zoran Obradović

摘要：

高斯条件随机场（Gaussian Conditional Random Fields，GCRF）作为一种结构化回归模型，其设计目的是以牺牲执行时间为代价，同时考虑对象的相似性和非结构化预测器的输出，以达到比非结构化预测器更高的回归精度。与大多数结构模型一样，GCRF模型不能很好地扩展大型网络。其中一种方法是在因子图上执行计算（如果可能的话），而不是在整个图上执行计算，这在计算上更有效。图的克罗内克积似乎是图分解的自然选择。然而，这个想法是不直接适用于GCRF，因为表征的克罗内克积的图，GCRF是基于，从其因子图的谱的拉普拉斯谱一直是一个悬而未决的问题。在本文中，我们应用新的估计的拉普拉斯特征值和特征向量，并实现了高的预测精度的模型，而模型的计算复杂性，相比于原来的GCRF模型，从$O(n_{1}^{3}n_{2}^{3})$改善到$O(n_{1}^{3} + n_{2}^{3})$。此外，我们还研究了具有非Kronecker图的GCRF模型，其中该模型包括寻找初始图的最近Kronecker积。虽然所提出的模型更复杂，但它们也实现了较高的预测精度，同时与原始GCRF模型相比，执行时间仍然要好得多。所提出的模型的有效性的特点是三种类型的随机网络，其中所提出的模型始终比以前提出的多尺度网络GCRF模型更准确[杰西玻璃和佐兰奥布拉多维奇。多尺度网络上的结构化回归。IEEE Intelligent Systems，32（2）：23-30，2017。

英文摘要：

Gaussian Conditional Random Fields (GCRF), as a structured regression model, is designed to achieve higher regression accuracy than unstructured predictors at the expense of execution time, taking into account the objects similarities and the outputs of unstructured predictors simultaneously. As most structural models, the GCRF model does not scale well with large networks. One of the approaches consists of performing calculations on factor graphs (if it is possible) rather than on the full graph, which is more computationally efficient. The Kronecker product of the graphs appears to be a natural choice for a graph decomposition. However, this idea is not straightforwardly applicable for GCRF, since characterizing a Laplacian spectrum of the Kronecker product of graphs, which GCRF is based on, from spectra of its factor graphs has remained an open problem. In this paper we apply new estimations for the Laplacian eigenvalues and eigenvectors, and achieve high prediction accuracy of the proposed models, while the computational complexity of the models, compared to the original GCRF model, is improved from $O(n_{1}^{3}n_{2}^{3})$ to $O(n_{1}^{3} + n_{2}^{3})$. Furthermore, we study the GCRF model with a non-Kronecker graph, where the model consists of finding the nearest Kronecker product of graph for an initial graph. Although the proposed models are more complex, they achieve high prediction accuracy too, while the execution time is still much better compare to the original GCRF model. The effectiveness of the proposed models is characterized on three types of random networks where the proposed models were consistently away more accurate than the previously presented GCRF model for multiscale networks [Jesse Glass and Zoran Obradovic. Structured regression on multiscale networks. IEEE Intelligent Systems, 32(2):23-30, 2017.].

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文