Topological Bayesian Optimization with Persistence Diagrams-猫眼课题宝

DOI：

10.3233/faia200255

发表时间：

2019-02

期刊：

ArXiv

影响因子：

通讯作者：

中科院分区：

其他

文献类型：

作者：

T. Shiraishi;Tam Le;H. Kashima;M. Yamada

寻找黑箱函数的最优参数对于寻找稳定的材料结构和最优的神经网络结构具有重要意义，而贝叶斯优化算法被广泛用于此目的。然而，现有的贝叶斯优化算法大多只能处理矢量数据，无法处理复杂的结构化数据。本文提出了拓扑贝叶斯优化算法，它可以利用\emph{拓扑信息}从结构化数据中有效地找到最优解。更具体地说，为了将贝叶斯优化应用于结构化数据，我们从结构中提取有用的拓扑信息，并度量结构之间的适当相似性。为此，我们利用了持久同源，这是一种最近应用于机器学习的拓扑数据分析方法。此外，我们提出了贝叶斯优化算法，该算法可以处理多种类型的拓扑信息，通过对持久性图使用核的线性组合。通过实验，我们发现与随机搜索基线和图贝叶斯优化算法相比，持久同源提取的拓扑信息有助于更有效地搜索最优结构。

Finding an optimal parameter of a black-box function is important for searching stable material structures and finding optimal neural network structures, and Bayesian optimization algorithms are widely used for the purpose. However, most of existing Bayesian optimization algorithms can only handle vector data and cannot handle complex structured data. In this paper, we propose the topological Bayesian optimization, which can efficiently find an optimal solution from structured data using \emph{topological information}. More specifically, in order to apply Bayesian optimization to structured data, we extract useful topological information from a structure and measure the proper similarity between structures. To this end, we utilize persistent homology, which is a topological data analysis method that was recently applied in machine learning. Moreover, we propose the Bayesian optimization algorithm that can handle multiple types of topological information by using a linear combination of kernels for persistence diagrams. Through experiments, we show that topological information extracted by persistent homology contributes to a more efficient search for optimal structures compared to the random search baseline and the graph Bayesian optimization algorithm.

Topological Bayesian Optimization with Persistence Diagrams

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