论文标题
内核脊回归使用重要性抽样,并应用于地震反应预测
Kernel Ridge Regression Using Importance Sampling with Application to Seismic Response Prediction
论文作者
论文摘要
可扩展的内核方法(包括内核脊回归)通常使用Nystrom方法依赖于低级别矩阵近似值,nystrom方法涉及从大数据集中选择地标点。选择地标的现有方法通常是计算要求的,因为它们需要在输入或特征空间中操纵和执行大型矩阵的计算。在本文中,我们的贡献是双重的。第一个贡献是提出一种新颖的地标选择方法,该方法使用有效的两步方法促进多样性。我们的地标选择技术遵循一个粗略的策略,其中第一步通过一次通过整个数据来计算重要性得分。第二步在构造的核心上执行K-均值聚类,以将所获得的质心用作地标。因此,引入的方法在准确性和效率之间提供了可调整的权衡。我们的第二个贡献是使用内核方法的新应用来研究几种具有里程碑意义的选择技术的性能,以预测由于地震载荷和物质不确定性而导致的结构响应。我们的实验表现出针对基准的提议地标选择方案的优点。
Scalable kernel methods, including kernel ridge regression, often rely on low-rank matrix approximations using the Nystrom method, which involves selecting landmark points from large data sets. The existing approaches to selecting landmarks are typically computationally demanding as they require manipulating and performing computations with large matrices in the input or feature space. In this paper, our contribution is twofold. The first contribution is to propose a novel landmark selection method that promotes diversity using an efficient two-step approach. Our landmark selection technique follows a coarse to fine strategy, where the first step computes importance scores with a single pass over the whole data. The second step performs K-means clustering on the constructed coreset to use the obtained centroids as landmarks. Hence, the introduced method provides tunable trade-offs between accuracy and efficiency. Our second contribution is to investigate the performance of several landmark selection techniques using a novel application of kernel methods for predicting structural responses due to earthquake load and material uncertainties. Our experiments exhibit the merits of our proposed landmark selection scheme against baselines.