论文标题
正常的捆绑引导程序
Normal-bundle Bootstrap
论文作者
论文摘要
数据集的概率模型通常表现出显着的几何结构。这种现象是在多种分布假设中概括的，可以在概率学习中利用。在这里，我们提供了正常的捆绑引导程序（NBB），该方法生成了保留给定数据集的几何结构的新数据。受到差异几何形状中流形学习和概念的算法的启发，我们的方法将潜在的概率度量分解为在正常空间上学习的数据歧管和条件度量的边缘化度量。该算法将数据歧管估计为密度脊，并通过引导投影向量并将它们添加到山脊中来构建新数据。我们将我们的方法应用于密度脊和相关统计数据的推断，以及数据扩展以减少过度拟合。
Probabilistic models of data sets often exhibit salient geometric structure. Such a phenomenon is summed up in the manifold distribution hypothesis, and can be exploited in probabilistic learning. Here we present normal-bundle bootstrap (NBB), a method that generates new data which preserve the geometric structure of a given data set. Inspired by algorithms for manifold learning and concepts in differential geometry, our method decomposes the underlying probability measure into a marginalized measure on a learned data manifold and conditional measures on the normal spaces. The algorithm estimates the data manifold as a density ridge, and constructs new data by bootstrapping projection vectors and adding them to the ridge. We apply our method to the inference of density ridge and related statistics, and data augmentation to reduce overfitting.
