论文标题
通过Cantor嵌入和Wasserstein距离探索预测状态
Exploring Predictive States via Cantor Embeddings and Wasserstein Distance
论文作者
论文摘要
随机过程的预测状态是一种非参数且可解释的结构，在许多建模范式中具有相关性。从时间序列数据中，自我监督重建预测状态的最新进展重点是使用繁殖内核希尔伯特空间。在这里，我们检查了如何使用Wasserstein距离来检测符号数据中的预测等效性。我们使用基于基于基础几何形状的cantor的有限维嵌入序列的序列嵌入分布之间的分布之间的瓦斯恒星距离（“预测”）。我们表明，通过层次聚类和尺寸缩小使用所得几何形状进行探索性数据分析提供了对从相对简单（例如，有限态态隐藏的马可福音模型）到非常复杂（例如，Infinite state Index index index的语法）的过程的时间结构。
Predictive states for stochastic processes are a nonparametric and interpretable construct with relevance across a multitude of modeling paradigms. Recent progress on the self-supervised reconstruction of predictive states from time-series data focused on the use of reproducing kernel Hilbert spaces. Here, we examine how Wasserstein distances may be used to detect predictive equivalences in symbolic data. We compute Wasserstein distances between distributions over sequences ("predictions"), using a finite-dimensional embedding of sequences based on the Cantor for the underlying geometry. We show that exploratory data analysis using the resulting geometry via hierarchical clustering and dimension reduction provides insight into the temporal structure of processes ranging from the relatively simple (e.g., finite-state hidden Markov models) to the very complex (e.g., infinite-state indexed grammars).
