Towards Understanding Evolving Patterns in Sequential Data

In many machine learning tasks, data is inherently sequential. Most existing algorithms learn from sequential data in an auto-regressive manner, which predicts the next unseen data point based on the observed sequence, implicitly assuming the presence of an \emph{evolving pattern} embedded in the data that can be leveraged. However, identifying and assessing evolving patterns in learning tasks often relies on subjective judgments rooted in the prior knowledge of human experts, lacking a standardized quantitative measure. Furthermore, such measures enable us to determine the suitability of employing sequential models effectively and make informed decisions on the temporal order of time series data, and feature/data selection processes. To address this issue, we introduce the Evolving Rate (EvoRate), which quantitatively approximates the intensity of evolving patterns in the data with Mutual Information. Furthermore, in some temporal data with neural mutual information estimations, we only have snapshots at different timestamps, lacking correspondence, which hinders EvoRate estimation. To tackle this challenge, we propose EvoRate$_\mathcal{W}$, aiming to establish correspondence with optimal transport for estimating the first-order EvoRate. Experiments on synthetic and real-world datasets including images and tabular data validate the efficacy of our EvoRate.