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流形时间序列的平稳性AI 解读

In modern interdisciplinary research, manifold time series data have been garnering more attention. A critical question in analyzing such data is “stationarity”, which reflects the underlying dynamic behavior and is crucial across various fields like cell biology, neuroscience and empirical finance. Yet, there has been an absence of a formal definition of stationarity that is tailored to manifold time series. This work bridges this gap by proposing the first definitions of…

Wasserstein 回归AI 解读

The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the Wasserstein metric, we develop a class of regression models for such data, where random distributions serve as predictors and the responses are either also distributions or scalars. To define this regression model, we use the geometry of…