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Manifold learning techniques for dynamical systems and time series have shown their utility for a broad spectrum of applications in recent years. While these methods are effective at learning a low-dimensional representation, they are often insufficient for visualizing the global and local structure of the data. In this paper, we present DIG (Dynamical Information Geometry), a visualization method for multivariate time series data that extracts an information geometry from a diffusion framework. Specifically, we implement a novel group of distances in the context of diffusion operators, which may be useful to reveal structure in the data that may not be accessible by the commonly used diffusion distances. Finally, we present a case study applying our visualization tool to EEG data to visualize sleep stages.
This study investigates the theoretical foundations of t-distributed stochastic neighbor embedding (t-SNE), a popular nonlinear dimension reduction and data visualization method. A novel theoretical framework for the analysis of t-SNE based on the gr
Stochastic linear bandits with high-dimensional sparse features are a practical model for a variety of domains, including personalized medicine and online advertising. We derive a novel $Omega(n^{2/3})$ dimension-free minimax regret lower bound for s
One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations lie on a low
The complexity of human cancer often results in significant heterogeneity in response to treatment. Precision medicine offers potential to improve patient outcomes by leveraging this heterogeneity. Individualized treatment rules (ITRs) formalize prec
A number of universally consistent dependence measures have been recently proposed for testing independence, such as distance correlation, kernel correlation, multiscale graph correlation, etc. They provide a satisfactory solution for dependence test