相关论文: Wasserstein Geometry of Information Loss in Nonlin…

The celebrated Takens' embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical theorem assumes that the underlying system is deterministic…

The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few…

Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete…

In this paper, we propose Wasserstein Isometric Mapping (Wassmap), a nonlinear dimensionality reduction technique that provides solutions to some drawbacks in existing global nonlinear dimensionality reduction algorithms in imaging…

Identifying the qualitative changes in time-series data provides insights into the dynamics associated with such data. Such qualitative changes can be detected through topological approaches, which first embed the data into a…

Analyzing data from paleoclimate archives such as tree rings or lake sediments offers the opportunity of inferring information on past climate variability. Often, such data sets are univariate and a proper reconstruction of the system's…

In nonlinear time series analysis and dynamical systems theory, Takens' embedding theorem states that the sliding window embedding of a generic observation along trajectories in a state space, recovers the region traversed by the dynamics.…

The celebrated Takens' embedding theorem concerns embedding an attractor of a dynamical system in a Euclidean space of appropriate dimension through a generic delay-observation map. The embedding also establishes a topological conjugacy. In…

To generate coherent responses, language models infer unobserved meaning from their input text sequence. One potential explanation for this capability arises from theories of delay embeddings in dynamical systems, which prove that…

In recent years, self-supervised learning has played a pivotal role in advancing machine learning by allowing models to acquire meaningful representations from unlabeled data. An intriguing research avenue involves developing…

We introduce a novel geometry-informed irreversible perturbation that accelerates convergence of the Langevin algorithm for Bayesian computation. It is well documented that there exist perturbations to the Langevin dynamics that preserve…

A time-delay embedding (TDE), grounded in the framework of Takens's Theorem, provides a mechanism to represent and analyze the inherent dynamics of time-series data. Recently, topological data analysis (TDA) methods have been applied to…

The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…

A new and accurate method to determine the time delay and embedding dimension for state space reconstruction of a high dimensional system from a scalar time series using time delay embedding is presented. The time delay is obtained to…

In non-destructive imaging the information about the spatial pattern of a samples interior has to be transferred to the sample surface by certain waves, e.g. ultrasound or electromagnetic waves. At the sample surface these waves can be…

Prediction models that capture and use the structure of state-space dynamics can be very effective. In practice, however, one rarely has access to full information about that structure, and accurate reconstruction of the dynamics from…

Irregularly sampled time series (ISTS), characterized by non-uniform time intervals with natural missingness, are prevalent in real-world applications. Existing approaches for ISTS modeling primarily rely on observed values to impute…

Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…

In the analysis of complex, nonlinear time series, scientists in a variety of disciplines have relied on a time delayed embedding of their data, i.e. attractor reconstruction. The process has focused primarily on heuristic and empirical…

Experimental measurements of physical systems often have a limited number of independent channels, causing essential dynamical variables to remain unobserved. However, many popular methods for unsupervised inference of latent dynamics from…