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Hurst Exponent has been widely used in different fields as a measure of long range dependence in time series. It has been studied in hydrology and geophysics, economics and finance, and recently, it is still a hot topic in the different…
The Hurst exponent is a significant metric for characterizing time sequences with long-term memory property and it arises in many fields. The available methods for estimating the Hurst exponent can be categorized into time-domain and…
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…
This paper introduces a comprehensive unified framework for constructing multi-view diffusion geometries through intertwined multi-view diffusion trajectories (MDTs), a class of inhomogeneous diffusion processes that iteratively combine the…
Diffusion models have become a central tool in deep generative modeling, but standard formulations rely on a single network and a single diffusion schedule to transform a simple prior, typically a standard normal distribution, into the…
Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent…
In order to interpret and explain the physiological signal behaviors, it can be interesting to find some constants among the fluctuations of these data during all the effort or during different stages of the race (which can be detected…
Diffusion distillation provides an effective approach for learning lightweight and few-steps diffusion models with efficient generation. However, evaluating their generalization remains challenging: theoretical metrics are often impractical…
Persistence diagrams (PD)s play a central role in topological data analysis. This analysis requires computing distances among such diagrams such as the $1$-Wasserstein distance. Accurate computation of these PD distances for large data sets…
Topological Data Analysis (TDA) is an approach to handle with big data by studying its shape. A main tool of TDA is the persistence diagram, and one can use it to compare data sets. One approach to learn on the similarity between two…
We present a purely deep neural network-based approach for estimating long memory parameters of time series models that incorporate the phenomenon of long-range dependence. Parameters, such as the Hurst exponent, are critical in…
Statistics of the Hurst scaling exponents calculated with the use of two methods: recently introduced Detrended Moving Average Analysis(DMA) and Detrended Fluctuation Analysis (DFA)are compared. Analysis is done for artificial stochastic…
Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence…
Wasserstein Discriminant Analysis (WDA) is a new supervised method that can improve classification of high-dimensional data by computing a suitable linear map onto a lower dimensional subspace. Following the blueprint of classical Linear…
Dimensionality reduction is critical across various domains of science including neuroscience. Probabilistic Principal Component Analysis (PPCA) is a prominent dimensionality reduction method that provides a probabilistic approach unlike…
Topological Data Analysis (TDA) has emerged as a powerful framework for extracting robust and interpretable features from noisy high-dimensional data. In the context of Social Choice Theory, where preference profiles and collective…
We consider diffusion-controlled release of particles from $d$-dimensional radially-symmetric geometries. A quantity commonly used to characterise such diffusive processes is the proportion of particles remaining within the geometry over…
We propose a novel algorithm for supervised dimensionality reduction named Manifold Partition Discriminant Analysis (MPDA). It aims to find a linear embedding space where the within-class similarity is achieved along the direction that is…
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…
Quantifying degrees of fusion and separability between data groups in representation space is a fundamental problem in representation learning, particularly under domain shift. A meaningful metric should capture fusion-altering factors like…