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This work presents a novel framework for time series analysis using entropic measures based on the kernel density estimate (KDE) of the time series' Takens' embeddings. Using this framework we introduce two distinct analytical tools: (1) a…
Time series analysis is crucial in fields like finance, economics, environmental science, and biomedical engineering, aiding in forecasting, pattern identification, and understanding underlying mechanisms. While traditional time-domain…
This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for…
This paper explores the utility of diffusion-based models for anomaly detection, focusing on their efficacy in identifying deviations in both compact and high-resolution datasets. Diffusion-based architectures, including Denoising Diffusion…
Recent success of diffusion models has inspired a surge of interest in developing sampling techniques using reverse diffusion processes. However, accurately estimating the drift term in the reverse stochastic differential equation (SDE)…
We propose a method for computing the transfer entropy between time series using Ulam's approximation of the Perron-Frobenius (transfer) operator associated with the map generating the dynamics. Our method differs from standard transfer…
We introduce a graph-signal generalisation of Sample Entropy, denoted SampEn$_{G}$, to quantify irregularity of graph signals on a continuous state space, complementing existing methods on symbolic dynamics. Our approach replaces the…
The proliferation and ubiquity of temporal data across many disciplines has sparked interest for similarity, classification and clustering methods specifically designed to handle time series data. A core issue when dealing with time series…
Differential equations are pivotal in modeling and understanding the dynamics of various systems, offering insights into their future states through parameter estimation fitted to time series data. In fields such as economy, politics, and…
ReduNet is a deep neural network model that leverages the principle of maximal coding rate \textbf{redu}ction to transform original data samples into a low-dimensional, linear discriminative feature representation. Unlike traditional deep…
Sampling in control applications is increasingly done non-equidistantly in time. This includes applications in motion control, networked control, resource-aware control, and event-based control. Some of these applications, like the ones…
The practical performance of generative diffusion models depends on the appropriate choice of the noise scheduling function, which can also be equivalently expressed as a time reparameterization. In this paper, we present a time scheduler…
In the phased-array radar (PAR) signals from each antenna are transmitted at the same carrier frequency, which yields narrowly focused only angle dependent beampattern. In contrast, in the frequency-diverse-array (FDA) radar signals from…
We introduce the diffusion and superposition distances as two metrics to compare signals supported in the nodes of a network. Both metrics consider the given vectors as initial temperature distributions and diffuse heat trough the edges of…
Malicious encryption techniques continue to evolve, bypassing conventional detection mechanisms that rely on static signatures or predefined behavioral rules. Spectral analysis presents an alternative approach that transforms system…
Entropy is a fundamental concept in the field of information theory. During measurement, conventional entropy measures are susceptible to length and amplitude changes in time series. A new entropy metric, neural network entropy (NNetEn),…
Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…
On account of a greater need for understanding the complexity of time series like physiological time series, financial time series, and many more that enter into picture for their inculpation with real-world problems, several complexity…
Using a graph-based approach, we propose a multiscale permutation entropy to explore the complexity of multivariate time series over multiple time scales. This multivariate multiscale permutation entropy (MPEG) incorporates the interaction…
This paper presents a method to explain how the information of each input variable is gradually discarded during the forward propagation in a deep neural network (DNN), which provides new perspectives to explain DNNs. We define two types of…