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Volatility for financial assets returns can be used to gauge the risk for financial market. We propose a deep stochastic volatility model (DSVM) based on the framework of deep latent variable models. It uses flexible deep learning models to…

Stein Variational Gradient Descent (SVGD) is a highly efficient method to sample from an unnormalized probability distribution. However, the SVGD update relies on gradients of the log-density, which may not always be available. Existing…

Objective: The present study introduces a fractional wavelet scattering network (FrScatNet), which is a generalized translation invariant version of the classical wavelet scattering network (ScatNet). Methods: In our approach, the FrScatNet…

One of the key challenges in the area of signal processing on graphs is to design transforms and dictionaries methods to identify and exploit structure in signals on weighted graphs. In this paper, we first generalize graph Fourier…

Stochastic Variational Method (SVM) is the generalization of the variation method to the case with stochastic variables. In the series of papers, we investigate the applicability of SVM as an alternative field quantization scheme. Here, we…

Given a time series vector, how can we efficiently compute a specified part of Fourier coefficients? Fast Fourier transform (FFT) is a widely used algorithm that computes the discrete Fourier transform in many machine learning applications.…

We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous semi-martingales, which is based on Fourier analysis. The co-volatility is reconstructed as a stochastic function of time by…

Mixture models with Gamma and or inverse-Gamma distributed mixture components are useful for medical image tissue segmentation or as post-hoc models for regression coefficients obtained from linear regression within a Generalised Linear…

Variational inference (VI) is a popular method for approximating intractable posterior distributions in Bayesian inference and probabilistic machine learning. In this paper, we introduce a general framework for quantifying the statistical…

I discuss the nature of a Fractional Discrete Fourier Transform (FrDFT) described algorithmically by a combination of chirp transforms and ordinary DFTs. The transform is shown to be consistent with a continuous two-dimensional rotation…

Fractional cumulative residual entropy (FCRE) is a powerful tool for the analysis of complex systems. Most of the theoretical results and applications related to the FCRE of the lifetime random variable are based on the distribution…

Standard Gradient Descent and its modern variants assume local, Markovian weight updates, making them highly susceptible to noise and overfitting. This limitation becomes critically severe in extremely imbalanced datasets such as financial…

We propose a convolution-FFT method for pricing European options under the Heston model that leverages a continuously differentiable representation of the joint characteristic function. Unlike existing Fourier-based methods that rely on…

We derive a multifractal model for the velocity probability density distribution function (PDF), which is valid from the inertial range to the viscous range. The model gives a continuous evolution of velocity PDFs from large to small…

In this paper, we propose a new regression-based algorithm to compute Graph Fourier Transform (GFT). Our algorithm allows different regularizations to be included when computing the GFT analysis components, so that the resulting components…

Graph spectral representations are fundamental in graph signal processing, offering a rigorous framework for analyzing and processing graph-structured data. The graph fractional Fourier transform (GFRFT) extends the classical graph Fourier…

A method for determining the current signature faults using Fractional Fourier Transform (FrFT) has been developed. The method has been applied to the real-time steady-state current of the inverter-fed high power induction motor for fault…

The recently introduced independent fluctuating two-ray (IFTR) fading model, consisting of two specular components fluctuating independently plus a diffuse component, has proven to provide an excellent fit to different wireless…

Computer simulations play an important role in scientific discovery and engineering innovation. Reliable computer models enable virtual experimentation that reduces the need for costly and time-consuming physical testing. However, the…

The continuous observation of the financial markets has identified some stylized facts which challenge the conventional assumptions, promoting the born of new approaches. On the one hand, the long-range dependence has been faced replacing…