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Numerical solutions to fractional differential equations can be extremely computationally intensive due to the effect of non-local derivatives in which all previous time points contribute to the current iteration. In finite difference…
As a highly expressive generative model, diffusion models have demonstrated exceptional success across various domains, including image generation, natural language processing, and combinatorial optimization. However, as data distributions…
Accelerated coordinate descent is widely used in optimization due to its cheap per-iteration cost and scalability to large-scale problems. Up to a primal-dual transformation, it is also the same as accelerated stochastic gradient descent…
The Discrete Fourier Transform (DFT) is central to the analysis of uniformly sampled signals, yet many practical applications involve non-uniform sampling, requiring the Non-Uniform Discrete Fourier Transform (NUDFT). While quantum…
Proportionate type algorithms were developed and excessively used in the echo cancellation problems due to sparse characteristics of the echo channels. In the past, most of the attention was paid to a particular type of proportionate…
A fractional derivative is a temporally nonlocal operation which is computationally intensive due to inclusion of the accumulated contribution of function values at past times. In order to lessen the computational load while maintaining the…
Steerable networks, which process data with intrinsic symmetries, often use Fourier-based nonlinearities that require sampling from the entire group, leading to a need for discretization in continuous groups. As the number of samples…
This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error…
Simulation is an efficient tool in the design and control of power electronic systems. However, quick and accurate simulation of them is still challenging, especially when the system contains a large number of switches and state variables.…
The era of huge data necessitates highly efficient machine learning algorithms. Many common machine learning algorithms, however, rely on computationally intensive subroutines that are prohibitively expensive on large datasets. Oftentimes,…
We propose a new discrete-time online parameter estimation algorithm that combines two different aspects, one that adds momentum, and another that includes a time-varying learning rate. It is well known that recursive least squares based…
Non-uniform fast Fourier Transform (NUFFT) and inverse NUFFT (INUFFT) algorithms, based on the Fast Multipole Method (FMM) are developed and tested. Our algorithms are based on a novel factorization of the FFT kernel, and are implemented…
The research paper addresses linear decomposition of time series of non-additive metrics that allows for the identification and interpretation of contributing factors (input features) of variance. Non-additive metrics, such as ratios, are…
In this paper, adaptive non-uniform compressive sampling (ANCS) of time-varying signals, which are sparse in a proper basis, is introduced. ANCS employs the measurements of previous time steps to distribute the sensing energy among…
We present a computationally efficient algorithm for stable numerical differentiation from noisy, uniformly-sampled data on a bounded interval. The method combines multi-interval Fourier extension approximations with an adaptive domain…
Adaptive sampling algorithms are modern and efficient methods that dynamically adjust the sample size throughout the optimization process. However, they may encounter difficulties in risk-averse settings, particularly due to the challenge…
This paper proposes a data-adaptive factor model (DAFM), a novel framework for extracting common factors that explain the structures of high-dimensional data. DAFM adopts a composite quantile strategy to adaptively capture the full…
The symmetric Nonnegative Matrix Factorization (NMF), a special but important class of the general NMF, has found numerous applications in data analysis such as various clustering tasks. Unfortunately, designing fast algorithms for the…
Nonnegative matrix factorization (NMF) has an established reputation as a useful data analysis technique in numerous applications. However, its usage in practical situations is undergoing challenges in recent years. The fundamental factor…
Consider a discrete memoryless multiple source with $m$ components of which $k \leq m$ possibly different sources are sampled at each time instant and jointly compressed in order to reconstruct all the $m$ sources under a given distortion…