Related papers: Exclusive robustness of Gegenbauer method to trunc…
Recent advancements in Spectral Graph Convolutional Networks (SpecGCNs) have led to state-of-the-art performance in various graph representation learning tasks. To exploit the potential of SpecGCNs, we analyze corresponding graph filters…
Time-frequency analysis, such as the Gabor transform, plays an important role in many signal processing applications. The redundancy of such representations is often directly related to the computational load of any algorithm operating in…
We present a generic scheme to construct corrected trapezoidal rules with spectral accuracy for integral operators with weakly singular kernels in arbitrary dimensions. We assume that the kernel factorization of the form,…
Kernel adaptive filtering (KAF) integrates traditional linear algorithms with kernel methods to generate nonlinear solutions in the input space. The standard approach relies on the representer theorem and the kernel trick to perform…
We introduce a fast Fourier spectral method for the spatially homogeneous Boltzmann equation with non-cutoff collision kernels. Such kernels contain non-integrable singularity in the deviation angle which arise in a wide range of…
We explore the geometric implications of introducing a spectral cut-off on Riemannian manifolds. This is naturally phrased in the framework of non-commutative geometry, where we work with spectral triples that are \emph{truncated} by…
It is well known that approximation of functions on $[0,1]$ whose periodic extension is not continuous fail to converge uniformly due to rapid Gibbs oscillations near the boundary. Among several approaches that have been proposed toward the…
Despite being the most popular methods of data analysis, Fourier-based techniques suffer from the problem of static resolution that is currently believed to be a fundamental limitation of the Fourier Transform. Although alternative…
Many real-world time series exhibit strong periodic structures arising from physical laws, human routines, or seasonal cycles. However, modern deep forecasting models often fail to capture these recurring patterns due to spectral bias and a…
An important step in using observations of gravitational waves from bounded sources is to relate the observed waveforms far away from a source to the local dynamics and environment of the source. To isolate and identify different features…
This paper introduces an effcient class of adaptive stencil extension reconstruction methods based on a discontinuity feedback factor, addressing the challenges of weak robustness and high computational cost in high-order schemes,…
The optimization with orthogonality has been shown useful in training deep neural networks (DNNs). To impose orthogonality on DNNs, both computational efficiency and stability are important. However, existing methods utilizing Riemannian…
A machine learning model, under the influence of observed or unobserved confounders in the training data, can learn spurious correlations and fail to generalize when deployed. For image classifiers, augmenting a training dataset using…
Convolutional Gridding is a technique (algorithm) extensively used in Radio Interferometric Image Synthesis for fast inversion of functions sampled with irregular intervals on the Fourier plane. In this thesis, we propose some modifications…
The Discrete Fourier Transform (DFT) underpins the solution to many inverse problems commonly possessing missing or un-measured frequency information. This incomplete coverage of Fourier space always produces systematic artefacts called…
Gaussian graphical models (GGMs) are widely used for statistical modeling, because of ease of inference and the ubiquitous use of the normal distribution in practical approximations. However, they are also known for their limited modeling…
In this paper we address the problem of constructing a feature extractor which combines Mallat's scattering transform framework with time-frequency (Gabor) representations. To do this, we introduce a class of frames, called uniform covering…
In this paper, we apply the Feature Space Decomposition (FSD) method developed in [LS24, GLS25, LSSW26, ALSS26] to obtain, under fairly general conditions, matching upper and lower bounds for the population excess risk of spectral methods…
The high-order accuracy of Fourier method makes it the method of choice in many large scale simulations. We discuss here the stability of Fourier method for nonlinear evolution problems, focusing on the two prototypical cases of the…
In this paper, we study high-dimensional estimation from truncated samples. We focus on two fundamental and classical problems: (i) inference of sparse Gaussian graphical models and (ii) support recovery of sparse linear models. (i) For…