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Graph Learning (GL) is at the core of inference and analysis of connections in data mining and machine learning (ML). By observing a dataset of graph signals, and considering specific assumptions, Graph Signal Processing (GSP) tools can…
A spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes O(m^2n)…
Matching a target spectrum with known spectra in a spectral library is a common method for material identification in hyperspectral imaging research. Hyperspectral spectra exhibit precise absorption features across different wavelength…
Endmember (EM) spectral variability can greatly impact the performance of standard hyperspectral image analysis algorithms. Extended parametric models have been successfully applied to account for the EM spectral variability. However, these…
Spectral unmixing is a crucial processing step when analyzing hyperspectral data. In such analysis, most of the work in the literature relies on the widely acknowledged linear mixing model to describe the observed pixels. Unfortunately,…
Large language models and deep neural networks achieve strong performance but suffer from reliability issues and high computational cost. This thesis proposes a unified framework based on spectral geometry and random matrix theory to…
In this note, we are concerned with the asymptotic approximation of a class of double integrals which can be represented as an angular spectrum superposition. These double integrals typically appear in electromagnetic scattering problems.…
We present a methodology for using unlabeled data to design semi-supervised learning (SSL) methods that improve the predictive performance of supervised learning for regression tasks. The main idea is to design different mechanisms for…
Distributed estimation methods have recently been used to compute the maximum likelihood estimate of the precision matrix for large graphical Gaussian models. Our aim, in this paper, is to give a Bayesian estimate of the precision matrix…
Two popular approaches for relating correlated measurements of a non-Gaussian response variable to a set of predictors are to fit a marginal model using generalized estimating equations and to fit a generalized linear mixed model by…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
We discuss the problem of parameter estimation in nonlinear stochastic differential equations based on sampled time series. A central message from the theory of integrating stochastic differential equations is that there exists in general…
We study asymptotic behavior of one-step $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent $M$-estimators. These…
During the last decade, a large number of different numerical methods have been proposed to tackle the automatic identification and quantification in {\gamma}-ray spectrometry. However, the lack of common benchmarks, including datasets,…
In the framework of mapped pseudospectral methods, we introduce a new polynomial-type mapping function in order to describe accurately the dynamics of systems developing almost singular structures. Using error criteria related to the…
In this paper, we develop spectral and post-spectral estimators for grouped panel data models. Both estimators are consistent in the asymptotics where the number of observations $N$ and the number of time periods $T$ simultaneously grow…
A tacit assumption in linear regression is that (response, predictor)-pairs correspond to identical observational units. A series of recent works have studied scenarios in which this assumption is violated under terms such as ``Unlabeled…
The spectral numerical mode-matching (SNMM) method is developed to simulate the 3D layered multi-region structures. The SNMM method is a semi-analytical solver having the properties of dimensionality reduction to reduce computational costs;…
This paper develops asymptotic theory for estimation of parameters in regression models for binomial response time series where serial dependence is present through a latent process. Use of generalized linear model (GLM) estimating…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…