arXiv subjects

Sergiy Pereverzyev Jr.

Publications and source records attributed to Sergiy Pereverzyev Jr..

6 recordsLinked to original sources

arXiv2026

Towards regularized learning from functional data with covariate shift

This paper investigates a general regularization framework for unsupervised domain adaptation in vector-valued regression under the covariate shift assumption, utilizing vector-valued reproducing kernel Hilbert spaces (vRKHS). Covariate shift occurs when the input distributions of the training and test data differ, introducing significant challenges for reliable learning. By restricting the hypothesis space, we develop a practical operator learning algorithm capable of handling functional outputs. We establish optimal convergence rates for the proposed framework under a general source condition, providing a theoretical foundation for regularized learning in this setting. We also propose an aggregation-based approach that forms a linear combination of estimators corresponding to different regularization parameters and different kernels. The proposed approach addresses the challenge of selecting appropriate tuning parameters, which is crucial for constructing a good estimator, and we provide a theoretical justification for its effectiveness. Furthermore, we illustrate the proposed method on a real-world face image dataset, demonstrating robustness and effectiveness in mitigating distributional discrepancies under covariate shift.

math.ST↗

arXiv2025

Multiparameter regularization and aggregation in the context of polynomial functional regression

Most of the recent results in polynomial functional regression have been focused on an in-depth exploration of single-parameter regularization schemes. In contrast, in this study we go beyond that framework by introducing an algorithm for multiple parameter regularization and presenting a theoretically grounded method for dealing with the associated parameters. This method facilitates the aggregation of models with varying regularization parameters. The efficacy of the proposed approach is assessed through evaluations on both synthetic and some real-world medical data, revealing promising results.

stat.ML↗

arXiv2018

Operator learning approach for the limited view problem in photoacoustic tomography

In photoacoustic tomography, one is interested to recover the initial pressure distribution inside a tissue from the corresponding measurements of the induced acoustic wave on the boundary of a region enclosing the tissue. In the limited view problem, the wave boundary measurements are given on the part of the boundary, whereas in the full view problem, the measurements are known on the whole boundary. For the full view problem, there exist various fast and robust reconstruction methods. These methods give severe reconstruction artifacts when they are applied directly to the limited view data. One approach for reducing such artefacts is trying to extend the limited view data to the whole region boundary, and then use existing reconstruction methods for the full view data. In this paper, we propose an operator learning approach for constructing an operator that gives an approximate extension of the limited view data. We consider the behavior of a reconstruction formula on the extended limited view data that is given by our proposed approach. Approximation errors of our approach are analyzed. We also present numerical results with the proposed extension approach supporting our theoretical analysis.

math.NA↗

arXiv2017

Galaxy And Mass Assembly: Automatic Morphological Classification of Galaxies Using Statistical Learning

We apply four statistical learning methods to a sample of $7941$ galaxies ($z<0.06$) from the Galaxy and Mass Assembly (GAMA) survey to test the feasibility of using automated algorithms to classify galaxies. Using $10$ features measured for each galaxy (sizes, colours, shape parameters \& stellar mass) we apply the techniques of Support Vector Machines (SVM), Classification Trees (CT), Classification Trees with Random Forest (CTRF) and Neural Networks (NN), returning True Prediction Ratios (TPRs) of $75.8\%$, $69.0\%$, $76.2\%$ and $76.0\%$ respectively. Those occasions whereby all four algorithms agree with each other yet disagree with the visual classification (`unanimous disagreement') serves as a potential indicator of human error in classification, occurring in $\sim9\%$ of ellipticals, $\sim9\%$ of Little Blue Spheroids, $\sim14\%$ of early-type spirals, $\sim21\%$ of intermediate-type spirals and $\sim4\%$ of late-type spirals \& irregulars. We observe that the choice of parameters rather than that of algorithms is more crucial in determining classification accuracy. Due to its simplicity in formulation and implementation, we recommend the CTRF algorithm for classifying future galaxy datasets. Adopting the CTRF algorithm, the TPRs of the 5 galaxy types are : E, $70.1\%$; LBS, $75.6\%$; S0-Sa, $63.6\%$; Sab-Scd, $56.4\%$ and Sd-Irr, $88.9\%$. Further, we train a binary classifier using this CTRF algorithm that divides galaxies into spheroid-dominated (E, LBS \& S0-Sa) and disk-dominated (Sab-Scd \& Sd-Irr), achieving an overall accuracy of $89.8\%$. This translates into an accuracy of $84.9\%$ for spheroid-dominated systems and $92.5\%$ for disk-dominated systems.

astro-ph.GA↗

arXiv2017

A Galerkin least squares approach for photoacoustic tomography

The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper we address this issue for photoacoustic computed tomography in circular geometry. We investigate the Galerkin least squares method for that purpose. For approximating the function to be recovered we use subspaces of translation invariant spaces generated by a single Funktion. This includes many systems that have previously been employed in PAT such as generalized Kaiser-Bessel basis functions or the natural pixel basis. By exploiting an isometry property of the forward problem we are able to efficiently set up the Galerkin equation for a wide class of generating functions and Devise efficient algorithms for its solution. We establish a convergence analysis and present numerical simulations that demonstrate the efficiency and accuracy of the derived algorithm.

math.NA↗

arXiv2017

The quasi-optimality criterion in the linear functional strategy

The linear functional strategy for the regularization of inverse problems is considered. For selecting the regularization parameter therein, we propose the heuristic quasi-optimality principle and some modifications including the smoothness of the linear functionals. We prove convergence rates for the linear functional strategy with these heuristic rules taking into account the smoothness of the solution and the functionals and imposing a structural condition on the noise. Furthermore, we study these noise conditions in both a deterministic and stochastic setup and verify that for mildly-ill-posed problems and Gaussian noise, these conditions are satisfied almost surely, where on the contrary, in the severely-ill-posed case and in a similar setup, the corresponding noise condition fails to hold. Moreover, we propose an aggregation method for adaptively optimizing the parameter choice rule by making use of improved rates for linear functionals. Numerical results indicate that this method yields better results than the standard heuristic rule.

math.NA↗