arXiv subjects

Vasyl Semenov

Publications and source records attributed to Vasyl Semenov.

3 recordsLinked to original sources

arXiv2026

Convergence Analysis of Nyström Subsampling in Covariate Shift Adaptation for Misspecified case

This paper investigates convergence properties of regularized Nyström subsampling applied to the unsupervised domain adaptation problem under covariate shift. We focus on the low-smoothness (misspecified) case where the target function lies outside the reproducing kernel Hilbert space. By combining Tikhonov regularization with Nyström projection onto a subsampled subspace, we obtain upper bounds on the excess risk that hold with high probability and are expressed in terms of the source condition, the effective dimension, and the sample sizes. We further extend the analysis to the setting where the Radon-Nikodym derivative between the target and source marginal distributions is unknown and must be approximated, and we identify the minimal additional sample sizes required to maintain the same convergence rate as in the oracle case.

stat.ML↗

arXiv2026

On the explicit formula linking a function to the order of its fractional derivative

In this paper, given a certain regularity of a function $v$, we derive an explicit formula relating the order $ν_0\in(0,1)$ of the leading fractional derivative in a fractional differential operator $\mathbf{D_t}$ with the variable coefficients $r_i=r_i(x,t)$ and the function $v$ on which this operator acts. Moreover, we discuss application of this result in the reconstruction of the memory order of semilinear subdiffusion with memory terms. To achieve this aim, we analyze some inverse problems to multi-term fractional in time ordinary and partial differential equations with smooth local or nonlocal additional measurements for small time. In conclusion, we discuss how this formula may be exploited to numerical computation of $ν_0$ in the case of discrete noisy observation in the corresponding inverse problems. Our theoretical results along with the computational algorithm are supplemented by numerical tests.

math.AP↗

arXiv2025

Galaxy Morphological Classification with Manifold Learning

We address the problem of morphological classification of galaxies from the Galaxy Zoo DECaLS dataset using classical machine learning techniques. Our approach employs a dimensionality reduction method followed by a classical classifier to categorize galaxies based on shape (cigar/in-between/round; edge-on/face-on) and texture (smooth/featured). We evaluate various dimensionality reduction methods, including Locally Linear Embedding (LLE), Isomap, Uniform Manifold Approximation and Projection (UMAP), t-SNE, and Principal Component Analysis (PCA). Our results demonstrate that most classical classifiers achieve their highest performance when combined with LLE, attaining accuracy comparable to that of simple neural networks. Moreover, in the case of shape classification, the three-dimensional representation remains interpretable, in contrast to the commonly observed loss of interpretability following nonlinear transformations. Additionally, we explore dimensionality reduction followed by k-means clustering to assess whether the data exhibits a natural tendency toward a specific number of clusters. We evaluate clustering performance using silhouette, elbow, Dunn, and Davies-Bouldin scores. While the Davies-Bouldin score indicates a slight preference for four clusters (closely aligning with classifications made by human astronomers) the other metrics do not support a distinct clustering structure.

astro-ph.GA↗