?
Semiparametric estimation of the signal subspace
Journal of machine learning and data analysis. 2012. Vol. 1. No. 3. P. 140–147.
Let a high-dimensional random vector $\vX$ be represented as a sum of two components - a signal $\vS$ that belongs to some low-dimensional linear subspace $\S$, and a noise component $\vN$. This paper presents a new approach for estimating the subspace $\S$ based on the ideas of the Non-Gaussian Component Analysis. Our approach avoids the technical difficulties that usually appear in similar methods - it requires neither the estimation of the inverse covariance matrix of $\vX$ nor the estimation of the covariance matrix of $\vN.
Language:
English
Piontkovski D., / Series arXiv "math". 2026.
A noncommutative projective variety is defined, following Artin and Zhang, by a graded coherent algebra 𝐴. The category of coherent sheaves is then the quotient qgr(𝐴) of the category of finitely presented graded modules by the subcategory of torsion modules. We consider the categorical and polynomial entropies of the Serre twist, that is, of the ...
Added: June 23, 2026
Piontkovski D., / Series arXiv "math". 2025.
If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed ...
Added: June 23, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Derkacheva A., Sakirkina M., Kraev G. et al., /. 2026.
Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...
Added: April 28, 2026
Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...
Added: April 20, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Popkov Y., Popkov A. Y., Dubnov Y. A., Mathematical Models and Computer Simulations 2021 Vol. 13 No. 3 P. 382–394
© 2021, Pleiades Publishing, Ltd.Abstract: We develop/propose the method reducing the dimension of a data matrix, based on its direct and inverse projection, and the calculation of projectors that minimize the cross-entropy functional, remove. We introduce the concept of information capacity of a matrix, which is used as a constraint in the optimal reduction problem, ...
Added: October 28, 2022
Panov V., / Series Discussion paper SFB 649 "Economic risk". 2010. No. 2010-050.
Let a high-dimensional random vector $\vX$ be represented as a sum of two components - a signal $\vS$ that belongs to some low-dimensional linear subspace $\S$, and a noise component $\vN$. This paper presents a new approach for estimating the subspace $\S$ based on the ideas of the Non-Gaussian Component Analysis. Our approach avoids the ...
Added: September 3, 2015
Panov V., / Series Discussion paper SFB 649 "Economic risk". 2010. No. 2010-026.
In this article, we present new ideas concerning Non-Gaussian Component Analysis (NGCA). We use the structural assumption that a high-dimensional random vector $\vX$ can be represented as a sum of two components - a low-dimensional signal $\vS$ and a noise component $\vN$. We show that this assumption enables us for a special representation for the ...
Added: September 3, 2015
Karasev M., Novikova E., Mathematical notes 2014 Vol. 96 No. 6 P. 965–970
We discuss the general opportunity to create (asymptotically) a comletely integrable system from the original perturbed system by inserting additional perturbing terms. After such an artificial insertion, there appears an opportunity to make the secondary averaging and secondary reduction of the original system. Thus, by this way, the $3D$-system becomes $1$-dimensional. We demonstrate this approach ...
Added: November 25, 2014