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Gaussian processes with multidimensional distribution inputs via optimal transport and Hilbertian embedding
Electronic journal of statistics. 2020. Vol. 14. No. 2. P. 2742–2772.
In this work, we propose a way to construct Gaussian processes indexed by multidimensional distributions. More precisely, we tackle the problem of defining positive definite kernels between multivariate distributions via notions of optimal transport and appealing to Hilbert space embeddings. Besides presenting a characterization of radial positive definite and strictly positive definite kernels on general Hilbert spaces, we investigate the statistical properties of our theoretical and empirical kernels, focusing in particular on consistency as well as the special case of Gaussian distributions. A wide set of applications is presented, both using simulations and implementation with real data.
Trubochkina N. K., М.: Издательство «Юрайт», 2026.
This textbook is designed to develop students' holistic understanding of modern production processes and methods for their analysis and management using machine learning technologies. In the context of the fourth industrial revolution, where traditional engineering disciplines are inextricably intertwined with intelligent data processing methods, there is a growing need for specialists capable of integrating knowledge ...
Added: August 8, 2026
Kulev Y., Maksaev A., Promyslov V., Linear Algebra and its Applications 2026 Vol. 730 P. 51–72
The notion of λ-th upper scrambling index was introduced by Huang and Liu in 2010, as a generalization of a notion considered by Akelbek and Kirkland in 2009. For a primitive digraph D, it is defined as the smallest positive integer k such that for every λ vertices of D there exist directed paths of lengths k from these vertices to a common vertex. This ...
Added: August 7, 2026
Kanunnikov A., Promyslov V., Vassilieva E., Electronic Journal of Combinatorics 2024 Vol. 31 No. 3 Article P3.6
Introduced by Goulden and Jackson in their 1996 paper, the matchings-Jack conjecture and the hypermap-Jack conjecture (also known as the b-conjecture) are two major open questions relating Jack symmetric functions, the representation theory of the symmetric groups and combinatorial maps. They show that the coefficients in the power sum expansion of some Cauchy sum for ...
Added: August 7, 2026
Фирсанова В. И., ACM, 2026.
The inclusion of autistic people can be augmented by a mobile app that provides information without a human mediator making information perception more liberating for people in the spectrum. This paper is an overview of a doctoral work dedicated to the development of a web-based mobile tool for supporting the inclusion of people on the ...
Added: August 4, 2026
Фирсанова В. И., Хлусова Я. К., CEUR Workshop Proceedings, 2025.
Knowledge graphs are widely used in Retrieval Augmented Generation (RAG) and Explainable AI (XAI), since they can illustrate semantic relationships generated by Large Language Models (LLMs). Recent studies focus on generating knowledge graphs from unstructured data to improve RAG performance; however, they do not explain the underlying graph structure. The analysis of synthetic graphs behind ...
Added: August 4, 2026
Spiridonov V. P., Belousov N. M., Sarkissian G. A., Analysis and Mathematical Physics 2026 Vol. 16 Article 96
Hyperbolic hypergeometric integrals are defined as Barnes-type integrals of products of hyperbolic gamma functions. Their reduction to ordinary hypergeometric functions is well known. We study in detail their degeneration to complex hypergeometric functions. Namely, using uniform bounds on the integrands, we prove that the univariate hyperbolic beta integral and the conical function degenerate to two-dimensional ...
Added: August 4, 2026
Gayfullin S., Kikteva V., Results in Mathematics 2026 Vol. 81 No. 5 Article 146
In this paper we obtain a criterion of flexibility for an affine complexity-zero horospherical variety. This result generalizes previously known results on flexibility of normal horospherical varieties, horospherical varieties with an action of a semisimple group, and non-normal toric varieties. ...
Added: August 3, 2026
Lunts V., Функциональный анализ и его приложения 2026 Т. 60 № 3 С. 127–129
Доказано, что канонические полуортогональные разложения производной категории диаграммной схемы индуцируют аналогичные разложения подкатегории совершенных комплексов. ...
Added: August 3, 2026
Belomestny D., Gasnikov A., Gladin E. et al., Russian Mathematical Surveys 2026 Vol. 81 No. 4(490) P. 3–90
Reinforcement learning (RL) is increasingly grounded in tools from probability, optimization, and operator theory. This survey organizes the mathematical structures that underpin the design and analysis of modern algorithms in RL. We begin from Markov decision processes (MDPs) and the Bellman operators, emphasizing contraction mappings, monotonicity, and fixed-point theory that yield convergence guarantees and rates ...
Added: August 3, 2026
Chepovskiy A., Мастерская Печати Идей, 2026.
The textbook presents methods and algoгithms for automatic analysis
of соrроrа of texts in natural languages. It is intended fоr sfudenБ of
methods of processing texts in паtчrаl languages and creating training
arays of texts.
Fоr students, graduate students and researchers studying methods
of computational linguistics and word processing. ...
Added: August 1, 2026
A. Radomskii, Mathematical notes 2026 Vol. 119 No. 6 P. 1136–1147
We obtain an upper bound for the sum $\sum_{n\leq N} (a_{n}/\varphi (a_{n}))^{s}$, where $\varphi$ is Euler's totient function, $s\in\mathbb{N}$, and $a_{1},\ldots, a_{N}$ are positive integers (not necessarily distinct) with some restrictions. As applications, for any $t>0$, we obtain an upper bound for the number of $n\in [1,N]$ such that $a_{n}/ \varphi (a_{n})> t$. ...
Added: July 31, 2026
Абызов А. Н., Буутай П. Н., Математика и теоретические компьютерные науки 2026 Т. 4 № 2 С. 4–75
This paper is expository and methodological in nature and is devoted to the development of E.I. Zolotarev’s ideas embedded in his approach to the proof of the quadratic reciprocity law (1872). We consider extensions of Zolotarev’s approach to abstract number rings presented in the work of A. Brunyate and P.L. Clark (2015), and to finite ...
Added: July 30, 2026
Ponomarenko A., / Series Computer Science "arxiv.org". 2025.
This paper addresses the challenge of merging hierarchical navigable small world (HNSW) graphs, a critical operation for distributed systems, incremental indexing, and database compaction. We propose three algorithms for this task: Naive Graph Merge (NGM), Intra Graph Traversal Merge (IGTM), and Cross Graph Traversal Merge (CGTM). These algorithms differ in their approach to vertex selection ...
Added: July 30, 2026
Уилкокс П., Romanov A., М.: ДМК Пресс, 2025.
Книга, которую вы держите в руках, продолжает серию «Книжная полка истового
инженера», которая издается при поддержке компании YADRO.
Данная книга представляет собой учебник по теоретическим основам продвинутой
функциональной верификации и содержит лучшие практики, используемые в настоящее
время. В ней подробно описана унифицированная методология верификации
(UVM) и раскрыты такие темы, как функциональный виртуальный прототип, функциональное
покрытие, утверждения, формальная верификация, тестбенчи, косимуляция,
эмуляция, аппаратное ...
Added: July 30, 2026
Mikhaylets E. V., Razorenova A. М., Chernyshev V. L. et al., Scientific Reports 2026 Vol. 16 Article 23560
Meditation offers a naturalistic paradigm for studying introspection, yet the neural dynamics of advanced tantric practices remain largely unexplored. Buddhist Highest Yoga Tantra (BHYT) comprises a sequence of eight dissolution stages culminating in the “clear light” state. We recorded EEG during eyes-closed BHYT meditation performed in monasteries and hermitages (51 sessions from 36 male practitioners; ...
Added: July 29, 2026
Попеленский Ф. Ю., Математический сборник 2026 Т. 217 № 2 С. 108–153
In a recent paper Buchstaber and the author introduced a new structure on the cohomology of Hopf algebras in terms of the Buchstaber spectral sequence (Bss). We fully calculate this structure on the cohomology (known for a long time) of the important Hopf subalgebra A(1) of the classical Steenrod algebra A2.
As part of a demonstration ...
Added: July 28, 2026
Ramazyan T., Hushchyn M., Derkach D., , in: ECAI 2024. 27th European Conference on Artificial Intelligence, October 19 – 24 October 2024, Santiago de Compostela, Spain – Including 13th Conference on Prestigious Applications of Intelligent Systems (PAIS 2024).: IOS Press, 2024. P. 2394–2401.
We propose a new uncertainty estimator for gradient-free optimisation of black-box simulators using deep generative surrogate models. Optimisation of these simulators is especially challenging for stochastic simulators and higher dimensions. To address these issues, we utilise a deep generative surrogate approach to model the black box response for the entire parameter space. We then leverage ...
Added: December 1, 2024
Kurochkin S. V., Rodina V., Экономический журнал Высшей школы экономики 2024 Т. 28 № 3 С. 412–426
One of the key techniques in the fixed-income portfolio management is immunization which involves a managed change in the portfolio value under interest rate fluctuations given a similar pattern in a portfolio of liabilities. Since the classic work by Redington, scholars have developed a variety of immunization models. Yet, these models are built on restrictive ...
Added: October 17, 2024
Erlygin L., Zholobov V., Baklanova V. et al., , in: 2023 IEEE International Conference on Data Mining Workshops (ICDMW) 1–4 December 2023, Shanghai, China.: Shanghai: IEEE Computer Society, 2023. P. 1247–1258.
Machine learning models play a vital role in time series forecasting. These models, however, often overlook an important element: point uncertainty estimates. Incorporating these estimates is crucial for effective risk management, informed model selection, and decision-making.To address this issue, our research introduces a method for uncertainty estimation. We employ a surrogate Gaussian process regression model. ...
Added: March 20, 2024
Kelbert M., Сухов Ю. М., Известия Саратовского университета. Новая серия. Серия: Математика. Механика. Информатика 2023 Vol. 23 No. 4 P. 422–434
We present a number of low and upper bounds for L\эevy – ´Prokhorov, Wasserstein, Frechet, and Hellinger distances between ´ probability distributions of the same or different dimensions. The weighted (or context-sensitive) total variance and Hellinger distances are introduced. The upper and low bounds for these weighted metrics are proved. The low bounds for the ...
Added: October 29, 2023
Kelbert M., Analytics 2023 Vol. 2 No. 1 P. 225–245
We present a number of upper and lower bounds for the total variation distances between
the most popular probability distributions. In particular, some estimates of the total variation
distances in the cases of multivariate Gaussian distributions, Poisson distributions, binomial distributions,
between a binomial and a Poisson distribution, and also in the case of negative binomial
distributions are given. Next, ...
Added: March 1, 2023
Chigarev V., Kazakov A., Пиковский А., Chaos 2020 Vol. 30 No. 7 Article 073114
We consider several examples of dynamical systems demonstrating overlapping attractor and repeller. These systems are constructed via introducing controllable dissipation to prototypic models with chaotic dynamics (Anosov cat map, Chirikov standard map, and incompressible three-dimensional flow of the ABC-type on a three-torus) and ergodic non-chaotic behavior (skew-shift map). We employ the Kantorovich–Rubinstein–Wasserstein distance to characterize the ...
Added: October 31, 2020
A. I. Zhdanov, V. I. Piterbarg, Theory Probability and its Applications 2018 Vol. 63 No. 1 P. 1–21
Let $\mathbf{\boldsymbol{\xi}}(t)=(\xi_{1}(t),\ldots,\xi_{d}(t))$ be a Gaussian zero mean stationary a.s. continuous vector process. Let $g\colon{\mathbb{R}}^{d}\to {\mathbb{R}}$ be a homogeneous function of positive degree. We study probabilities of high extrema of the Gaussian chaos process $g(\mathbf{\boldsymbol{\xi}}(t))$. Important examples are products of Gaussian processes, $\prod_{i=1}^{d}\xi_{i}(t)$, and quadratic forms $\sum_{i,j=1}^{d}a_{ij}\xi_{i}(t)\xi_{j}(t)$. Methods of our studies include the Laplace saddle point ...
Added: November 14, 2019
A. I. Zhdanov., Theory Probability and its Applications 2015 Vol. 60 No. 3 P. 520–527
Let $(X(t),Y(t))$, $t\ge0$, be a zero-mean stationary Gaussian vector process with a covariance functions for components $r_i(t)$ satisfying Pickand's condition $r_i(t)=1-c_i|t|^{\alpha_i}(1+o(1))$, $t\to 0$, $c_i>0$, $0<\alpha_i\le2$, $i=1,2.$ Let $r_i(t)<1$, $i=1,2$, $t>0.$ Assuming that $r\equiv {\bf E}\,X(t)Y(t)\in(-1,1)$ and $\lim_{t,s\rightarrow0}({\bf E}\,X(t)Y(s)-r)/|t-s|^{\min(\alpha_1,\alpha_2)}$ exists, we study the behavior of probability ${\bf P}(\max_{t\in\lbrack0,p]}X(t)Y(t)>u)$ as $u\rightarrow\infty$ for any $p$. In particular, we ...
Added: November 14, 2019