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Diffusion approximations and control variates for MCMC
Computational Mathematics and Mathematical Physics. 2024. Vol. 64. No. 4. P. 693–738.
A new method is introduced for the construction of control variates to reduce the variance of additive functionals of Markov Chain Monte Carlo (MCMC) samplers. These control variates are obtained by minimizing the asymptotic variance associated with the Langevin diffusion over a family of functions. To motivate our approach, we then show that the asymptotic variance of some well-known MCMC algorithms, including the Random Walk Metropolis and the (Metropolis) Unadjusted/Adjusted Langevin Algorithm, are well approximated by that of the Langevin diffusion. We finally theoretically justify the use of a class of linear control variates we introduce. In particular, we show that the variance of the resulting estimators is smaller, for a given computational complexity, than the standard Monte Carlo estimator. Several examples of Bayesian inference problems support our findings showing, in some cases, very significant reduction of the variance.
Netherlands: ScienceDirect, 2025.
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Added: June 28, 2026
Seidel A., Weske M., Montali M. et al., Information Systems 2026 Vol. 141 Article 102728
Business process management employs process models and event logs to represent the behavior of the information systems under study. Traditional case-centric notions consider the order of activities and events in isolated process instances. The emerging field of object-centric processes challenges this assumption by putting objects in the center. Object-centric process mining and modeling approaches identify ...
Added: June 27, 2026
IEEE, 2024.
A.S. Popov Russian Science and Technical Society with support from V. A. Trapeznikov Institute of Control Sciences, V.A. Kotelnikov Institute of Radio Engineering and Electronics, Autex Ltd. is leading the ХХVIII International Conference «Digital Signal Processing and its Applications — DSPA-2024» ...
Added: June 27, 2026
Ivchenko A., Дворкович А. В., Телекоммуникации 2020 Т. 12 С. 2–11
Dynamic Adaptive Streaming over HTTP (DASH) technology powers most multimedia services. Its specific features (re-buffering, quality switching, etc.) necessitate the development of specialized methods for assessing user subjective quality of experience (QoE) based on objective parameters. This article examines the impact of various metrics on QoE and presents assessment models with Spearman correlation coefficients up ...
Added: June 27, 2026
Ivchenko A., Nigmatullin R. R., Dorokhin S. V., Mathematics 2026 Vol. 9 No. 4 Article 381
n this paper, we focus on the generalization of the Hurst empirical law and suggest a set of reduced parameters for quantitative description of long-time series. These series are usually considered as a specific response of a complex system (economic, geophysical, electromagnetic and other systems), where successive fixations of external factors become impossible. We consider ...
Added: June 27, 2026
Ivchenko A., Шестопёров А. И., Фомина Е. В., Microgravity Science and Technology 2025 Vol. 37 No. 19 P. 1–19
The paper is dedicated to the analysis of medico-biological data obtained during locomotor testing of astronauts. Accurate data interpretation plays a crucial role in locomotion system monitoring, prophylaxis of long-duration spaceflight negative effects and thus in the development of an autonomous medical support system for deep space expeditions. During the locomotor testing the astronaut changes ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., 2023 3rd International Conference on Innovative Research in Applied Science, Engineering and Technology (IRASET) Mohammedia, Morocco 2023 P. 1–6
The article proposes the architecture for eventdriven Emergency Operation Center with Machine Vision Component. Sources of information are analyzed and approaches to machine vision events for tactical situations detection and estimation are discussed. Messages from Machine Vision Components are converted to Common Alerting Protocol and processed by Operation Center environment for tactical situations recognition. ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., Компьютерные исследования и моделирование 2022 Т. 14 № 6 С. 1255–1268
This work contains a description of the results of modeling the process of maintaining the readiness of a section of the road network under strikes of with specified parameters. A one-dimensional section of road up to 40 km long with a total number of strikes up to 100 during the work of the brigade is ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., Лукьянченко П. П., Computer Research and Modeling 2023 Vol. 15 No. 1 P. 129–140
In this article we propose a new approach to the analysis of econometric industry parameters for the industry consolidation level. The research is based on the simple industry automatic control model. The state of the industry is measured by quarterly obtained econometric parameters from each industry’s company provided by the tax control regulator. An approach ...
Added: June 26, 2026
Gladin E., Alkousa M., Gasnikov A., Automation and Remote Control 2021 Vol. 82 P. 1679–1691
The article deals with some approaches to solving convex problems of the min-min type with smoothness and strong convexity in only one of the two groups of variables. It is shown that the proposed approaches based on Vaidya’s method, the fast gradient method, and the accelerated gradient method with variance reduction have linear convergence. It ...
Added: November 29, 2024
Gladin E., Borodich E., Computer Research and Modeling 2022 Vol. 14 No. 2 P. 257–275
The paper is devoted to convex-concave saddle point problems where the objective is a sum of a large number of functions. Such problems attract considerable attention of the mathematical community due to the variety of applications in machine learning, including adversarial learning, adversarial attacks and robust reinforcement learning, to name a few. The individual functions ...
Added: November 29, 2024
Belomestny D., Goldman A., Naumov A. et al., Mathematics and Computers in Simulation 2024 Vol. 220 P. 382–405
In this paper, we propose a variance reduction approach for Markov chains based on additive control variates and the minimization of an appropriate estimate for the asymptotic variance. We focus on the particular case when control variates are represented as deep neural networks. We derive the optimal convergence rate of the asymptotic variance under various ...
Added: June 28, 2023
Durmus A., Moulines E., Naumov A. et al., / Series arXiv "math". 2023.
In this paper, we establish novel deviation bounds for additive functionals of geometrically ergodic Markov chains similar to Rosenthal and Bernstein-type inequalities for sums of independent random variables. We pay special attention to the dependence of our bounds on the mixing time of the corresponding chain. Our proof technique is, as far as we know, ...
Added: June 18, 2023
Belomestny D., Kaledin M., Golubev A., /. 2022.
Policy-gradient methods in Reinforcement Learning(RL) are very universal and widely applied in practice but their performance suffers from the high variance of the gradient estimate. Several procedures were proposed to reduce it including actor-critic(AC) and advantage actor-critic(A2C) methods. Recently the approaches have got new perspective due to the introduction of Deep RL: both new control ...
Added: April 14, 2023
Samsonov S., Lagutin E., Gabrie M. et al., , in: Thirty-Sixth Conference on Neural Information Processing Systems : NeurIPS 2022.: Curran Associates, Inc., 2022. P. 5178–5193.
Added: February 1, 2023
Cardoso G., Samsonov S., Thin A. et al., , in: Thirty-Sixth Conference on Neural Information Processing Systems : NeurIPS 2022.: Curran Associates, Inc., 2022. P. 716–729.
Added: February 1, 2023
Belomestny Denis, Iosipoi L., Paris Q. et al., Bernoulli: a journal of mathematical statistics and probability 2022 Vol. 28 No. 2 P. 1382–1407
We study the problem of empirical minimization for variance-type functionals over functional classes. Sharp non-asymptotic bounds for the excess variance are derived under mild conditions. In particular, it is shown that under some restrictions imposed on the functional class fast convergence rates can be achieved including the optimal non-parametric rates for expressive classes in the ...
Added: April 17, 2022
Eduard Gorbunov, Kovalev D., Makarenko D. et al., , in: Advances in Neural Information Processing Systems 33 (NeurIPS 2020).: Curran Associates, Inc., 2020. P. 20889–20900.
Added: December 7, 2020
Gadetsky A., Struminsky K., Robinson C. et al., , in: Thirty-Fourth AAAI Conference on Artificial IntelligenceVol. 34.: AAAI Press, 2020. P. 10126–10135.
Added: October 11, 2020
Belomestny D., Moulines E., Samsonov S., Statistics and Computing 2022 Vol. 32 No. 1 Article 16
In this paper, we propose an efficient variance reduction approach for additive functionals of Markov chains relying on a novel discrete-time martingale representation. Our approach is fully non-asymptotic and does not require the knowledge of the stationary distribution (and even any type of ergodicity) or specific structure of the underlying density. By rigorously analyzing the ...
Added: August 31, 2020
Belomestny D., Iosipoi L., Moulines E. et al., SIAM-ASA Journal on Uncertainty Quantification 2021 Vol. 9 No. 2 P. 507–535
In this paper we propose a novel and practical variance reduction approach for additive functionals of dependent sequences. Our approach combines the use of control variates with the minimisation of an empirical variance estimate. We analyse finite sample properties of the proposed method and derive finite-time bounds of the excess asymptotic variance to zero. We ...
Added: August 18, 2020
Gadetsky A., Struminsky K., Robinson C. et al., / Series 2019 "Bayesian Deep Learning NeurIPS 2019 Workshop". 2019.
Learning models with discrete latent variables using stochastic gradient descent remains a challenge due to the high variance of gradients. Modern variance reduction techniques mostly consider categorical distributions and have limited applicability when the number of possible outcomes becomes large. In this work, we consider models with latent permutations and propose control variates for the Plackett-Luce distribution. Our proof-of-concept experiment ...
Added: January 9, 2020
Burovskiy E., Janke W., Guskova M. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2019 Vol. 100 No. 6 P. 063303-1–063303-8
We study properties of Markov chain Monte Carlo simulations of classical spin models with local updates. We derive analytic expressions for the mean value of the acceptance rate of single-spin-flip algorithms for the one-dimensional Ising model. We find that for the Metropolis algorithm the average acceptance rate is a linear function of energy. We further provide numerical results ...
Added: November 5, 2019
Belomestny D., Moulines E., Iosipoi L. et al., Statistics and Computing 2020 No. 30 P. 973–997
In this paper we propose a novel variance reduction approach for additive functionals of Markov chains based on minimization of an estimate for the asymptotic variance of these functionals over suitable classes of control variates. A distinctive feature of the proposed approach is its ability to significantly reduce the overall finite sample variance. This feature ...
Added: October 10, 2019