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Algorithmic Statistics: Forty Years Later.
Lecture Notes in Computer Science. 2017. Vol. 10010. P. 669–737.
Vereshchagin N., Shen A.
Algorithmic statistics has two different (and almost orthogonal) motivations. From the philosophical point of view, it tries to formalize how the statistics works and why some statistical models are better than others. After this notion of a "good model" is introduced, a natural question arises: it is possible that for some piece of data there is no good model? If yes, how often these bad ("non-stochastic") data appear "in real life"? Another, more technical motivation comes from algorithmic information theory. In this theory a notion of complexity of a finite object (=amount of information in this object) is introduced; it assigns to every object some number, called its algorithmic complexity (or Kolmogorov complexity). Algorithmic statistic provides a more fine-grained classification: for each finite object some curve is defined that characterizes its behavior. It turns out that several different definitions give (approximately) the same curve. In this survey we try to provide an exposition of the main results in the field (including full proofs for the most important ones), as well as some historical comments. We assume that the reader is familiar with the main notions of algorithmic information (Kolmogorov complexity) theory.
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
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
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
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
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
Petrovanov I., Sergeev A., / Series Computer Science "arxiv.org". 2025. No. 2512.18332.
Transport coding reduces message delay in packet-switched networks by introducing controlled redundancy at the transport layer: original packets are encoded into coded packets, and the message is reconstructed after the first successful deliveries, effectively shifting latency from the maximum packet delay to the -th order statistic. We present a concise, reproducible discrete-event implementation of transport coding in OMNeT++, including ...
Added: December 24, 2025
Semenov A., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2025 Т. 527 № S С. 7–12
The paper proposes a system of definitions for the basic concepts of computability theory that underlie the mathematics of the digital world: algorithm, computability, calculus, object complexity, close to modern undertnding. Hierarchies of the finite and the problem of consistency are considered. ...
Added: December 6, 2025
Hessian-based lightweight neural network for brain vessel segmentation on a minimal training dataset
Меньшиков И. А., Бернадотт А. К., Elvimov N. S., / Series arXie "Statistical mechanics". 2025.
Accurate segmentation of blood vessels in brain magnetic resonance angiography (MRA) is essential for successful surgical procedures, such as aneurysm repair or bypass surgery. Currently, annotation is primarily performed through manual segmentation or classical methods, such as the Frangi filter, which often lack sufficient accuracy. Neural networks have emerged as powerful tools for medical image ...
Added: December 1, 2025
Rubchinskiy A., Chubarova D., / Series WP7 "Математические методы анализа решений в экономике, бизнесе и политике". 2025. No. WP7/2025/01.
The article examines one of the most famous examples of socio-economic systems, characterized by significant uncertainty – the S&P-500 stock market, where shares of 500 largest US companies are traded. No assumptions are made about the probabilistic characteristics of the stock market. A flexible algorithm for daily trading has been developed, based on both known fixed data ...
Added: November 9, 2025
Semenov A., Shen A., Vereshchagin N., Theory of Probability and its Applications, USA 2024 Vol. 68 No. 4 P. 582–606
The definition of descriptional complexity of finite objects suggested by Kolmogorov and other authors in the mid-1960s is now well known. In addition, Kolmogorov pointed out some approaches to a more fine-grained classification of finite objects, such as the resource-bounded complexity (1965), structure function (1974), and the notion of $(\alpha,\beta)$-stochasticity (1981). Later it turned out ...
Added: January 16, 2025
Vereshchagin N., / Series arXiv "math". 2024.
The fine approach to measure information dependence is based on the total conditional complexity CT(y|x), which is defined as the minimal length of a total program that outputs y on the input x. It is known that the total conditional complexity can be much larger than than the plain conditional complexity. Such strings x, y ...
Added: August 19, 2024
Bauwens B. F., Zimand M., Journal of the ACM 2023 Vol. 70 No. 2 Article 9
In a lossless compression system with target lengths, a compressor 𝒞 maps an integer m and a binary string x to an m-bit code p, and if m is sufficiently large, a decompressor 𝒟 reconstructs x from p. We call a pair (m,x) achievable for (𝒞,𝒟) if this reconstruction is successful. We introduce the notion ...
Added: March 22, 2023
Bauwens B. F., Gács P., Romashchenko A. et al., Computability 2022 Vol. 11 No. 3-4 P. 165–185
Finding all linear inequalities for entropies remains an important open question in information theory. For a long time the only known inequalities for entropies of tuples of random variables were Shannon (submodularity) inequalities. Only in 1998 Zhang and Yeung 1998 found the first inequality that cannot be represented as a convex combination of Shannon inequalities, and ...
Added: December 23, 2022
Vereshchagin N., Theoretical Computer Science 2023 Vol. 940 P. 108–122
We consider the network consisting of three nodes 1, 2, 3 connected by two open channels
1 → 2 and 1 → 3. The information present in the node 1 consists of four strings x , y , z , w.
The nodes 2, 3 know x , w and need to know y , z, respectively. ...
Added: December 19, 2022
Milovanov A., , in: Computer Science – Theory and Applications: 16th International Computer Science Symposium in Russia, CSR 2021, Sochi, Russia, June 28–July 2, 2021, Proceedings.: Springer, 2021. Ch. 17 P. 283–295.
We combine Solomonoff’s approach to universal prediction with algorithmic statistics and suggest to use the computable measure that provides the best “explanation” for the observed data (in the sense of algorithmic statistics) for prediction. In this way we keep the expected sum of squares of prediction errors bounded (as it was for the Solomonoff’s predictor) ...
Added: August 11, 2021
Bauwens B. F., Blinnikov I., , in: Computer Science – Theory and Applications 15th International Computer Science Symposium in Russia, CSR 2020, Yekaterinburg, Russia, June 29 – July 3, 2020, ProceedingsVol. 12159.: Springer, 2020. P. 130–141.
It is known that the normalized algorithmic information distance is not computable and not semicomputable. We show that for all 𝜀<1/2, there exist no semicomputable functions that differ from N by at most 𝜀. Moreover, for any computable function f such that |lim𝑡𝑓(𝑥,𝑦,𝑡)−N(𝑥,𝑦)|≤𝜀 and for all n, there exist strings x, y of length n such that ...
Added: February 5, 2021
Bauwens B. F., , in: 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)Vol. 154: Leibniz International Proceedings in Informatics (LIPIcs).: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2020. P. 46:1–46:14.
Added: March 20, 2020
Vereshchagin N., Theoretical Computer Science 2020 Vol. 809 P. 531–537
The purpose of this paper is to answer two questions left open in [B. Durand, A. Shen, and N. Vereshchagin, Descriptive Complexity of Computable Sequences, Theoretical Computer Science 171 (2001), pp. 47--58]. Namely, we consider the following two complexities of an infinite computable 0-1-sequence $\alpha$: $C^{0'}(\alpha )$, defined as ...
Added: January 17, 2020
Shen A., Vereshchagin N., , in: Computability and Complexity.: Berlin: Springer, 2017. P. 669–737.
Algorithmic statistics has two different (and almost orthogonal) motivations. From the philosophical point of view, it tries to formalize how the statistics works and why some statistical models are better than others. After this notion of a "good model" is introduced, a natural question arises: it is possible that for some piece of data there ...
Added: October 26, 2018
Milovanov A., Theory of Computing Systems 2019 Vol. 63 No. 4 P. 833–848
Algorithmic statistics looks for models of observed data that are good in the following sense: a model is simple (i.e., has small Kolmogorov complexity) and captures all the algorithmically discoverable regularities in the data. However, this idea can not be used in practice as is because Kolmogorov complexity is not computable. In this paper we ...
Added: October 17, 2018
Posobin G. I., Shen A., Andreev M., , in: 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)Vol. 117.: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2018. P. 1–24.
In this paper we analyze the notion of "stopping time complexity", informally defined as the amount of information needed to specify when to stop while reading an infinite sequence. This notion was introduced by Vovk and Pavlovic (2016). It turns out that plain stopping time complexity of a binary string x could be equivalently defined as (a) ...
Added: October 11, 2018
Rubtsov A. A., , in: Developments in Language Theory 22nd International Conference, DLT 2018, Tokyo, Japan, September 10-14, 2018, Proceedings.: Cham: Springer, 2018. P. 553–565.
We present a new structural lemma for deterministic con- text free languages. From the first sight, it looks like a pumping lemma, because it is also based on iteration properties, but it has significant distinctions that makes it much easier to apply. The structural lemma is a combinatorial analogue of KC-DCF-Lemma (based on Kolmogorov complexity), ...
Added: September 12, 2018