English
Related papers

Related papers: Testing statistical laws in complex systems

200 papers

A systematic, comparative investigation into the effects of low-quality data reveals a stark spectrum of robustness across modern probabilistic models. We find that autoregressive language models, from token prediction to…

Artificial Intelligence · Computer Science 2025-12-16 Liu Peng , Yaochu Jin

This paper is about how we study statistical methods. As an example, it uses the random regressions model, in which the intercept and slope of cluster-specific regression lines are modeled as a bivariate random effect. Maximizing this…

Other Statistics · Statistics 2019-05-22 James S. Hodges

Studying the reliability of complex systems using machine learning techniques involves facing a series of technical and practical challenges, ranging from the intrinsic nature of the system and data to the difficulties in modeling and…

Machine Learning · Computer Science 2024-10-08 Maria Luz Gamiz , Fernando Navas-Gomez , Rafael Nozal-Cañadas , Rocio Raya-Miranda

Zipf's law states that sequential frequencies of words in a text correspond to a power function. Its probabilistic model is an infinite urn scheme with asymptotically power distribution. The exponent of this distribution must be estimated.…

Statistics Theory · Mathematics 2017-06-15 Mikhail Chebunin , Artyom Kovalevskii

Fractals, 1/f noise, Zipf's law, and the occurrence of large catastrophic events are typical ubiquitous general empirical observations across the individual sciences which cannot be understood within the set of references developed within…

Physics and Society · Physics 2018-12-21 Yanguang Chen

The ubiquity of power-law relations in empirical data displays physicists' love of simple laws and uncovering common causes among seemingly unrelated phenomena. However, many reported power laws lack statistical support and mechanistic…

Physics and Society · Physics 2016-01-21 Sun-Ting Tsai , Chin-De Chang , Ching-Hao Chang , Meng-Xue Tsai , Nan-Jung Hsu , Tzay-Ming Hong

Here we present a new class of optimality for coding systems. Members of that class are displaced linearly from optimal coding and thus exhibit Zipf's law, namely a power-law distribution of frequency ranks. Within that class, Zipf's law,…

Computation and Language · Computer Science 2025-10-31 Ramon Ferrer-i-Cancho

Zipf's law is the main regularity of quantitative linguistics. Despite of many works devoted to foundations of this law, it is still unclear whether it is only a statistical regularity, or it has deeper relations with information-carrying…

Computation and Language · Computer Science 2018-09-25 Weibing Deng , Armen E. Allahverdyan

Not all experiments publish their results with a description of the correlations between the data points. This makes it difficult to do hypothesis tests or model fits with that data, since just assuming no correlation can lead to an over-…

Data Analysis, Statistics and Probability · Physics 2021-06-30 Lukas Koch

Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…

Physics and Society · Physics 2014-11-11 Filippo Radicchi

In a language corpus, the probability that a word occurs $n$ times is often proportional to $1/n^2$. Assigning rank, $s$, to words according to their abundance, $\log s$ vs $\log n$ typically has a slope of minus one. That simple Zipf's law…

Populations and Evolution · Quantitative Biology 2019-03-27 Steven A. Frank

The review summarizes the main methodological concepts used in studying natural language from the perspective of complexity science and documents their applicability in identifying both universal and system-specific features of language in…

Physics and Society · Physics 2024-01-09 Tomasz Stanisz , Stanisław Drożdż , Jarosław Kwapień

Bayesian modelling and statistical text analysis rely on informed probability priors to encourage good solutions. This paper empirically analyses whether text in medical discharge reports follow Zipf's law, a commonly assumed statistical…

Computation and Language · Computer Science 2020-11-09 Juan C Quiroz , Liliana Laranjo , Catalin Tufanaru , Ahmet Baki Kocaballi , Dana Rezazadegan , Shlomo Berkovsky , Enrico Coiera

We checked that the distribution of words in text should uniform, which gives Heaps' law as natural result, that is, the number of types of words can be expressed as a power law of the number of tokens within text. We developed a…

Physics and Society · Physics 2025-04-16 Kim Chol-jun

The word embedding space in neural models is skewed, and correcting this can improve task performance. We point out that most approaches for modeling, correcting, and measuring the symmetry of an embedding space implicitly assume that the…

Computation and Language · Computer Science 2024-11-04 Sho Yokoi , Han Bao , Hiroto Kurita , Hidetoshi Shimodaira

The problem of compression in standard information theory consists of assigning codes as short as possible to numbers. Here we consider the problem of optimal coding -- under an arbitrary coding scheme -- and show that it predicts Zipf's…

Computation and Language · Computer Science 2020-09-24 Ramon Ferrer-i-Cancho , Christian Bentz , Caio Seguin

Statistical regularities in human language have fascinated researchers for decades, suggesting deep underlying principles governing its evolution and information structuring for efficient communication. While Zipf's Law describes the…

Physics and Society · Physics 2025-04-29 Alessandro Bellina , Vito D. P. Servedio

We present an impossibility result, called a theorem about facts and words, which pertains to a general communication system. The theorem states that the number of distinct words used in a finite text is roughly greater than the number of…

Information Theory · Computer Science 2022-11-03 Łukasz Dębowski

We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…

Data Analysis, Statistics and Probability · Physics 2007-07-17 D. Sornette

In this paper we deal with the structural properties of weighted networks. Starting from an empirical analysis of a linguistic network, we analyse the differences between the statistical properties of a real and a shuffled network and we…

Data Analysis, Statistics and Probability · Physics 2009-09-07 A. P. Masucci , G. J. Rodgers