Related papers: The Foundation of Big Data: Experiments, Formulati…
Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…
Big Data concern large-volume, growing data sets that are complex and have multiple autonomous sources. Earlier technologies were not able to handle storage and processing of huge data thus Big Data concept comes into existence. This is a…
There exists a wide variety of works on the dynamics of large populations ranging from simple heuristic modeling to those based on advanced computer supported methods. Their interconnections, however, remain mostly vague, which…
Big Data is reforming many industrial domains by providing decision support through analyzing large data volumes. Big Data testing aims to ensure that Big Data systems run smoothly and error-free while maintaining the performance and…
A new approach to the problem of finding the asymptotical behaviour of large orders of semiclassical expansion is suggested. Asymptotics of high orders not only for eigenvalues, but also for eigenfunctions, are constructed. Thus, one can…
The success of AI models relies on the availability of large, diverse, and high-quality datasets, which can be challenging to obtain due to data scarcity, privacy concerns, and high costs. Synthetic data has emerged as a promising solution…
Compositional understanding is crucial for human intelligence, yet it remains unclear whether contemporary vision models exhibit it. The dominant machine learning paradigm is built on the premise that scaling data and model sizes will…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated…
Social scientists are increasingly turning to unstructured datasets to unlock new empirical insights, e.g., estimating descriptive statistics of or causal effects on quantitative measures derived from text, audio, or video data. In many…
Modern data and applications pose very different challenges from those of the 1950s or even the 1980s. Students contemplating a career in statistics or data science need to have the tools to tackle problems involving massive, heavy-tailed…
A critical examination of some basic conceptual issues in classical statistical mechanics is attempted, with a view to understanding the origins, structure and statuts of that discipline. Due attention is given to the interplay between…
Turing's (1936) paper on computable numbers has played its role in underpinning different perspectives on the world of information. On the one hand, it encourages a digital ontology, with a perceived flatness of computational structure…
This article focuses on the problem of the authenticity of knowledge. It argues that the failure to integrate the observer into the act of observing is the main source of the disagreements and divisions in contemporary science and…
The goal of Science is to understand phenomena and systems in order to predict their development and gain control over them. In the scientific process of knowledge elaboration, a crucial role is played by models which, in the language of…
Let $S$ be a finite set, and $X_1,\ldots,X_n$ an i.i.d. uniform sample from $S$. To estimate the size $|S|$, without further structure, one can wait for repeats and use the birthday problem. This requires a sample size of the order…
Many ground-breaking advancements in machine learning can be attributed to the availability of a large volume of rich data. Unfortunately, many large-scale datasets are highly sensitive, such as healthcare data, and are not widely available…
This is a review of the Riemann-Hilbert approach to the large $N$ asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach to…
A network is a typical expressive form of representing complex systems in terms of vertices and links, in which the pattern of interactions amongst components of the network is intricate. The network can be static that does not change over…
There are two main opposing schools of statistical reasoning, Frequentist and Bayesian approaches. Until recent days, the frequentist or classical approach has dominated the scientific research, but Bayesianism has reappeared with a strong…