RANDOM VARIABLE GENERATION ALGORITHMS

Generative algorithms are a rapidly developing field in artificial intelligence. The generation and retrieval of text, images, and video are becoming increasingly popular tools to assist in content creation. In recent years, training machine learning algorithms using big data has become one of the key tasks of modern science and practice. However, in a number of areas, the availability of truly large data sets is limited or impossible due to confidentiality, the high cost of collecting information, or the rarity of events. In such cases, synthetic data generation becomes particularly important, providing opportunities for data augmentation, modeling, and experimental evaluation without the risk of exposing sensitive information. Modern approaches to synthetic data rely both on statistical methods for generating random variables and on advanced generative models, such as Variational Autoencoders (VAE), Generative Adversarial Networks (GAN), and diffusion models, which demonstrate high accuracy and flexibility across various applied tasks. This paper provides a review of algorithms that generate discrete and continuous random variables. Special attention is given to models for sequential data, including TimeGAN, and RTSGAN, which enable effective modeling of time series in healthcare, financial forecasting, and autonomous systems. The article discusses the architectures of these models, their training methodologies, key innovations, and practical applications. Additionally, methods for evaluating the quality of synthetic data, their reliability, and ethical considerations are addressed. Based on an analysis of recent research, promising areas for the development of generative models aimed at improving interpretability, reliability, and specific focus on subject areas are identified.

synthetic data, generative algorithms, generalised entropy method, neural networks, competitive generative models, variational autoencoders.

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2026-03-30