Образование и право2076-150310.24412/2076-1503-2026-5-704-712OtherАНАЛИТИЧНОСТЬ ФУНКЦИЙ КАК ОСНОВА ПРОГНОЗИРОВАНИЯ И МОДЕЛИРОВАНИЯ В МАШИННОМ ОБУЧЕНИИFUNCTION ANALYTICITY AS A BASIS FOR FORECASTING AND MODELING IN MACHINE LEARNINGСеменовАлександр АлександровичSemenovAlexander Alexandrovichmail@law-books.ruГончарВладимир ВладимировичGoncharVladimir Vladimirovichvg0778@bk.ruChief Researcher, Federal State Budgetary Institution “STIS”, of the Ministry of Internal Affairs of Russiaнаучный сотрудник ФКУ НПО «СТиС» МВД РоссииAssociate Professor, Department of Information, Technology and Cybercrime Investigation, Moscow Academy of the Investigative Committee, of the Russian Federation named after A. Ya. SukharevДоцент кафедры информационных технологий и, организации расследования киберпреступлений, Московская академия Следственного комитета, Российской Федерации имени А.Я. Сухарева2705202657047121505202627052026

В работе рассматривается аналитичность функции как ключевое свойство, определяющее возможность прогнозирования еёзначений по ограниченным данным. Показано, что степень аналитичности связана с непрерывностью, гладкостью и поведением производных различных порядков. Анализируется роль производных и их численного вычисления при отсутствии явного выражения функции, а также связь с рядом Тейлора. Подчеркивается, что методы прогнозирования, включая машинное обучение, опираются на предположение об аналитичности, а еёуровень напрямую влияет на точность восстановления и интерпретации зависимостей

This paper examines the analyticity of a function as a keyproperty determining the ability to predict itsvalues from limited data. It is shown that the degree of analyticity is related to the continuity, smoothness, and behavior of derivatives of different orders. The role of derivatives and their numerical calculation in the absence of an explicit expression of the function is analyzed, aswell astheir relationship with the Taylor series. It is emphasized that forecasting methods, including machine learning, rely on the assumption of analyticity, and itslevel directly affects the accuracy of recovery and interpretation of dependencies

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