Метод крестовой тензорной интерполяции для глобальной дискретной оптимизации в задаче байесовского вывода графов

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Аннотация

Глобальная дискретная оптимизация является сложной задачей из-за отсутствия градиентов и невозможности полного перебора при большом числе переменных. Эффективным методом для аппроксимации многомерных тензоров (и дискретизированных функций) являются крестовые интерполяции, использующие небольшое число адаптивно выбранных строк и столбцов в тензоре, пересекающихся на подматрицах (почти) максимального объема. Такие подматрицы часто содержат большие по модулю элементы, поэтому элементы тензора, найденные в методе крестовой интерполяции, являются хорошими приближениями глобального максимума в тензоре. В этой статье мы рассматриваем эпидемический процесс на уровне индивидуумов, и задачу байесовского вывода социального графа индивидуумов по данным наблюдений эпидемических состояний индивидуумов во времени. Численные эксперименты демонстрируют, что данный граф может быть найден с высокой точностью путем максимизации правдоподобия с помощью метода крестовой тензорной интерполяции. Предложенный подход является достаточно общим и может применяться для глобальной дискретной оптимизации в других задачах, например, для настройки дискретных параметров моделей.

Об авторах

С. Долгов

Университет Бата

Email: S.Dolgov@bath.ac.uk
Бат, Великобритания

Д. Савостьянов

Университет Эссекса

Email: D.Savostyanov@essex.ac.uk
Колчестер, Великобритания

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