A review on probabilistic graphical models in evolutionary computation

Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Evolutionary algorithms is one such discipline that has employed probabilistic graphical models to improve the search for optimal solutions in complex problems. This paper shows how probabilistic graphical models have been used in evolutionary algorithms to improve their performance in solving complex problems. Specifically, we give a survey of probabilistic model building-based evolutionary algorithms, called estimation of distribution algorithms, and compare different methods for probabilistic modeling in these algorithms

Markov Properties of Discrete Determinantal Point Processes

Determinantal point processes (DPPs) are probabilistic models for repulsion. When used to represent the occurrence of random subsets of a finite base set, DPPs allow to model global negative associations in a mathematically elegant and direct way. Discrete DPPs have become popular and computationally tractable models for solving several machine learning tasks that require the selection of diverse objects, and have been successfully applied in numerous real-life problems. Despite their popularity, the statistical properties of such models have not been adequately explored. In this note, we derive the Markov properties of discrete DPPs and show how they can be expressed using graphical models.Comment: 9 pages, 1 figur