This webpage provides a collection of research activities and publications on
Large amounts of data in high dimensions are becoming progressively available and accessible from various sources such as business enterprises, transaction-based information, social media, remote sensing technologies, wireless sensor networks, the Internet of Things as well as the Internet search and web analytics, and will continue to fuel exponential growth in data for the unforeseeable future. Therefore, the ability to analyse such large datasets, so-called big data, has become a key basis of competition, underpinning new waves of productivity growth, technological innovation, and consumer surplus. Achievements in these areas involve tasks requiring statistical manipulation and optimization over large sets of parameters, such as training artificial neural networks. Hence, it has become increasingly important, not only to be able to navigate high-dimensional landscapes but also to do so in a reasonable time.
For large-scale optimization problems, such as the ones originated by high dimensional machine learning problems, metaheuristics inspired by biological, social or opinion dynamics, have emerged as the go-to method. While metaheuristics offer high-level robust procedures that coordinate local and global search strategies to ‘quickly’ find sufficiently good-quality solutions, many lack any proof or guarantee of the quality of solutions. Well-known metaheuristics include simulated annealing, genetic algorithms, particle swarm optimization, ant colony optimization, artificial bee colony optimization, and hybrids thereof. On the other hand, interacting particle systems (IPS) are frequently used to investigate the emergence of collective behaviour in various applications such as mathematical biology, swarming, crowd dynamics, and opinion formation on social networks. In search of macroscopic patterns from microscopic interactions among agents, techniques from kinetic and mean-field theory are often employed. Purpose-driven Interacting Particle Systems aims in bringing the two fields together to develop a mathematical framework in which metaheuristics for optimization or sampling can be theoretically analyzed.