Starts 9 Apr 2013 12:30
Ends 9 Apr 2013 20:00
Central European Time
ICTP
Leonardo da Vinci Building Luigi Stasi Seminar Room
Strada Costiera, 11 I - 34151 Trieste (Italy)
The study of complex systems is limited by the fact that only few variables are accessible for modeling and sampling, which are not necessarily the most relevant ones. In addition, empirical data typically under sample the space of possible states. We study a class of complex systems, which are systems of many interacting degrees of freedom, which are known only in part, that optimize a given function. We show that the information that a sample contains on the behavior of the system is quantified by the entropy of the frequency with which different states occur. This allows us to characterize the properties of maximally informative samples: In the under-sampling regime, the most informative frequency size distributions have power law behavior and Zipf's law emerges at the crossover between the under sampled regime and the regime where the sample contains enough statistics to make inference on the behavior of the system. These ideas are illustrated in some applications, showing that they can be used to identify relevant variables or to select most informative representations of data, e.g. in data clustering.
  • M. Poropat