Information geomerty of multidimensional models in statistics and artificial intelligence.

Multidimensional and highly-structured distributions underpin a number models in statistics and artificial intelligence with broad applications. Their theoretical background includes modern methods of statistics and calculi of uncertainty, involving theinformation geomerty as well. The goal of this project is investigation and development of geometrical approaches to these mathematical models, in particular, of the theory of exponential families, with applications in self-learning systems, and the theory of multidimensional models based on qualitative knowledge like conditional independence, graphically specified dependencies and symmetry. Expected theoretical results should enrich areas of the probability theory, statistics, calculi of uncertainty, theory of information and complexity, and open new application horizons in artificial intelligence.