Cohomological Characterization of Information Structures

Explore the cohomological characterization of information and higher order statistical structures in this 58-minute lecture by Pierre Baudot from Median Technologies. Delve into methods quantifying statistical interactions within datasets using information theory in cohomology, expressed through statistical physics and machine learning. Examine the Information Cohomology formalism, which uniquely characterizes entropy as the first class of cohomology and Multivariate Mutual Informations as coboundary. Investigate applications of the simplicial subcase to genetic expression and machine learning datasets, understanding how mutual statistical independence relates to vanishing k-MI and how cohomology quantifies the obstruction to statistical factorization. Discover the implications for genetic expression analysis, cell-type classification, and deep learning architectures. Gain insights into the topological approach to information theory and its relevance to both theoretical and applied domains in data science and bioinformatics.