Joint work with Flore Sentenac (CREST)
Although robust learning and local differential privacy are both widely studied fields of research, combining the two settings is an almost unexplored topic. We...
Yannic Vargas (University of Potsdam)
The study of relations between moments and cumulants plays a central role in both classical and non-commutative probability theory. In the last decade, the work of Patras and Ebrahimi-Fard provided several tools related to the group of characters on a combinatorial Hopf algebra H of "words on words", and its corresponding Lie algebra of infinitesimal characters. This enables the study of distinct families of cumulants corresponding to different types of independences: free, boolean and monotone. We discuss several formulas for the (known) free-to-moment and boolean-to-moment relations, obtained from the antipode of H. Also, using a weighted Möbius inversion, we deduce a new relation of monotone cumulants in terms of moments.
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