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UID:20250803T203149EDT-4289oPKHdc@132.216.98.100
DTSTAMP:20250804T003149Z
DESCRIPTION:Title: Generalized Hoeffding decomposition and the (surprising)
  linear nature of non-linearities.\n\nAbstract: Hoeffding's functional dec
 omposition plays a crucial role in global sensitivity analysis and explain
 able AI\, enabling the extraction of meaningful insights from black-box mo
 dels. However\, its application traditionally relies on the assumption of 
 mutual independence among the model's inputs. Generalizing this result to 
 non-mutually independent inputs has been an important challenge in the fie
 ld of uncertainty quantification.\n\nIn this talk\, we will explore how th
 is decomposition can be extended to accommodate dependent inputs\, given t
 wo reasonable assumptions: non-perfect functional dependence and non-degen
 erate stochastic dependence. This generalization requires approaching the 
 problem using a framework at the cornerstone of probability theory\, funct
 ional analysis\, and combinatorics. This generalization can be approached 
 as a direct-sum decomposition problem of generated Lebesgue space\, unveil
 ing a surprisingly linear approach to handling stochastic and functional n
 on-linearities. The proposed 'ortho-canonical decomposition' relies on obl
 ique projections rather than the traditional conditional expectations.\n\n
 In Person: Burnside Hall\, Room 719A\, 805 Rue Sherbrooke O\, Montréal\, Q
 C H3A 2K6\n\nZoom Link: https://umontreal.zoom.us/j/87805116449?pwd=Zqn2bG
 upljZwDftmU9iiAi7kpHMXaF.1\n\n \n
DTSTART:20240912T163000Z
DTEND:20240912T173000Z
LOCATION:Room 719A\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Marouane Il Idrissi (UQAM)
URL:/mathstat/channels/event/marouane-il-idrissi-uqam-
 359336
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