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UID:179@isdm.umontpellier.fr
DTSTART;TZID=Europe/Paris:20260618T140000
DTEND;TZID=Europe/Paris:20260618T140000
DTSTAMP:20260825T115948Z
URL:https://isdm.umontpellier.fr/events/the-distribution-of-calibrated-lik
 elihood-functions-on-the-probability-likelihood-simplex-2/
SUMMARY:The distribution of calibrated likelihood functions on the probabil
 ity-likelihood simplex
DESCRIPTION:Room 167\, Building 2\, St Priest campus\n\nMachine Learning in
  Montpellier\, Theory &amp\; Practice - Paul-Gauthier Noé (LIS - CNRS / A
 ix Marseille Université)\n\nWhile calibration of probabilistic prediction
 s has been widely studied\, we will rather discuss calibration of likeliho
 od functions. This has been studied\, especially in biometrics\, in cases 
 with only two exhaustive and mutually exclusive hypotheses (or classes): w
 here likelihood functions can be written as log-likelihood-ratios (LLRs). 
 After defining calibration for LLRs and its connection with the concept of
  weight-of-evidence\, I will present the idempotence property and its asso
 ciated constraint on the distribution of the LLRs. Although these results 
 have been known for decades\, they have been limited to the binary case. I
 n this talk\, we will see how the Aitchison geometry of the simplex allows
  us to extend these results to cases with more than two hypotheses. To be 
 more precise\, it recovers\, in a vector form\, the additive form of the B
 ayes' rule\; extending therefore the LLR and the weight-of-evidence to any
  number of hypotheses. Especially\, we will extend the definition of calib
 ration\, the idempotence\, and the constraint on the distribution of likel
 ihood functions to this multiple hypotheses and multiclass counterpart of 
 the LLR: the isometric-log-ratio transformed likelihood function. Even if 
 this work is mainly conceptual\, we will discuss one application to machin
 e learning by presenting a non-linear discriminant analysis where the disc
 riminant components form a calibrated likelihood function over the classes
 \, improving therefore the interpretability and the reliability of the met
 hod.\n\nMachine Learning in Montpellier\, Theory &amp\; Practice
ATTACH;FMTTYPE=image/jpeg:https://isdm.umontpellier.fr/wp-content/uploads/
 2026/06/ml-mtp-gC78d5.png
CATEGORIES:ML MTP
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DTSTART:20260329T030000
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