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SUMMARY:Construction of Admissible Decision Procedures in Statistical Clas
sification
DTSTART;VALUE=DATE-TIME:20220803T123000Z
DTEND;VALUE=DATE-TIME:20220803T125000Z
DTSTAMP;VALUE=DATE-TIME:20231211T162954Z
UID:indico-contribution-1221@conference2.aau.at
DESCRIPTION:To classify an observation\, we assume that each class can be
represented by a probability distribution\, which might be the result of a
previous estimate. An older but famous example is provided by Fisher's cl
assification of iris species based on length measurements of their sepals
and petals with class-related distributions. With the increasing relevance
of machine learning methods\, classification is a current research topic.
Applications include object classification in image recognition or text c
lassification\, often referring to the example of spam filters. Although c
lassification problems arise almost everywhere in the digital world and nu
merous algorithmic solutions are being worked on\, even elementary mathema
tical foundations seem to have been treated only incompletely or for speci
al cases so far.\n\nFraming classification in terms of statistical decisio
n theory\, we consider a classification problem as a family of probability
distributions $(P_i:i \\in I)$ with a finite class index set $I$ being th
e decision space\, and investigate several optimality criteria of randomis
ed decision procedures. In this regard\, we obtained the result that a gen
eralization of the Neyman-Pearson lemma characterizes all admissible proce
dures\, that is\, procedures with minimal error probabilities. In certain
binary problems\, this characterization yields procedures representable by
class separating nonlinear hypersurfaces. Note that hyperplanes therefore
generally do not provide admissible classification\, even if the training
data should be linearly separable. The aim of this talk is to present som
e further geometrical conditions for admissibility based on the risk set\,
and to deduce an analytical method for determining admissible procedures\
, in particular those that additionally fulfill the minimax condition\, an
d to indicate further questions we intend to pursue.\n\nhttps://conference
2.aau.at/event/131/contributions/1221/
LOCATION:Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1221/
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