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SUMMARY:Data Depth: Methodology and Computation - Pavlo Mozharovskyi (Tele
 com Paris\, Institut Polytechnique de Paris)
DTSTART:20250506T091500Z
DTEND:20250506T101500Z
UID:TALK230434@talks.cam.ac.uk
DESCRIPTION:Data depth is a statistical function that measures centrality 
 of an observation with respect to a probability distribution\, with an emp
 irical measure (on a data set) being its most important particular case. B
 y exploiting the geometry of data\, the depth function is fully non-parame
 tric\, robust to both outliers and heavy tailed distributions\, and satisf
 ies desirable invariances. By dint of these advantages\, it is used in a v
 ariety of tasks as a generalisation of quantiles in higher dimensions and 
 as an alternative to the probability density. Introduced in the second hal
 f of the twentieth century and having undergone theoretical and computatio
 nal developments since then\, data depth became a universal methodology fo
 r ordering complex data and is now employed in numerous applications: supe
 rvised and unsupervised machine learning\, robust optimisation\, financial
  risk assessment\, statistical quality control\, extreme value theory\, im
 putation of missing data\, etc.\nIn this presentation\, we should survey t
 he notion of data depth and highlight its most relevant advantages. We sha
 ll start with the formal definition of statistical data depth function and
  study of its (most important) properties. This will be followed by an ass
 ortment and analysis of commonly used depth notions. Furthermore\, relevan
 t computational aspects will be regarded including most recent advances th
 at allow depth-based applications on contemporary scale. The presentation 
 shall be accompanied by application examples on synthetic and real data se
 ts. Finally\, several open questions will be discussed in the outlook.
LOCATION:Seminar Room 1\, Newton Institute
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