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DTSTART:20220313T070000
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DTSTART:20211107T060000
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DTSTART;TZID=America/Toronto:20221020T160000
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URL:https://uwaterloo.ca/statistics-and-actuarial-science/events/distinguis
 hed-lecture-claudia-kluppelberg
LOCATION:M3 - Mathematics 3 M3 3127 Waterloo Canada
SUMMARY:Distinguished Lecture by Claudia Klüppelberg
CLASS:PUBLIC
DESCRIPTION:Please Note: This seminar will be given in-person.\n\nDistingu
 ished Lecture\n\nCLAUDIA KLÜPPELBERG \n_Technical University of Munich_\n
 \nRoom: M3 3127\n\nMAX-LINEAR GRAPHICAL MODELS FOR EXTREME RISK MODELLING\
 n\n-------------------------\n\nGraphical models can represent multivariat
 e distributions in an\nintuitive way and\, hence\, facilitate statistical 
 analysis of\nhigh-dimensional data. Such models are usually modular so tha
 t\nhigh-dimensional distributions can be described and handled by careful\
 ncombination of lower dimensional factors. Furthermore\, graphs are\nnatur
 al data structures for algorithmic treatment. Moreover\, graphical\nmodels
  can allow for causal interpretation\, often provided through a\nrecursive
  system on a directed acyclic graph (DAG) and the max-linear\nBayesian net
 work we introduced in [1] is a specific example. This talk\ncontributes to
  the recently emerged topic of graphical models for\nextremes\, in particu
 lar to max-linear Bayesian networks\, which are\nmax-linear graphical mode
 ls on DAGs. \n\nIn this context\, the Latent River Problem has emerged as
  a flagship\nproblem for causal discovery in extreme value statistics. In 
 [2] we\nprovide a simple and efficient algorithm QTree to solve the Laten
 t\nRiver Problem. QTree returns a directed graph and achieves almost\nperf
 ect recovery on the Upper Danube\, the existing benchmark dataset\,\nas we
 ll as on new data from the Lower Colorado River in Texas. It can\nhandle m
 issing data\, and has an automated parameter tuning procedure.\nIn our pap
 er\, we also show that\, under a max-linear Bayesian network\nmodel for ex
 treme values with propagating noise\, the QTree algorithm\nreturns asympto
 tically a.s. the correct tree. Here we use the fact\nthat the non-noisy mo
 del has a left-sided atom for every bivariate\nmarginal distribution\, whe
 n there is a directed edge between the the\nnodes.\n\nFor linear graphical
  models\, algorithms are often based on Markov\nproperties and conditional
  independence properties. In [3] we\ncharacterise conditional independence
  properties of max-linear\nBayesian networks and in my talk I will present
  some of these results\nand exemplify the difference to linear networks. 
DTSTAMP:20260501T153213Z
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