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UID:388@isdm.umontpellier.fr
DTSTART;TZID=Europe/Paris:20250310T140000
DTEND;TZID=Europe/Paris:20250310T140000
DTSTAMP:20260828T114219Z
URL:https://isdm.umontpellier.fr/events/distributional-matrix-completion-v
 ia-nearest-neighbors-in-the-wasserstein-space-3/
SUMMARY:Distributional Matrix Completion via Nearest Neighbors in the Wasse
 rstein Space
DESCRIPTION:Online\n\nMachine Learning in Montpellier\, Theory &amp\; Pract
 ice\n\nWe study the problem of distributional matrix completion: Given a s
 parsely observed matrix of empirical distributions\, we seek to impute the
  true distributions associated with both observed and unobserved matrix en
 tries. This is a generalization of traditional matrix completion where the
  observations per matrix entry are scalar-valued. To do so\, we utilize to
 ols from optimal transport to generalize the nearest neighbors method to t
 he distributional setting. Under a suitable latent factor model on probabi
 lity distributions\, we establish that our method recovers the distributio
 ns in the Wasserstein metric. We demonstrate through simulations that our 
 method (i) provides better distributional estimates for an entry compared 
 to using observed samples for that entry alone\, (ii) yields accurate esti
 mates of distributional quantities such as standard deviation and value-at
 -risk\, and (iii) inherently supports heteroscedastic distributions. In ad
 dition\, we demonstrate our method on a real-world quarterly earnings pred
 ictions dataset. We also prove novel asymptotic results for Wasserstein ba
 rycenters over one-dimensional distributions.\n\nMachine Learning in Montp
 ellier\, 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:20241027T020000
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