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URL;TYPE=URI:https://www.wpi.edu/news/calendar/events/mathematical-sciences
 -department-colloquium-anna-seigal-harvard-university
SUMMARY:Mathematical Sciences Department Colloquium: Anna Seigal, Harvard U
 niversity
DESCRIPTION:Mathematical Sciences Colloquium\nAnna Seigal, Harvard Universi
 ty\nFriday, September 18\n11:00 am\n\nTitle: Multi-context principal compo
 nent analysis\nAbstract: Principal component analysis (PCA)finds axes that
  explain variation in data.Across domains, a current challenge is to under
 stand how data change across contexts (for example, patients across diseas
 es or words across genres). We propose multi-context principal component a
 nalysis (MCPCA), a generalization of PCA to find variance-optimal axes of 
 variation and the combinations of contexts in which they appear. Just as u
 sual principal component analysis is a low-rank approximation of the covar
 iance matrix, MCPCA finds a low rank approximation of the third-order tens
 or obtained by stacking covariance matrices across contexts. I’ll describe
  our algorithm for MCPCA, its theoretical guarantees, and applications to 
 study gene expression across disease types and contextualized word embeddi
 ngs across genres of text. Based on joint work with Kexin Wang, Salil Bhat
 e, João Pereira, Joe Kileel, and Matylda Figlerowicz\n
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