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UID:518@fds.yale.edu
DTSTART;TZID=America/New_York:20240417T113000
DTEND;TZID=America/New_York:20240417T130000
DTSTAMP:20250916T142133Z
URL:https://fds.yale.edu/events/fds-member-colloquium-van-vu-department-of
 -mathematics/
SUMMARY:FDS Member Colloquium: Van Vu (Department of Mathematics)\, “New 
 perturbation bounds for matrices with rapidly decaying spectrum”
DESCRIPTION:\n\n\n\n\n\n\n\nSpeaker: Van Vu\n\n\n\nPercey F. Smith Professo
 r of MathematicsDepartment of Mathematics\,Yale University\n\n\n\nWednesda
 y\, April 17\, 2024\n\n\n\n11:30 am: Lunch (Kitchen)12:00 pm - 1:00 pm: Ta
 lk (Seminar Room #1327)\n\n\n\nLocation: Yale Institute for Foundations of
  Data Science\, Kline Tower\, 13th floor and via Zoom (starts at 12:00 pm)
 : https://yale.zoom.us/s/7859884026 (meeting ID: 7859884026)\n\n\n\n\n\nAb
 stract: Matrix perturbation bounds (such as Weyl and Davis-Kahan) form an 
 important part of the mathematical foundation of data science.\n\n\n\nIn m
 any recent studies\, it has been observed/assumed that large data matrices
  have rapidly decaying spectrum(low rank is an extreme example).\n\n\n\nWe
  are going to discuss new perturbation bounds for these matrices. Our focu
 s will be on the perturbation of eigenvectors and eigensubspaces (Davis-Ka
 han type bounds). Our new results will improve the original Davis-Kahan bo
 und in several aspects. In particular\, we will not require the gap-to-noi
 se ratio to be large. More importantly\, the new bounds take into account 
 the interaction between the noise matrix and the eigenvectors of the data 
 matrix.\n\n\n\nWe will present few applications\, including a new error an
 alysis for:\n\n\n\n1\, PCA of sample covariance matrices.2\, Low rank appr
 oximation.\n\n\n\n(Partially joined with P. Tran\, S. O'rourke\, K. Wang)\
 n\n\n\n\n\n\n\n\n\n\n\n\n
ATTACH;FMTTYPE=image/jpeg:https://fds.yale.edu/wp-content/uploads/2024/02/
 VU-h-300x300.jpeg
CATEGORIES:FDS Events,Colloquium,Seminar Series
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