Speaker: Van Vu
Percey F. Smith Professor of Mathematics
Department of Mathematics,
Yale University
Wednesday, April 17, 2024
11:30 am: Lunch (Kitchen)
12:00 pm – 1:00 pm: Talk (Seminar Room #1327)
Location: 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)
Abstract: Matrix perturbation bounds (such as Weyl and Davis-Kahan) form an important part of the mathematical foundation of data science.
In many recent studies, it has been observed/assumed that large data matrices have rapidly decaying spectrum
(low rank is an extreme example).
We are going to discuss new perturbation bounds for these matrices. Our focus will be on the perturbation of eigenvectors and eigensubspaces (Davis-Kahan type bounds). Our new results will improve the original Davis-Kahan bound in several aspects. In particular, we will not require the gap-to-noise 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.
We will present few applications, including a new error analysis for:
1, PCA of sample covariance matrices.
2, Low rank approximation.
(Partially joined with P. Tran, S. O’rourke, K. Wang)
