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UID:600@fds.yale.edu
DTSTART;TZID=America/New_York:20230112T150000
DTEND;TZID=America/New_York:20230112T160000
DTSTAMP:20250916T142120Z
URL:https://fds.yale.edu/events/fds-seminar-arnab-auddy-columbia/
SUMMARY:FDS Seminar: Arnab Auddy (Columbia)
DESCRIPTION:"Statistical Benefits and Computational Challenges of Tensor Sp
 ectral Learning"\n\n\nTalk Abstract:Given multivariate observations from a
  statistical model\, tensors are a natural way of recording higher order i
 nteractions among variables. Tensor spectral learning is a collection of m
 ethods wherein we aim to decompose a tensor into its components\, each of 
 which correspond to interpretable features of the model. This approach has
  recently received a lot of attention for its application to latent variab
 le models. In this talk\, I will focus on orthogonally decomposable tensor
 s\, which arise naturally in many problems. These tensors have a decomposi
 tion that can be interpreted very similarly to matrix SVD\, but automatica
 lly provides much better identifiability properties than their matrix coun
 terparts. I will show that in such a tensor decomposition\, a small pertur
 bation affects each singular vector in isolation\, and their estimatibilit
 y does not depend on the gap between consecutive singular values. In contr
 ast to these attractive statistical properties\, in general\, tensor metho
 ds present us with intriguing computational considerations. I will illustr
 ate these phenomena in the particular application to a spiked tensor PCA p
 roblem and in Independent Component Analysis (ICA). Interestingly there is
  a gap within the information theoretic and computationally tractable limi
 ts of both problems. Above the computational threshold\, we provide noise 
 robust algorithms based on spectral truncation\, which provide rate optima
 l estimators. Our estimators are also asymptotically normal thus allowing 
 confidence interval construction. Finally I will present some examples dem
 onstrating our theoretical findings.\n\n\n\nThis talk was held virtually o
 n January 12\, 2023 @ 3:00 pm\n
CATEGORIES:FDS Events,Postdoctoral Applicants
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