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UID:20250917T210313EDT-0116FDpsjl@132.216.98.100
DTSTAMP:20250918T010313Z
DESCRIPTION:Title: Optimal vintage factor analysis with deflation varimax.
 \n\nAbstract:\n\nVintage factor analysis is one important type of factor a
 nalysis that aims to first find a low-dimensional representation of the or
 iginal data\, and then to seek a rotation such that the rotated low-dimens
 ional representation is scientifically meaningful. The most widely used vi
 ntage factor analysis is the Principal Component Analysis (PCA) followed b
 y the varimax rotation. Despite its popularity\, little theoretical guaran
 tee can be provided to date mainly because varimax rotation requires to so
 lve a non-convex optimization over the set of orthogonal matrices.\n\nIn t
 his paper\, we propose a deflation varimax procedure that solves each row 
 of an orthogonal matrix sequentially. In addition to its net computational
  gain and flexibility\, we are able to fully establish theoretical guarant
 ees for the proposed procedure in a broader context. Adopting this new def
 lation varimax as the second step after PCA\, we further analyze this two 
 step procedure under a general class of factor models. Our results show th
 at it estimates the factor loading matrix in the minimax optimal rate when
  the signal-to-noise-ratio (SNR) is moderate or large. In the low SNR regi
 me\, we offer possible improvement over using PCA and the deflation varima
 x when the additive noise under the factor model is structured. The modifi
 ed procedure is shown to be minimax optimal in all SNR regimes. Our theory
  is valid for finite sample and allows the number of the latent factors to
  grow with the sample size as well as the ambient dimension to grow with\,
  or even exceed\, the sample size. Extensive simulation and real data anal
 ysis further corroborate our theoretical findings.\n\nSpeaker\n\nXin has b
 een an Assistant Professor in the Department of Statistical Sciences at th
 e University of Toronto since March\, 2022. He finished his Ph.D. in Stati
 stics at Cornell University\, advised jointly by Florentina Bunea and Mart
 en Wegkamp. Xin’s research interest generally lies in mathematical statist
 ics and developing new methodology with theoretical guarantees to tackle m
 odern statistical problems such as high-dimensional statistics\, mixture m
 odels\, statistical and computational trade-offs. He is also interested in
  applications of statistical methods to genetics\, neuroscience\, immunolo
 gy\, and other areas.\n
DTSTART:20250919T203000Z
DTEND:20250919T213000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Xin Bing (University of Toronto)
URL:/science/channels/event/xin-bing-university-toront
 o-367771
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