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DTSTART:20241103T020000
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DESCRIPTION:BIS 526 students are required to attend in person. Others are 
 allowed to attend in person but may also attend via zoom. Speaker- Lingzh
 ou Xue\, Ph.D. Title- Dimension Reduction for Fréchet Regression Abstract
  With the rapid development of data collection techniques\, complex data 
 objects are frequently encountered in new statistical applications. Fréch
 et regression model (Peterson & Müller 2019) provides a promising framewo
 rk for regression analysis with metric space-valued responses. In this pa
 per\, we introduce a flexible sufficient dimension reduction (SDR) method
  for Fréchet regression to achieve two purposes: to mitigate the curse of
  dimensionality caused by high-dimensional predictors and to provide a vi
 sual inspection tool for Fréchet regression. Our approach is flexible eno
 ugh to turn any existing SDR method for Euclidean (X\, Y) into one for Eu
 clidean X and metric space-valued Y. The basic idea is to first map the m
 etric-space valued random object Y to a real-valued random variable f(Y) 
 using a class of functions and then perform classical SDR to the transfor
 med data. If the class of functions is sufficiently rich\, then we are gu
 aranteed to uncover the Fréchet SDR space. We showed that such a class\, 
 which we call an ensemble\, can be generated by a universal kernel. We es
 tablished the consistency and asymptotic convergence rate of the proposed
  methods. The finite-sample performance of the proposed methods is illust
 rated through simulation studies for several commonly encountered metric 
 spaces that include Wasserstein space\, the space of symmetric positive d
 efinite matrices\, and the sphere. We illustrated the data visualization 
 aspect of our method by exploring the human mortality distribution data a
 cross countries and by studying the distribution of hematoma density.\n\n
 Speaker:\nLingzhou Xue\n\nAdmission:\nFree\n\nDetails URL:\nhttps://medic
 ine.yale.edu/event/ysph-biostatistics-seminar-tba-march-7th/\n
DTEND;TZID=America/New_York:20230307T130000
DTSTAMP:20261021T062108Z
DTSTART;TZID=America/New_York:20230307T120000
GEO:41.302961;-72.931638
LOCATION:106A&B\, 47 College Street\, New Haven\, CT\, United States
SEQUENCE:0
STATUS:Confirmed
SUMMARY:YSPH Biostatistics Seminar: Dimension Reduction for Fréchet Regres
 sion
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