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SUMMARY:Inference for eigenstructure of high-dimensional covariance matric
 es - Jana Jankova (University of Cambridge)
DTSTART:20180515T100000Z
DTEND:20180515T110000Z
UID:TALK106999@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Sparse principal component analysis (PCA) has become one
  of the most widely used techniques for dimensionality reduction in high-d
 imensional datasets. The main challenge underlying sparse PCA is to estima
 te the first vector of loadings of the population covariance matrix\, prov
 ided that<span><br> only a certain number of loadings are non-zero. A vast
  number of methods have been proposed in literature for point estimation o
 f eigenstructure of the covariance matrix. In this work\, we study uncerta
 inty quantification and propose methodology for inference and hypothesis t
 esting for individual loadings and for the largest eigenvalue of the covar
 iance matrix. We base our methodology on a Lasso-penalized M-estimator whi
 ch\, despite non-convexity\, may be solved by a polynomial-time algorithm 
 such as coordinate or gradient descent. Our results provide theoretical gu
 arantees for asymptotic normality of the new estimators and may be used fo
 r valid hypothesis testing and variable selection.&nbsp\;</span></span>  <
 br><br><br><br>
LOCATION:Seminar Room 2\, Newton Institute
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