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SUMMARY:Statistical-Computational Tradeoffs in Mixed Sparse Linear Regress
 ion  - Gabriel Arpino\, University of Cambridge
DTSTART:20231115T140000Z
DTEND:20231115T150000Z
UID:TALK207589@talks.cam.ac.uk
CONTACT:Prof. Ramji Venkataramanan
DESCRIPTION: Large-scale datasets\, other than being high-dimensional\, ca
 n be highly heterogeneous. Real-world observations\, when combined to form
  large datasets\, often incorporate signals from different subpopulations.
  In this talk we will consider _Mixed Sparse Linear Regression_\, a simple
  heterogeneous model for high-dimensional inference. This model includes  
 the widely studied  linear regression and phase retrieval models as specia
 l cases. We provide rigorous evidence for the existence of a fundamental s
 tatistical-computational tradeoff in this model\, whenever the model param
 eters are sufficiently symmetric. Outside of this symmetric regime\, we pr
 ove that an efficient algorithm is sample-optimal. To the best of our know
 ledge\, this is the first thorough study of the interplay between mixture 
 symmetry\, signal sparsity\, and their joint impact on the computational h
 ardness of mixed sparse linear regression. This is joint work with Ramji V
 enkataramanan.
LOCATION:MR5\, CMS Pavilion A
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