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SUMMARY:Orbit recovery from invariants - Jonathan Weed (MIT)
DTSTART:20180427T150000Z
DTEND:20180427T160000Z
UID:TALK101941@talks.cam.ac.uk
CONTACT:Quentin Berthet
DESCRIPTION:We focus on the following problem\, which we call "orbit recov
 ery": how many samples are required to estimate a signal when each sample 
 has been acted on by a random element of a known\, compact group? This que
 stion is motivated by and generalizes various "synchronization" problems\,
  such as multi-reference alignment and the reconstruction problem from cry
 o-electon microscopy. Using tools from algebraic geometry and invariant th
 eory\, we give precise relationships between algebraic properties of the g
 roup action and the sample complexity of the statistical problem\, under v
 arious success criteria. We also consider variations of this problem invol
 ving projection and heterogenous mixtures of signals. Based on joint work 
 with Afonso S. Bandeira\, Ben Blum-Smith\, Amelia Perry\, Philippe Rigolle
 t\, Amit Singer and Alexander S. Wein.
LOCATION:MR12
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