Phase diagram and approximate message passing for blind calibration and dictionary learning

@article{Krzakala2013PhaseDA,
  title={Phase diagram and approximate message passing for blind calibration and dictionary learning},
  author={Florent Krzakala and Marc M{\'e}zard and Lenka Zdeborov{\'a}},
  journal={2013 IEEE International Symposium on Information Theory},
  year={2013},
  pages={659-663}
}
We consider dictionary learning and blind calibration for signals and matrices created from a random ensemble. We study the mean-squared error in the limit of large signal dimension using the replica method and unveil the appearance of phase transitions delimiting impossible, possible-but-hard and possible inference regions. We also introduce an approximate message passing algorithm that asymptotically matches the theoretical performance, and show through numerical tests that it performs very… CONTINUE READING
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tistical physics - based reconstruction in compressed sensing

  • M. Mézard F. Krzakala, F. Sausset, Y. Sun, L. Zdeborová
  • Phys . Rev . X
  • 2012

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