Department of Mathematics

Applied Mathematics

  •  Jonathan Scarlett, National University of Singapore
  •  Beyond Sparsity: Compressive Sensing with (Deep) Generative Modeling Assumptions
  •  09/02/2021
  •  4:30 AM - 5:30 AM
  •  Online (virtual meeting) (Virtual Meeting Link)
  •  Olga Turanova (turanova@msu.edu)

The problem of estimating an unknown vector from linear measurements has a long history in statistics, machine learning, and signal processing. Classical studies focus on the "n >> p" regime (#measurements >> #parameters), and more recent studies handle the "n << p" regime by exploiting low-dimensional structure such as sparsity or low-rankness. Such variants are commonly known as compressive sensing. In this talk, I will overview recent methods that move beyond these simple notions of structure, and instead assume that the underlying vector is well-modeled by a generative model (e.g., produced by deep learning methods such as GANs). I will highlight algorithmic works that demonstrated up to 5-10x savings in the number of measurements over sparsity-based methods, and then move on to our theoretical work characterizing the order-optimal sample complexity in terms of quantities such as (i) the Lipschitz constant of the model, or (ii) the depth/width in a neural network model. I will also briefly highlight some recent results on non-linear observation models.

 

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