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Applied Math Seminar: Optimal Transport Meets Bayesian Inversion

Event Type: 
Seminar
Speaker: 
Mohammad Motamed
Event Date: 
Monday, February 10, 2020 -
3:00pm to 4:00pm
Location: 
SMLC 356
Audience: 
General PublicFaculty/StaffStudentsAlumni/Friends

Event Description: 

I will present a Bayesian framework based on likelihood functions driven by two optimal transport (OT) metrics, namely Wasserstein metric and Sinkhorn divergence. Compared to conventional Bayesian models based on Gaussian likelihood functions driven by the least-squares norm (L2 norm), the new framework features two major advantages. First, it does does not rely on the likelihood of the measurement noise and hence can treat complicated noise structures such as those present in medical imaging and radio astronomy. Moreover, unlike the normal likelihood function, the proposed OT-based likelihood functions do not usually generate multiple local extrema. As a result, the new framework features better convergence to correct posteriors when a Markov Chain Monte Carlo sampling algorithm is employed.

The talk consists of two parts. First I will present the new framework through its application to a class of signal processing problems, that is, the inverse uncertainty quantification of waveforms, and demonstrate its advantages compared to Bayesian models with normal likelihood functions. Next, I will present a fast method for computing OT distances. The method combines Sinkhorn’s matrix scaling iteration with a low-rank hierarchical representation of the scaling matrices, enableing a near-linear (and hence optimal) complexity.

 

 

Event Contact

Contact Name: Mohammad Motamed

Contact Email: motamed@math.unm.edu