2020/11/15 by Yixiang Mao, Mao, Yixiang
Decision Sciences · Physics and Astronomy · Engineering · #Probabilistic and Robust Engineering Design #Statistical Mechanics and Entropy #Control Systems and Identification
paper · pdf · doi:10.48550/arxiv.2011.08441
This thesis develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and exploit a representation as an infimum convolution of optimal transport cost and relative entropy. We include examples of computation and approximation of the divergence, and its applications in uncertainty quantification in discrete models and Gauss-Markov models.