Orthogonal Decomposition of Discretization-Induced Transport-Information Cost under Rank-Deficient Parametrizations (opens in new tab)

When we consider discretization of continuous probability distributions, it inevitably induces irreversible geometric distortion of local measure on the discretized support. While such discretziation-induced distortion is extrinsic to information geometry (IG) alone, we recently demonstrate that the discretization cost can be naturally characterized by the standard Kullback-Leibler (KL) divergence between continuous distributions as expectation ...