Bounds between Contraction Coefficients

In this paper, we delineate how the contraction coefficient of the strong data processing inequality for KL divergence can be used to learn likelihood models. We then present an alternative formulation to learn likelihood models that forces the input KL divergence of the data processing inequality to vanish, and achieves a contraction coefficient equivalent to the squared maximal correlation. This formulation turns out to admit a linear algebraic solution. To analyze the performance loss in using this simple but suboptimal procedure, we bound these contraction coefficients in the discrete and finite regime, and prove their equivalence in the Gaussian regime.