We investigate Gaussian Kullback-Leibler (G-KL) variational approximate inference techniques for Bayesian generalised linear models and various extensions. In particular we make the following novel contributions: sufficient conditions for which the G-KL objective is differentiable and convex are described; constrained parameterisations of Gaussian covariance that make G-KL methods fast and scal...

We define a new distance measure the resistor-average distance between two probability distributions that is closely related to the Kullback-Leibler distance. While the KullbackLeibler distance is asymmetric in the two distributions, the resistor-average distance is not. It arises from geometric considerations similar to those used to derive the Chernoff distance. Determining its relation to we...

For the simplest colored branching process, we prove an analog to the McMillan theorem and calculate the Hausdorff dimensions of random fractals defined in terms of the limit behavior of empirical measures generated by finite genetic lines. In this setting, the role of Shannon’s entropy is played by the Kullback–Leibler divergence, and the Hausdorff dimensions are computed by means of the so-ca...

The classical Csiszz ar{Kullback inequality bounds the L 1 {distance of two probability densities in terms of their relative (convex) entropies. Here we generalize such inequalities to not necessarily normalized and possibly non-positive L 1 functions. Also, our generalized Csiszz ar{Kullback inequalities are in many important cases sharper than the classical ones (in terms of the functional de...

The problem of automatic image recognition based on the minimum information discrimination principle is formulated and solved. Color histograms comparison in the Kullback–Leibler information metric is proposed. It’s combined with method of directed enumeration alternatives as opposed to complete enumeration of competing hypotheses. Results of an experimental study of the Kullback-Leibler discri...