Kernel estimation of residual extropy function under α-mixing dependence condition

As in the context of introducing the concept of residual entropy in the literature, Qiu and Jia (2018b) introduced the concept, residual extropy to measure the residual uncertainty of a random variable. In this work, we propose a nonparametric estimator for the residual extropy, where the observations under consideration are exhibiting α-mixing (strong mixing) dependence condition. Asymptotic properties of the estimator is derived under suitable regular conditions. A Monte Carlo simulation study is carried out to evaluate the performance of the estimator using the mean squared errors

Loop Calculus for Non-Binary Alphabets using Concepts from Information Geometry

The Bethe approximation is a well-known approximation of the partition function used in statistical physics. Recently, an equality relating the partition function and its Bethe approximation was obtained for graphical models with binary variables by Chertkov and Chernyak. In this equality, the multiplicative error in the Bethe approximation is represented as a weighted sum over all generalized loops in the graphical model. In this paper, the equality is generalized to graphical models with non-binary alphabet using concepts from information geometry.Comment: 18 pages, 4 figures, submitted to IEEE Trans. Inf. Theor