There are many applications that benefit from computing the exact divergence between 2 discrete probability measures, including machine learning. Unfortunately, in absence of any assumptions on structure or independencies within these distributions, them is an intractable problem high dimensions. We show we able to compute a wide family functionals and divergences, such as alpha-beta divergence...

Abstract Using quantum Riemannian geometry, we solve for a Ricci = 0 static spherically-symmetric solution in 4D, with the S 2 at each t , r noncommutative fuzzy sphere, finding dimension jump solutions having time and radial form of classical 5D Tangherlini black hole. Thus, even small amount angular noncommutativity leads to radically different behaviour, modifying Laplacian weak gravity limi...

In this paper at rst, a history of mathematical models is given.Next, some basic information about random variables, stochastic processesand Markov chains is introduced. As follows, the entropy for a discrete timeMarkov process is mentioned. After that, the entropy for SIS stochastic modelsis computed, and it is proved that an epidemic will be disappeared after a longtime.

Human decision making underlies data generating process in multiple application areas, and models explaining and predicting choices made by individuals are in high demand. Discrete choice models are widely studied in economics and computational social sciences. As digital social networking facilitates information flow and spread of influence between individuals, new advances in modeling are nee...

The statistical literature discusses different types of Markov properties for chain graphs that lead to four possible classes of chain graph Markov models. The different models are rather well understood when the observations are continuous and multivariate normal, and it is also known that one model class, referred to as models of LWF (Lauritzen–Wermuth–Frydenberg) or block concentration type,...