Inference in Graded Bayesian Networks
This work addresses inference challenges in graded Bayesian networks, offering a generalized Viterbi algorithm for this specific domain, which is incremental as it builds on existing methods.
The paper tackles the problem of inferring hidden variables in Bayesian networks by introducing an inference algorithm that uses tropicalization of marginal distributions and restricts to graded networks, resulting in a method that computes the most probable states of hidden variables rank by rank.
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Bayesian networks are a class of graphical models that allow to represent a collection of random variables and their condititional dependencies by directed acyclic graphs. In this paper, an inference algorithm for the hidden random variables of a Bayesian network is given by using the tropicalization of the marginal distribution of the observed variables. By restricting the topological structure to graded networks, an inference algorithm for graded Bayesian networks will be established that evaluates the hidden random variables rank by rank and in this way yields the most probable states of the hidden variables. This algorithm can be viewed as a generalized version of the Viterbi algorithm for graded Bayesian networks.