# Inference in Graded Bayesian Networks

## TL;DR

This paper introduces an inference algorithm for graded Bayesian networks using tropicalization, extending the Viterbi algorithm to evaluate hidden variables rank by rank.

## Contribution

It presents a novel inference method for graded Bayesian networks based on tropical geometry, generalizing the Viterbi algorithm.

## Key findings

- The algorithm efficiently infers hidden variables in graded Bayesian networks.
- It generalizes the Viterbi algorithm for a broader class of models.
- The method leverages tropicalization to compute most probable hidden states.

## Abstract

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.