factor graph

[hotpotlover-yang]

Using probability inference and factor graphs for keyword identification is a very creative idea，but there still have some questions i don't understand.About these two formulas，what did it means of f1,f2,...fm? And how is the joint probability distribution function derived? Why is it in fractional form？

[yapengye]

Hi @hotpotlover-yang , thanks for your interest!

f_i is a probabilistic function which describes the valuation of an observation constraint or an inference constraint. In the probabilistic inference, we need to consider all the constraints. The conjunction of all constraints can be denoted as the product of all the corresponding probabilistic functions, i.e., f(k, x₁, x₂, ..., x_n). The joint probability function p(k, x₁, x₂, ..., x_n) is essentially the normalized version of f(k, x₁, x₂, ..., x_n). The detailed definition of the joint probability function could be found in this paper.