Probabilistic Graphical Models (PGMs) allow us to map real world scenarios to a
declarative representation and use it as a basis for predictive analysis. It is a framework that
allows us to express complex probability distributions in a simple way. PGMs can be applied to a
variety of scenarios wherein a model is built to reflect the conditional dependencies between
random variables and then used to simulate the interactions between them to draw conclusions.
The framework further provides many algorithms to analyze these models and extract
One of the applications of PGMs is in solving mathematical puzzles such as Sudoku.
Sudoku is a popular number puzzle that involves filling in empty cells in an ‘N x N’ grid in such
a way that numbers 1 to N appear only once in each row, column and ‘N 1/2 x N 1/2 ’ sub-grid. We
can model this problem as a PGM and represent it in the form of a bipartite graph. The main
concepts we employ to obtain an algorithm to solve Sudoku puzzles are factor graphs and
message passing algorithms. In this project we attempt to modify the sum-product message
passing algorithm to solve the puzzle. Additionally, we implement a solution using Sinkhorn
balancing to overcome the impact of loopy propagation and compare its performance with the
Ananthagopal, Lakshmi, "Application of Message Passing and Sinkhorn Balancing Algorithms for Probabilistic Graphical Models" (2014). Master's Projects. 365.