How do you build a tree Junction?

So, to construct a junction tree we just have to extract a maximum weight spanning tree out of the clique graph. This can be efficiently done by, for example, modifying Kruskal’s algorithm. The last step is to apply belief propagation to the obtained junction tree.

What is loopy belief propagation?

2 Loopy Belief Propagation. The general idea behined Loopy Belief Propagation (LBP) is to run Belief Propagation on a graph containing loops, despite the fact that the presence of loops does not guarantee convergence.

What is the running intersection property?

Τ has the running intersection property if, whenever X ∈ Ci and X ∈ Cj , then X is also in every cluster in the (unique) path in Τ between Ci and Cj . Intuition: This holds in cluster trees induced by VE because a variable appears in every factor from the moment it is introduced until it is eliminated.

What is Bethe free energy?

We show that BP can only converge to a stationary point of an approximate free energy, known as the Bethe free energy in statistical physics. This result characterizes BP fixed-points and makes connections with variational approaches to approximate inference.

What are message-passing algorithms?

Message passing algorithm which is an iterative decoding algorithm factorizes the global function of many variables into product of simpler local functions, whose arguments are the subset of variables. In order to visualize this factorization we use factor graph.

What is a Sepset?

A sepset Sij is the subset of variables between nodes Ci and Cj that are in the intersection of the scopes of both nodes (scope simply means the list of variables node C depends on.

What are probabilistic graphical models used for?

A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional dependence structure between random variables. They are commonly used in probability theory, statistics—particularly Bayesian statistics—and machine learning.

What is sum product algorithm?

Sum-product Rule: At a factor node, take the product of f with. descendants; then perform not-sum over the parent. of f. Known as the sum-product algorithm.

What is belief propagation in Bayesian networks?

Belief propagation, also known as sum–product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields.

What are two examples of graphical models?

The two most common types of graph- ical models are Bayesian networks (also called belief networks or causal networks) and Markov networks (also called Markov random fields (MRFs)).

What are the main types of graphical Modelling?

The two most common forms of graphical model are directed graphical models and undirected graphical models, based on directed acylic graphs and undirected graphs, respectively.

What is a factor graph model?

A factor graph is a type of probabilistic graphical model. A factor graph has two types of nodes: Variables, which can be either evidence variables when their value is known, or query variables when their value should be predicted. Factors, which define the relationships between variables in the graph.