How are MRFs better than Bayesian networks?

  • They can model range of problems where there are no natural dependencies between random variables

  • Undirected graphs can better express certain dependencies that Bayesian network cannot easily describe

What are the drawbacks of MRFs?

  • Computing normalisation constant Z requires summing over all the assignments, which could grow exponentially. This will be an NP-hard problem and so many undirected models are actually intractable and approximation techniques are required

  • Undirected models may be difficult to interpret as they don’t necessarily model causality

  • It is much easier to generate data from a Bayesian network

What is moralisation?

Moralisation is the process of converting a Bayesian network to an MRF. Bayesian networks are a special case of MRFs with a specific type of clique factor and a normalisation constant of one. See below the figure of moralisation:

Overall, MRFs have more flexibility and power than Bayesian network but they might be intractable and so are more difficult to deal with. A rule of thumb is to use Bayesian network whenever possible and only switch to MRFs if there’s no natural way to model problem with a directed graph.



Data Scientist

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