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Assignment 3: Graphical Model Specialisations
Graphical models combine graph theory with statistical inference.
They generalise a lot of useful algorithms. This assignment requires
you to pick one such useful algorithm and summarise it in graphical
model terms. The idea is to ensure you're familiar with graphical
models and at least one of the common specialisations of them.
Suggestions for specialised algorithms to study are:
The list is
not limited to these methods, but reflects the most well
known specialisations. If you choose some other algorithm please ask me first.
In particular, your description should include:
- A line or two describing the kinds of applications the specialisation
can be used for.
- A description of the random variables in the graphical model,
which are observed and which are hidden?
- How are the probability distributions are represented, i.e., tables,
gaussians, or some other parameterised distribution?
- The structure of the graphical model (diagram please).
- How the specialised algorithm uses the sum-product algorithm (and/or max-product algorithm)
used for undirected acyclic graphs (tree structures), including
- what form do the messages take;
- which are the backward messages, which are the forward messages;
- what are the separating set variables;
- what efficiencies (if any) are introduced when considering the
specialised problem (hint, try constructing small instances and generating
the moralised graph and corresponding junction tree);
-
Does the specialised algorithm learn anything e.g., change any parameters?
If so, what part of the gaphical model is being learnt and for what reason?
How does the learning algorithm meld with the inference algorithm?
Some of these questions don't make sense for some specialisations. If so you
should explain why. I imagine these assignments will be about 2 pages and
will require a significiant amount of reading. Unless you have particularly neat handwriting I would appreciate this assignment being typed.
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