gilesc/factor-graph

Belief propagation over factor graphs in directed & undirected PGMs
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factor-graph

A factor graph is a generic representation of the factorization of a function, and can be used to represent a wide variety of operations, from Kalman filters to FFTs to undirected and directed probabilistic graphical models like Bayesian nets, Markov models, and CRFs.

This package is currently designed mainly from the perspective of probabilistic graphical models. For example, it can perform belief propagation over a Bayesian net given some evidence. Right now, it only supports discrete "functions", not continuous ones, and only does non-loopy belief propagation.

Usage

Directed PGMs (Bayes nets)

First, create a factor graph using Bayesian net style notation:

``````(use 'es.corygil.factor-graph)
(use 'es.corygil.factor-graph.bayes)
(def disaster
(bayes-net
{:burglary [0.001 0.999]
:earthquake [0.002 0.998]
:alarm 2
:john-calls 2
:mary-calls 2}
{[:alarm :burglary :earthquake]
[0.95 0.05 0.94 0.06 0.29 0.71 0.001 0.999]
[:john-calls :alarm] [0.9 0.1 0.05 0.95]
[:mary-calls :alarm] [0.7 0.3 0.01 0.99]}))
``````

The bayes-net function takes two arguments: the first is a map of all the variable nodes in the network. If the node has no parents, then in a Bayesian network, it requires a prior. So, in the above example, the prior probability of a burglary is 0.001 and the probability of not burglary is 0.999. If a node does have parents, then it is only necessary to specify the number of states it can assume.

The second argument contains the conditional probability tables in a flattened format. The first entry, for example, would be read as "the probability of alarm given burglary and earthquake", where 0.95 is the p(B,E,A) 0.05 is p(B,E,~A), 0.94 is p(B,~E,A), and so forth.

Now we can perform belief propagation:

``````(run-propagation disaster)
``````

will give us the marginals for all the variable nodes in the absence of any evidence. Or we can use evidence:

``````(run-propagation disaster {:john-calls [1 0]})

> {:burglary (0.016283729946769937 0.98371627005323),
:john-calls [1 0],
:mary-calls (0.03997202114194967 0.9600279788580504),
:alarm (0.04343771179992705 0.9565622882000729),
:earthquake (0.011394968773811182 0.9886050312261888)}
``````

TODO

TODO

• Loopy belief propagation
• More generic factor graph constructors
• Allow factors to be arbitrary functions, not just vectors