Interpreting min_dl (min value of nats per edge) for blockmodel on multigraphs
How would one best interpret the min_dl value returned by minimize_nested_blockmodel_dl and minimize_blockmodel_dl when a multigraph (weighted) graph is processed? The min_dl for a multigraph can be much lower for the same graph without multiplicities. What is a reasonable way to explain, using the min_dl values, that a multigraph version of graph produces a "better" (or not) description of the same graph without multiplicities? -- View this message in context: http://main-discussion-list-for-the-graph-tool-project.982480.n3.nabble.com/... Sent from the Main discussion list for the graph-tool project mailing list archive at Nabble.com.
On 16.08.2014 09:57, ayates wrote:
How would one best interpret the min_dl value returned by minimize_nested_blockmodel_dl and minimize_blockmodel_dl when a multigraph (weighted) graph is processed? The min_dl for a multigraph can be much lower for the same graph without multiplicities. What is a reasonable way to explain, using the min_dl values, that a multigraph version of graph produces a "better" (or not) description of the same graph without multiplicities?
Crudely, you should think of the edges as the "data points" which are being used to fit a model. If you add more of them, especially if you keep the number of nodes fixed, you should get a better fit. Now, if the additional edges do not follow exactly the same distribution as the previous ones, they can either reduce or increase the description length per edge. If the new edges are more randomly distributed, the DL/E will increase, and if they are more ordered it will decrease. Note that this only applies to the DL per edge. The total non-normalized DL will always increase if more edges are added. Best, Tiago -- Tiago de Paula Peixoto <tiago@skewed.de>
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Tiago de Paula Peixoto