# Question about output of get_edges_prob for spurious edges

Dear Tiago,

I am trying to understand the output of get_edges_prob when using it for
spurious edges. What value is the routine returning? Am I getting the
"likelihood" of the edge being spurious or the "likelihood" of it "actually"
existing? Say, if I have two edges I am assuming to be spurious, "a" and
"b", and edge "a" scores a higher likelihood ratio value than edge "b"
(having used s.get_edges_prob([],[a],
entropy_args=dict(partition_dl=False)) and s.get_edges_prob([],[b],
entropy_args=dict(partition_dl=False))). Is "a" more likely to be a
spurious edge than "b" or is it the other way round (i.e. "a" being more
likely to indeed exist than "b")?

Best,

Philipp

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Hi,

If anybody does have any thoughts on this I would be very grateful.

With best wishes,

Philipp

The former, i.e. the probability that the graph with the _removed_ edge is
generated by the inferred model, and hence that the removed edge does not
belong.

Hi Tiago,

Thank you for that explanation. A quick follow-up:

If calculating likelihoods of both missing and spurious edges would I expect the output to be on a continuous scale of existence likelihood? Assume there is an edge “c” which I am assuming to be a missing edge and I calculate the likelihood ratios by summing across all three edges (based on s.get_edges_prob([],[a], entropy_args=dict(partition_dl=False)), s.get_edges_prob([],[b], entropy_args=dict(partition_dl=False)) and s.get_edges_prob([c],[], entropy_args=dict(partition_dl=False))). If I find \lambda_a > \lambda_c > \lambda_b can I read this that “a” is more likely to be spurious than “c” is to be missing (which in turn is more likely to be spurious than "b" is to be missing)? Or is such a comparison not really meaningful anyways?

Best,

Philipp

Yes, this is totally fine. The "spurious" and "missing" edges are arbitrary
modifications to the graph, and the probabilistic model does not distinguish
between them.

Best,
Tiago