@@ -359,7 +359,7 @@ illustrate its use with the neural network of the `C. elegans
.. testsetup:: celegans
gt.seed_rng(43)
gt.seed_rng(47)
.. testcode:: celegans
...
...
@@ -411,10 +411,10 @@ which shows the number of nodes and groups in all levels:
.. testoutput:: celegans
l: 0, N: 297, B: 15
l: 1, N: 15, B: 6
l: 2, N: 6, B: 4
l: 3, N: 4, B: 1
l: 0, N: 297, B: 17
l: 1, N: 17, B: 9
l: 2, N: 9, B: 3
l: 3, N: 3, B: 1
The hierarchical levels themselves are represented by individual
:meth:`~graph_tool.inference.BlockState` instances obtained via the
...
...
@@ -428,10 +428,10 @@ The hierarchical levels themselves are represented by individual
.. testoutput:: celegans
<BlockState object with 15 blocks (15 nonempty), degree-corrected, for graph <Graph object, directed, with 297 vertices and 2359 edges at 0x...>, at 0x...>
<BlockState object with 6 blocks (6 nonempty), for graph <Graph object, directed, with 15 vertices and 133 edges at 0x...>, at 0x...>
<BlockState object with 4 blocks (4 nonempty), for graph <Graph object, directed, with 6 vertices and 33 edges at 0x...>, at 0x...>
<BlockState object with 1 blocks (1 nonempty), for graph <Graph object, directed, with 4 vertices and 16 edges at 0x...>, at 0x...>
<BlockState object with 17 blocks (17 nonempty), degree-corrected, for graph <Graph object, directed, with 297 vertices and 2359 edges at 0x...>, at 0x...>
<BlockState object with 9 blocks (9 nonempty), for graph <Graph object, directed, with 17 vertices and 156 edges at 0x...>, at 0x...>
<BlockState object with 3 blocks (3 nonempty), for graph <Graph object, directed, with 9 vertices and 57 edges at 0x...>, at 0x...>
<BlockState object with 1 blocks (1 nonempty), for graph <Graph object, directed, with 3 vertices and 9 edges at 0x...>, at 0x...>
This means that we can inspect the hierarchical partition just as before:
...
...
@@ -446,7 +446,7 @@ This means that we can inspect the hierarchical partition just as before:
.. testoutput:: celegans
5
7
0
0
...
...
@@ -476,8 +476,8 @@ case of the `C. elegans` network we have
.. testoutput:: model-selection
:options: +NORMALIZE_WHITESPACE
Non-degree-corrected DL: 8478.791367...
Degree-corrected DL: 8207.895440...
Non-degree-corrected DL: 8456.994339...
Degree-corrected DL: 8233.850036...
Since it yields the smallest description length, the degree-corrected
fit should be preferred. The statistical significance of the choice can
...
...
@@ -503,12 +503,12 @@ fits. In our particular case, we have
.. testoutput:: model-selection
:options: +NORMALIZE_WHITESPACE
ln Λ: -270.895926...
ln Λ: -223.144303...
The precise threshold that should be used to decide when to `reject a
hypothesis <https://en.wikipedia.org/wiki/Hypothesis_testing>`_ is
subjective and context-dependent, but the value above implies that the
particular degree-corrected fit is around :math:`\mathrm{e}^{270} \approx 10^{117}`
particular degree-corrected fit is around :math:`\mathrm{e}^{233} \approx 10^{96}`
times more likely than the non-degree corrected one, and hence it can be
safely concluded that it provides a substantially better fit.
...
...
@@ -530,12 +530,12 @@ example, for the American football network above, we have:
.. testoutput:: model-selection
:options: +NORMALIZE_WHITESPACE
Non-degree-corrected DL: 1747.500987...
Degree-corrected DL: 1780.576716...
ln Λ: -33.075729...
Non-degree-corrected DL: 1734.814739...
Degree-corrected DL: 1780.576716...
ln Λ: -45.761977...
Hence, with a posterior odds ratio of :math:`\Lambda \approx \mathrm{e}^{-33} \approx
10^{-14}` in favor of the non-degree-corrected model, it seems like the
Hence, with a posterior odds ratio of :math:`\Lambda \approx \mathrm{e}^{-45} \approx
10^{-19}` in favor of the non-degree-corrected model, it seems like the
degree-corrected variant is an unnecessarily complex description for
this network.
...
...
@@ -595,8 +595,8 @@ random partition into 20 groups
.. testoutput:: model-averaging
Change in description length: -358.602505...
Number of accepted vertex moves: 36528
Change in description length: -365.317522...
Number of accepted vertex moves: 38213
.. note::
...
...
@@ -619,8 +619,8 @@ random partition into 20 groups
.. testoutput:: model-averaging
Change in description length: 16.127057...
Number of accepted vertex moves: 39217
Change in description length: 1.660677...
Number of accepted vertex moves: 40461
Although the above is sufficient to implement model averaging, there is a
originates from Matplotlib (http://matplotlib.sf.net/) which has
the following license:
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