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Tiago Peixoto
graphtool
Commits
3ea457d1
Commit
3ea457d1
authored
Jul 20, 2016
by
Tiago Peixoto
Browse files
inference.rst: Update examples
parent
d0fc4754
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doc/demos/inference/inference.rst
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3ea457d1
...
...
@@ 73,7 +73,7 @@ We note that Eq. :eq:`modelposterior` can be written as
..
math
::
P
(\
boldsymbol
b

G
)
=
\
frac
{
e
^{
\
Sigma
}
}{
P
(
G
)}
P
(\
boldsymbol
b

G
)
=
\
frac
{
\
exp
(
\
Sigma
)
}{
P
(
G
)}
where
...
...
@@ 506,9 +506,9 @@ example, for the American football network above, we have:
.. testoutput:: modelselection
:options: +NORMALIZE_WHITESPACE
Nondegreecorrected DL: 17
38.00660528
Degreecorrected DL: 178
0.01146484
ln Λ: 
42.0048595573
Nondegreecorrected DL: 17
25.78502074
Degreecorrected DL: 178
4.77629595
ln Λ: 
58.9912752096
Hence, with a posterior odds ratio of :math:`\Lambda \sim e^{59} \sim
10^{25}` in favor of the nondegreecorrected model, it seems like the
...
...
@@ 792,7 +792,7 @@ network as above.
.. testoutput:: nestedmodelaveraging
Change in description length: 6.368298...
Number of accepted vertex moves:
3765
Number of accepted vertex moves:
5316
Similarly to the the nonnested case, we can use
:func:`~graph_tool.inference.mcmc_equilibrate` to do most of the boring
...
...
@@ 826,9 +826,9 @@ work, and we can now obtain vertex marginals on all hierarchical levels:
Marginal probabilities of group memberships of the network of
characters in the novel Les Misérables, according to the nested
degreecorrected SBM. The
`
pie fractions
<https://en.wikipedia.org/wiki/Pie_chart>`_
on the nodes correspond to
the probability of being in group
associated with the respective
color.
degreecorrected SBM. The pie fractions
on the nodes correspond to
the probability of being in group
associated with the respective
color.
We can also obtain a marginal probability of the number of groups
itself, as follows.
...
...
@@ 983,7 +983,7 @@ This approximation should be seen as an upper bound, since any existing
correlation between the nodes (which are ignored here) will yield
smaller entropy values.
A more
elabo
rate assumption is called the `Bethe approximation`
A more
accu
rate assumption is called the `Bethe approximation`
[mezardinformation2009]_, and takes into account the correlation
between adjacent nodes in the network,
...
...
@@ 1053,8 +1053,8 @@ evidence efficiently, as we show below, using
em = s.collect_edge_marginals(em)
dls.append(s.entropy())
# Now we collect the marginal distributions for exactly
1
00,000 sweeps
gt.mcmc_equilibrate(state, force_niter=
1
0000, mcmc_args=dict(niter=10),
# Now we collect the marginal distributions for exactly
2
00,000 sweeps
gt.mcmc_equilibrate(state, force_niter=
2
0000, mcmc_args=dict(niter=10),
callback=collect_marginals)
S_mf = gt.mf_entropy(g, vm)
...
...
@@ 1066,11 +1066,11 @@ evidence efficiently, as we show below, using
.. testoutput:: modelevidence
Model evidence for deg_corr = True: 
622.794364945
(mean field), 7
07.484453595
(Bethe)
Model evidence for deg_corr = False: 6
24.357861783
(mean field), 6
57.16406646
5 (Bethe)
Model evidence for deg_corr = True: 
599.280568166
(mean field), 7
44.851035413
(Bethe)
Model evidence for deg_corr = False: 6
37.320504421
(mean field), 6
69.53369363
5 (Bethe)
Despite the (expected) discrepancy between both
approximation
s
, the
outcome shows a clear
preference for the nondegreecorrected model.
If we consider the more accurate
approximation, the
outcome shows a
preference for the nondegreecorrected model.
When using the nested model, the approach is entirely analogous. The
only difference now is that we have a hierarchical partition
...
...
@@ 1117,8 +1117,8 @@ approach for the same network, using the nested model.
em = levels[0].collect_edge_marginals(em)
dls.append(s.entropy())
# Now we collect the marginal distributions for exactly
1
00,000 sweeps
gt.mcmc_equilibrate(state, force_niter=
1
0000, mcmc_args=dict(niter=10),
# Now we collect the marginal distributions for exactly
2
00,000 sweeps
gt.mcmc_equilibrate(state, force_niter=
2
0000, mcmc_args=dict(niter=10),
callback=collect_marginals)
S_mf = [gt.mf_entropy(sl.g, vm[l]) for l, sl in enumerate(state.get_levels())]
...
...
@@ 1131,17 +1131,15 @@ approach for the same network, using the nested model.
.. testoutput:: modelevidence
Model evidence for deg_corr = True: 549.845093934 (mean field), 688.382102062 (Bethe)
Model evidence for deg_corr = False: 593.581546241 (mean field), 621.257816805 (Bethe)
The results are interesting: Not only we observe a better evidence for
the nested models themselves, when comparing to the evidences for the
nonnested model  which is not quite surprising, since the nonnested
model is a special case of the nested one  but also we find that the
degreecorrected model yields the larger evidence. This is different
from the outcome using the nonnested model, but it is not a
contradiction, since these models are indeed different.
Model evidence for deg_corr = True: 508.072303996 (mean field), 703.774572649 (Bethe)
Model evidence for deg_corr = False: 565.034423817 (mean field), 662.335604507 (Bethe)
The results are similar: If we consider the most accurate approximation,
the nondegreecorrected model possesses the largest evidence. Note also
that we observe a better evidence for the nested models themselves, when
comparing to the evidences for the nonnested model  which is not
quite surprising, since the nonnested model is a special case of the
nested one.
Edge layers and covariates

...
...
@@ 1364,8 +1362,8 @@ above).
..
testoutput
::
missing

edges
likelihood

ratio
for
(
101
,
102
):
0.35
7594
likelihood

ratio
for
(
17
,
56
):
0.64
2406
likelihood

ratio
for
(
101
,
102
):
0.35
0445
likelihood

ratio
for
(
17
,
56
):
0.64
9555
From
which
we
can
conclude
that
edge
:
math
:`(
17
,
56
)`
is
around
twice
as
likely
as
:
math
:`(
101
,
102
)`
to
be
a
missing
edge
.
...
...
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