def test_issubset():
"""
FUNCTION: mysubset, in general.py.
"""
"""Create arrays small and large, where small IS a subset of large."""
small = np.array(([1, 3]))
large = np.array(([0, 1, 2, 3]))
"""Assert that small is a subset of large."""
assert general.issubset(small, large)
"""Assert that large is not a subset of small."""
assert not (general.issubset(large, small))
"""
Create array small so that it contains less elements than large,
but is not a subset of large.
"""
small = np.array(([1, 4]))
"""Assert that small is not a subset of large."""
assert not (general.issubset(small, large))
def triangulate(G, order):
"""
This function ensures that the input graph is triangulated (chordal),
i.e., every cycle of length > 3 has a chord. To find the maximal
cliques, we save each induced cluster (created by adding connecting
neighbors) that is not a subset of any previously saved cluster. (A
cluster is a complete, but not necessarily maximal, set of nodes.)
Parameters
----------
G: Numpy ndarray
G[i,j] = 1 iff there is an edge between node i and node j.
order: List
The order in which to eliminate the nodes.
"""
MG = G.copy()
"""Obtain the the number of nodes in the graph"""
n = G.shape[0]
eliminated = np.zeros((1,n))
cliques = []
for i in range(0,n):
"""Obtain the index of the next node to be eliminated"""
u = order[0,i]
U = find(eliminated == 0)
#nodes = np.intersect1d_nu(neighbours(G, u), U)#################################################################################################################################################
nodes = np.intersect1d(neighbours(G, u), U)
nodes = np.union1d(nodes, np.array([u]))
"""
Connect all uneliminated neighbours of the node to be eliminated
together.
"""
for i in nodes:
for j in nodes:
i=int(i)
j=int(j)
G[i, j] = 1
G = setdiag(G, 0)
u=int(u)
"""Mark the node as 'eliminated'"""
eliminated[0, u] = 1
"""
If the generated clique is a subset of an existing clique, then it is
not a maximal clique, so it is excluded from the list if cliques.
"""
exclude = False
for c in range(0, len(cliques)):
if issubset(nodes, np.array(cliques[c])):
exclude = True
break
if not exclude:
cliques.append(nodes)
return [G, cliques]
def neighbours(adj_mat, i):
"""
Returns the indices of the neighbours nodes of the input node, i, in the
given adjacency matrix.
Parameters
----------
adj_mat: Numpy ndarray
Adjacency matrix. If adj_mat[i, j] = 1, there exists a directed
edge from node i to node j.
i: Int
The index of the node whose parents are to be found.
"""
kids = np.array(children(adj_mat, i))
folks = np.array(parents(adj_mat, i))
if issubset(kids, folks) and issubset(folks, kids):
nbrs = kids
else:
nbrs = np.hstack((kids, folks)).tolist()
return nbrs
def triangulate(G, order):
"""
This function ensures that the input graph is triangulated (chordal),
i.e., every cycle of length > 3 has a chord. To find the maximal
cliques, we save each induced cluster (created by adding connecting
neighbors) that is not a subset of any previously saved cluster. (A
cluster is a complete, but not necessarily maximal, set of nodes.)
Parameters
----------
G: Numpy ndarray
G[i,j] = 1 iff there is an edge between node i and node j.
order: List
The order in which to eliminate the nodes.
"""
MG = G.copy()
"""Obtain the the number of nodes in the graph"""
n = G.shape[0]
eliminated = np.zeros((1,n))
cliques = []
for i in range(0,n):
"""Obtain the index of the next node to be eliminated"""
u = order[0,i]
U = find(eliminated == 0)
nodes = np.intersect1d_nu(neighbours(G, u), U)
nodes = np.union1d(nodes, np.array([u]))
"""
Connect all uneliminated neighbours of the node to be eliminated
together.
"""
for i in nodes:
for j in nodes:
G[i, j] = 1
G = setdiag(G, 0)
"""Mark the node as 'eliminated'"""
eliminated[0, u] = 1
"""
If the generated clique is a subset of an existing clique, then it is
not a maximal clique, so it is excluded from the list if cliques.
"""
exclude = False
for c in range(0, len(cliques)):
if issubset(nodes, np.array(cliques[c])):
exclude = True
break
if not exclude:
cliques.append(nodes)
return [G, cliques]
def neighbours(adj_mat, i):
"""
Returns the indices of the neighbours nodes of the input node, i, in the
given adjacency matrix.
Parameters
----------
adj_mat: Numpy ndarray
Adjacency matrix. If adj_mat[i, j] = 1, there exists a directed
edge from node i to node j.
i: Int
The index of the node whose parents are to be found.
"""
kids = np.array(children(adj_mat, i))
folks = np.array(parents(adj_mat,i))
if issubset(kids, folks) and issubset(folks, kids):
nbrs = kids
else:
nbrs = np.hstack((kids, folks)).tolist()
return nbrs
def test_issubset():
"""
FUNCTION: mysubset, in general.py.
"""
"""Create arrays small and large, where small IS a subset of large."""
small = np.array(([1, 3]))
large = np.array(([0, 1, 2, 3]))
"""Assert that small is a subset of large."""
assert general.issubset(small, large)
"""Assert that large is not a subset of small."""
assert not (general.issubset(large, small))
"""
Create array small so that it contains less elements than large,
but is not a subset of large.
"""
small = np.array(([1, 4]))
"""Assert that small is not a subset of large."""
assert not (general.issubset(small, large))
def update_ess(self, sample, expected_vals, node_id, model):
"""
Update the expected sufficient statistics for this CPD.
Parameters
----------
sample: List
A partially observed sample of the all the nodes in the model
this CPD is part of. sample[i] = [] if node i in unobserved.
expected_vals: marginal
A marginal object containing the expected values for any unobserved
nodes in this CPD.
node_sizes: Array
A list of the sizes of each node in the model. If sizes[2] = 10,
then node 2 can assume 1 of 10 different states.
"""
"""Determine which nodes were observed in this sample"""
node_sizes = model.node_sizes_unobserved
[hidden, observed] = general.determine_observed(sample)
"""If the entire domain of the CPD is hidden"""
if general.issubset(np.array(expected_vals.domain), np.array(hidden)):
"""
If the entire domain of the CPD was unobserved in
the last sample. Then the marginal over the CPD domain will
be just the CPD's entire CPT. Therefore we can add this
directly to the CPD's expected sufficient statistics.
"""
self.ess = self.ess + expected_vals.T.flatten()
else:
"""
If any part of the CPD's domain was observed, the expected values
for the observed domain has been marginalized out. Therefore
we need to pump the marginal up to its correct dimensions based
on the observed evidence, and place the observed values where the
'expected' values were for the observed nodes.
"""
expected_vals.add_ev_to_dmarginal(sample, node_sizes)
"""
Add the new values to the CPD's expected sufficient statistics.
"""
self.ess = self.ess + expected_vals.T.flatten()
def update_ess(self, sample, expected_vals, node_sizes):
"""
Update the expected sufficient statistics for this CPD.
Parameters
----------
sample: List
A partially observed sample of the all the nodes in the model
this CPD is part of. sample[i] = [] if node i in unobserved.
expected_vals: marginal
A marginal object containing the expected values for any unobserved
nodes in this CPD.
node_sizes: Array
A list of the sizes of each node in the model. If sizes[2] = 10,
then node 2 can assume 1 of 10 different states.
"""
"""Determine which nodes were observed in this sample"""
[hidden, observed] = general.determine_observed(sample)
"""If the entire domain of the CPD is hidden"""
if general.issubset(np.array(expected_vals.domain), np.array(hidden)):
"""
If the entire domain of the CPD was unobserved in
the last sample. Then the marginal over the CPD domain will
be just the CPD's entire CPT. Therefore we can add this
directly to the CPD's expected sufficient statistics.
"""
self.ess = self.ess + expected_vals.T.flatten()
else:
"""
If any part of the CPD's domain was observed, the expected values
for the observed domain has been marginalized out. Therefore
we need to pump the marginal up to its correct dimensions based
on the observed evidence, and place the observed values where the
'expected' values were for the observed nodes.
"""
expected_vals.add_ev_to_dmarginal(sample, node_sizes)
"""
Add the new values to the CPD's expected sufficient statistics.
"""
self.ess = self.ess + expected_vals.T.flatten()