def test_mrf_sumproduct():
"""
Testing: SUM-PRODUCT on MRF
This example is based on the lawn sprinkler example, and the Markov
random field has the following structure.
Cloudy - 0
/ \
/ \
/ \
Sprinkler - 1 Rainy - 2
\ /
\ /
\ /
Wet Grass -3
"""
"""Assign a unique numerical identifier to each node"""
C = 0
S = 1
R = 2
W = 3
"""Assign the number of nodes in the graph"""
nodes = 4
"""
The graph structure is represented as a adjacency matrix, dag.
If adj_mat[i, j] = 1, then there exists a undirected edge from node
i and node j.
"""
adj_mat = np.matrix(np.zeros((nodes, nodes)))
adj_mat[C, [R, S]] = 1
adj_mat[R, W] = 1
adj_mat[S, W] = 1
"""
Define the size of each node, which is the number of different values a
node could observed at. For example, if a node is either True of False,
it has only 2 possible values it could be, therefore its size is 2. All
the nodes in this graph has a size 2.
"""
ns = 2 * np.ones(nodes)
"""
Define the clique domains. The domain of a clique, is the indices of the
nodes in the clique. A clique is a fully connected set of nodes.
Therefore, for a set of node to be a clique, every node in the set must
be connected to every other node in the set.
"""
clq_doms = [[0, 1, 2], [1, 2, 3]]
"""Define potentials for the cliques"""
clqs = []
T = np.zeros((2, 2, 2))
T[:, :, 0] = np.array([[0.2, 0.2], [0.09, 0.01]])
T[:, :, 1] = np.array([[0.05, 0.05], [0.36, 0.04]])
clqs.append(cliques.clique(0, clq_doms[0], np.array([2, 2, 2]), T))
T[:, :, 0] = np.array([[1, 0.1], [0.1, 0.01]])
T[:, :, 1] = np.array([[0, 0.9], [0.9, 0.99]])
clqs.append(cliques.clique(1, clq_doms[1], np.array([2, 2, 2]), T))
"""Create the MRF"""
net = models.mrf(adj_mat, ns, clqs, lattice=False)
"""
Intialize the MRF's inference engine to use EXACT inference, by
setting exact=True.
"""
net.init_inference_engine(exact=True)
"""Create and enter evidence ([] means that node is unobserved)"""
all_ev = sprinkler_evidence();
all_prob = sprinkler_probs();
count = 0;
errors = 0;
for evidence in all_ev:
"""Execute the max-sum algorithm"""
net.sum_product(evidence)
ans = [1, 1, 1, 1]
marginal = net.marginal_nodes([C])
if evidence[C] is None:
ans[C] = marginal.T[1]
marginal = net.marginal_nodes([S])
if evidence[S] is None:
ans[S] = marginal.T[1]
marginal = net.marginal_nodes([R])
if evidence[R] is None:
ans[R] = marginal.T[1]
marginal = net.marginal_nodes([W])
if evidence[W] is None:
ans[W] = marginal.T[1]
errors = errors + \
np.round(np.sum(np.array(ans) - np.array(all_prob[count])), 3)
count = count + 1
assert errors == 0
def test_bnet_sumproduct():
"""
Testing: SUM-PRODUCT on BNET
This example is based on the lawn sprinkler example, and the Bayesian
network has the following structure, with all edges directed downwards:
Cloudy - 0
/ \
/ \
/ \
Sprinkler - 1 Rainy - 2
\ /
\ /
\ /
Wet Grass -3
"""
"""Assign a unique numerical identifier to each node"""
C = 0
S = 1
R = 2
W = 3
"""Assign the number of nodes in the graph"""
nodes = 4
"""
The graph structure is represented as a adjacency matrix, dag.
If dag[i, j] = 1, then there exists a directed edge from node
i and node j.
"""
dag = np.zeros((nodes, nodes))
dag[C, [R, S]] = 1
dag[R, W] = 1
dag[S, W] = 1
"""
Define the size of each node, which is the number of different values a
node could observed at. For example, if a node is either True of False,
it has only 2 possible values it could be, therefore its size is 2. All
the nodes in this graph has a size 2.
"""
node_sizes = 2 * np.ones(nodes)
"""
We now need to assign a conditional probability distribution to each
node.
"""
node_cpds = [[], [], [], []]
"""Define the CPD for node 0"""
CPT = np.array([0.5, 0.5])
node_cpds[C] = cpds.TabularCPD(CPT)
"""Define the CPD for node 1"""
CPT = np.array([[0.8, 0.2], [0.2, 0.8]])
node_cpds[R] = cpds.TabularCPD(CPT)
"""Define the CPD for node 2"""
CPT = np.array([[0.5, 0.5], [0.9, 0.1]])
node_cpds[S] = cpds.TabularCPD(CPT)
"""Define the CPD for node 3"""
CPT = np.array([[[1, 0], [0.1, 0.9]], [[0.1, 0.9], [0.01, 0.99]]])
node_cpds[W] = cpds.TabularCPD(CPT)
"""Create the Bayesian network"""
net = models.bnet(dag, node_sizes, node_cpds=node_cpds)
"""
Intialize the BNET's inference engine to use EXACT inference
by setting exact=True.
"""
net.init_inference_engine(exact=True)
"""Create and enter evidence ([] means that node is unobserved)"""
all_ev = sprinkler_evidence();
all_prob = sprinkler_probs();
count = 0;
errors = 0;
for evidence in all_ev:
"""Execute the max-sum algorithm"""
net.sum_product(evidence)
ans = [1, 1, 1, 1]
marginal = net.marginal_nodes([C])
if evidence[C] is None:
ans[C] = marginal.T[1]
marginal = net.marginal_nodes([S])
if evidence[S] is None:
ans[S] = marginal.T[1]
marginal = net.marginal_nodes([R])
if evidence[R] is None:
ans[R] = marginal.T[1]
marginal = net.marginal_nodes([W])
if evidence[W] is None:
ans[W] = marginal.T[1]
errors = errors + \
np.round(np.sum(np.array(ans) - np.array(all_prob[count])), 3)
count = count + 1
assert errors == 0
def test_bnet_sumproduct():
"""
Testing: SUM-PRODUCT on BNET
This example is based on the lawn sprinkler example, and the Bayesian
network has the following structure, with all edges directed downwards:
Cloudy - 0
/ \
/ \
/ \
Sprinkler - 1 Rainy - 2
\ /
\ /
\ /
Wet Grass -3
"""
"""Assign a unique numerical identifier to each node"""
C = 0
S = 1
R = 2
W = 3
"""Assign the number of nodes in the graph"""
nodes = 4
"""
The graph structure is represented as a adjacency matrix, dag.
If dag[i, j] = 1, then there exists a directed edge from node
i and node j.
"""
dag = np.zeros((nodes, nodes))
dag[C, [R, S]] = 1
dag[R, W] = 1
dag[S, W] = 1
"""
Define the size of each node, which is the number of different values a
node could observed at. For example, if a node is either True of False,
it has only 2 possible values it could be, therefore its size is 2. All
the nodes in this graph has a size 2.
"""
node_sizes = 2 * np.ones(nodes)
"""
We now need to assign a conditional probability distribution to each
node.
"""
node_cpds = [[], [], [], []]
"""Define the CPD for node 0"""
CPT = np.array([0.5, 0.5])
node_cpds[C] = cpds.TabularCPD(CPT)
"""Define the CPD for node 1"""
CPT = np.array([[0.8, 0.2], [0.2, 0.8]])
node_cpds[R] = cpds.TabularCPD(CPT)
"""Define the CPD for node 2"""
CPT = np.array([[0.5, 0.5], [0.9, 0.1]])
node_cpds[S] = cpds.TabularCPD(CPT)
"""Define the CPD for node 3"""
CPT = np.array([[[1, 0], [0.1, 0.9]], [[0.1, 0.9], [0.01, 0.99]]])
node_cpds[W] = cpds.TabularCPD(CPT)
"""Create the Bayesian network"""
net = models.bnet(dag, node_sizes, node_cpds=node_cpds)
"""
Intialize the BNET's inference engine to use EXACT inference
by setting exact=True.
"""
net.init_inference_engine(exact=True)
"""Create and enter evidence ([] means that node is unobserved)"""
all_ev = sprinkler_evidence()
all_prob = sprinkler_probs()
count = 0
errors = 0
for evidence in all_ev:
"""Execute the max-sum algorithm"""
net.sum_product(evidence)
ans = [1, 1, 1, 1]
marginal = net.marginal_nodes([C])
if evidence[C] is None:
ans[C] = marginal.T[1]
marginal = net.marginal_nodes([S])
if evidence[S] is None:
ans[S] = marginal.T[1]
marginal = net.marginal_nodes([R])
if evidence[R] is None:
ans[R] = marginal.T[1]
marginal = net.marginal_nodes([W])
if evidence[W] is None:
ans[W] = marginal.T[1]
errors = errors + \
np.round(np.sum(np.array(ans) - np.array(all_prob[count])), 3)
count = count + 1
assert errors == 0