def main():
"""
Main functiont to lunch the belief propagation algorithm
"""
M = model()
M.check_model()
#Belief propagation
bp = BeliefPropagation(M)
bp.calibrate()
print("maximal cliques are:")
print(bp.get_cliques())
# first query
print("computing probability of B=")
query1 = bp.query(variables=list('b'), show_progress=True)
print(query1)
#second query
print("computing probability of B|C")
query2 = bp.query(variables=['b', 'c'])
query2.marginalize(['c'])
print(query2)
#Third query
print("computing joint")
query3 = bp.query(['a', 'b', 'c', 'd', 'e'])
query3.normalize()
print(query3)
def get_partition_function_BP(G):
'''
Calculate partition function of G using belief propogation
'''
bp = BeliefPropagation(G)
bp.calibrate()
clique_beliefs = bp.get_clique_beliefs()
partition_function = np.sum(clique_beliefs.values()[0].values)
return partition_function
class IsingModel:
def __init__(self, theta, seed=None):
if seed is not None:
np.random.seed(seed)
# graph
self.G = MarkovModel()
for _, row in theta.iterrows():
# unary
if row["j"]==row["k"]:
self.G.add_node(str(int(row["j"])))
theta_jj = row["value"]
self.G.add_factors(DiscreteFactor([str(int(row["j"]))], [2],
np.exp([-theta_jj,theta_jj])))
# pairwise
elif row["value"]!=0:
self.G.add_edge(str(int(row["j"])), str(int(row["k"])))
theta_jk = row["value"]
self.G.add_factors(DiscreteFactor([str(int(row["j"])), str(int(row["k"]))],
[2, 2], np.exp([theta_jk, -theta_jk, -theta_jk, theta_jk])))
self.G.check_model()
self.infer = BeliefPropagation(self.G)
self.infer.calibrate()
def get_moments(self):
p = len(list(self.G.nodes))
factor_dict = self.infer.get_clique_beliefs()
mom_matrix = np.zeros([p,p])
for clique in factor_dict:
for pair in it.combinations(clique,2):
moment = factor_dict[clique].marginalize(set(clique).difference(set(pair)),inplace=False)
moment = moment.normalize(inplace=False)
pair_int = [int(x) for x in pair]
moment = moment.values[0,0]+moment.values[1,1]-moment.values[0,1]-moment.values[1,0]
mom_matrix[pair_int[0],pair_int[1]] = moment
mom_matrix[pair_int[1],pair_int[0]] = moment
for unary in it.combinations(clique,1):
unary_int = [int(x) for x in unary][0]
moment = factor_dict[clique].marginalize(set(clique).difference(set(unary)),inplace=False).normalize(inplace=False).values
moment = moment[1]-moment[0]
mom_matrix[unary_int,unary_int] = moment
return mom_matrix
def test_calibrate_clique_belief(self):
belief_propagation = BeliefPropagation(self.junction_tree)
belief_propagation.calibrate()
clique_belief = belief_propagation.get_clique_beliefs()
phi1 = Factor(['A', 'B'], [2, 3], range(6))
phi2 = Factor(['B', 'C'], [3, 2], range(6))
phi3 = Factor(['C', 'D'], [2, 2], range(4))
b_A_B = phi1 * (phi3.marginalize(['D'], inplace=False) * phi2).marginalize(['C'], inplace=False)
b_B_C = phi2 * (phi1.marginalize(['A'], inplace=False) * phi3.marginalize(['D'], inplace=False))
b_C_D = phi3 * (phi1.marginalize(['A'], inplace=False) * phi2).marginalize(['B'], inplace=False)
np_test.assert_array_almost_equal(clique_belief[('A', 'B')].values, b_A_B.values)
np_test.assert_array_almost_equal(clique_belief[('B', 'C')].values, b_B_C.values)
np_test.assert_array_almost_equal(clique_belief[('C', 'D')].values, b_C_D.values)
def test_calibrate_sepset_belief(self):
belief_propagation = BeliefPropagation(self.junction_tree)
belief_propagation.calibrate()
sepset_belief = belief_propagation.get_sepset_beliefs()
phi1 = Factor(['A', 'B'], [2, 3], range(6))
phi2 = Factor(['B', 'C'], [3, 2], range(6))
phi3 = Factor(['C', 'D'], [2, 2], range(4))
b_B = (phi1 * (phi3.marginalize(['D'], inplace=False) *
phi2).marginalize(['C'], inplace=False)).marginalize(['A'], inplace=False)
b_C = (phi2 * (phi1.marginalize(['A'], inplace=False) *
phi3.marginalize(['D'], inplace=False))).marginalize(['B'], inplace=False)
np_test.assert_array_almost_equal(sepset_belief[frozenset((('A', 'B'), ('B', 'C')))].values, b_B.values)
np_test.assert_array_almost_equal(sepset_belief[frozenset((('B', 'C'), ('C', 'D')))].values, b_C.values)
def test_calibrate_clique_belief(self):
belief_propagation = BeliefPropagation(self.junction_tree)
belief_propagation.calibrate()
clique_belief = belief_propagation.get_clique_beliefs()
phi1 = Factor(['A', 'B'], [2, 3], range(6))
phi2 = Factor(['B', 'C'], [3, 2], range(6))
phi3 = Factor(['C', 'D'], [2, 2], range(4))
b_A_B = phi1 * (phi3.marginalize(['D'], inplace=False) *
phi2).marginalize(['C'], inplace=False)
b_B_C = phi2 * (phi1.marginalize(['A'], inplace=False) *
phi3.marginalize(['D'], inplace=False))
b_C_D = phi3 * (phi1.marginalize(['A'], inplace=False) *
phi2).marginalize(['B'], inplace=False)
np_test.assert_array_almost_equal(clique_belief[('A', 'B')].values,
b_A_B.values)
np_test.assert_array_almost_equal(clique_belief[('B', 'C')].values,
b_B_C.values)
np_test.assert_array_almost_equal(clique_belief[('C', 'D')].values,
b_C_D.values)
def test_calibrate_clique_belief(self):
belief_propagation = BeliefPropagation(self.junction_tree)
belief_propagation.calibrate()
clique_belief = belief_propagation.get_clique_beliefs()
phi1 = DiscreteFactor(["A", "B"], [2, 3], range(6))
phi2 = DiscreteFactor(["B", "C"], [3, 2], range(6))
phi3 = DiscreteFactor(["C", "D"], [2, 2], range(4))
b_A_B = phi1 * (phi3.marginalize(["D"], inplace=False) *
phi2).marginalize(["C"], inplace=False)
b_B_C = phi2 * (phi1.marginalize(["A"], inplace=False) *
phi3.marginalize(["D"], inplace=False))
b_C_D = phi3 * (phi1.marginalize(["A"], inplace=False) *
phi2).marginalize(["B"], inplace=False)
np_test.assert_array_almost_equal(clique_belief[("A", "B")].values,
b_A_B.values)
np_test.assert_array_almost_equal(clique_belief[("B", "C")].values,
b_B_C.values)
np_test.assert_array_almost_equal(clique_belief[("C", "D")].values,
b_C_D.values)
def test_calibrate_sepset_belief(self):
belief_propagation = BeliefPropagation(self.junction_tree)
belief_propagation.calibrate()
sepset_belief = belief_propagation.get_sepset_beliefs()
phi1 = Factor(['A', 'B'], [2, 3], range(6))
phi2 = Factor(['B', 'C'], [3, 2], range(6))
phi3 = Factor(['C', 'D'], [2, 2], range(4))
b_B = (phi1 *
(phi3.marginalize(['D'], inplace=False) * phi2).marginalize(
['C'], inplace=False)).marginalize(['A'], inplace=False)
b_C = (phi2 * (phi1.marginalize(['A'], inplace=False) *
phi3.marginalize(['D'], inplace=False))).marginalize(
['B'], inplace=False)
np_test.assert_array_almost_equal(
sepset_belief[frozenset((('A', 'B'), ('B', 'C')))].values,
b_B.values)
np_test.assert_array_almost_equal(
sepset_belief[frozenset((('B', 'C'), ('C', 'D')))].values,
b_C.values)
PGM.add_nodes_from(['w1', 'w2', 'w3'])
PGM.add_edges_from([('w1', 'w2'), ('w2', 'w3')])
tr_matrix = np.array([1, 10, 3, 2, 1, 5, 3, 3, 2])
tr_matrix = np.array([1, 2, 3, 10, 1, 3, 3, 5, 2]).reshape(3, 3).T.reshape(-1)
phi = [DiscreteFactor(edge, [3, 3], tr_matrix) for edge in PGM.edges()]
print(phi[0])
print(phi[1])
PGM.add_factors(*phi)
# Calculate partition funtion
Z = PGM.get_partition_function()
print('The partition function is:', Z)
# Calibrate the click
belief_propagation = BeliefPropagation(PGM)
belief_propagation.calibrate()
# Output calibration result, which you should get
query = belief_propagation.query(variables=['w2'])
print('After calibration you should get the following mu(S):\n', query * Z)
# Get marginal distribution over third word
query = belief_propagation.query(variables=['w3'])
print('Marginal distribution over the third word is:\n', query)
#Get conditional distribution over third word
query = belief_propagation.query(variables=['w3'],
evidence={'w1': 0}) # 0 stays for "noun"
print(
'Conditional distribution over the third word, given that the first word is noun is:\n',
query)
import numpy as np from pgmpy.models import FactorGraph from pgmpy.factors.discrete import DiscreteFactor from pgmpy.inference import BeliefPropagation G = FactorGraph() G.add_node(0) G.add_node(1) G.add_node(2) f01 = DiscreteFactor([0, 1], [2, 2], np.random.rand(4)) f02 = DiscreteFactor([0, 2], [2, 2], np.random.rand(4)) f12 = DiscreteFactor([1, 2], [2, 2], np.random.rand(4)) G.add_factors(f01) G.add_factors(f02) G.add_factors(f12) G.add_edges_from([(0, f01), (1, f01), (0, f02), (2, f02), (1, f12), (2, f12)]) bp = BeliefPropagation(G) bp.calibrate()
def plot_causal_influence(self, file_path):
"""
Computes the odds of the target variable being value 1 over value 0 (i.e. the odds ratio)
by iterating through all other network variables/nodes, changing their values,
and observing how the probability of the target variable changes. Belief propagation
is used for inference. A forest plot is produced from this and saved to disk.
Arguments:
file_path: str, the absolute path to save the file to (e.g. "~/Desktop/forest_plot.png")
Returns:
None
"""
# Estimate CPTs
self._estimate_CPT()
if self.verbose:
print(f"Calculating influence of all nodes on target node")
if not self.bn_model.check_model():
print("""
There is a problem with your network structure. You have disconnected nodes
or separated sub-networks. Please examine your network plot and re-learn your
network structure with tweaked settings.
""")
return None
if self.target_variable not in self.bn_model.nodes:
print("""
Your target variable has no parent nodes! Can't perform inference! Please examine
your network plot and re-learn your network structure with tweaked settings.
""")
return None
# Prep for belief propagation
belief_propagation = BeliefPropagation(self.bn_model)
belief_propagation.calibrate()
# Iterate over all intervention nodes and values, calculating odds ratios w.r.t target variable
overall_dict = {}
variables_to_test = list(
set(list(self.bn_model.nodes)) - set(list(self.target_variable)))
for node in variables_to_test:
results = []
for value in self.filtered_df[node].unique():
prob = belief_propagation.query(
variables=[self.target_variable],
evidence={
node: value
},
show_progress=False,
).values
results.append([node, value, prob[0], prob[1]])
results_df = pd.DataFrame(
results,
columns=["node", "value", "probability_0", "probability_1"])
results_df["odds_1"] = (results_df["probability_1"] /
results_df["probability_0"])
results_df = results_df.sort_values(
"value", ascending=True, inplace=False).reset_index(drop=True)
overall_dict[node] = results_df
final_df_list = []
for node, temp_df in overall_dict.items():
first_value = temp_df["odds_1"].iloc[0]
temp_df["odds_ratio"] = (temp_df["odds_1"] / first_value).round(3)
final_df_list.append(temp_df)
final_df = pd.concat(final_df_list)[["node", "value", "odds_ratio"]]
self.odds_ratios = final_df
if self.verbose:
print(f"Saving forest plot to the following PNG file: {file_path}")
# Clean up the dataframe of odds ratios so plot can have nice labels
final_df2 = (pd.concat([
final_df,
final_df.groupby("node")["value"].apply(
lambda x: x.shift(-1).iloc[-1]).reset_index(),
]).sort_values(by=["node", "value"],
ascending=True).reset_index(drop=True))
final_df2["node"][final_df2["value"].isnull()] = np.nan
final_df2["value"] = final_df2["value"].astype("Int32").astype(str)
final_df2["value"].replace({np.nan: ""}, inplace=True)
final_df3 = final_df2.reset_index(drop=True).reset_index()
final_df3.rename(columns={"index": "vertical_index"}, inplace=True)
final_df3["y_label"] = final_df3["node"] + " = " + final_df3["value"]
final_df3["y_label"][final_df3["odds_ratio"] == 1.0] = (
final_df3["y_label"] + " (ref)")
final_df3["y_label"].fillna("", inplace=True)
# Produce large plot
plt.clf()
plt.title(
"Strength of Associations Between Interventions and Target Variable"
)
plt.scatter(
x=final_df3["odds_ratio"],
y=final_df3["vertical_index"],
s=70,
color="b",
alpha=0.5,
)
plt.xlabel("Odds Ratio")
plt.axvline(x=1.0, color="red", linewidth="1.5", linestyle="--")
plt.yticks(final_df3["vertical_index"], final_df3["y_label"])
for _, row in final_df3.iterrows():
if not np.isnan(row["odds_ratio"]):
plt.plot(
[0, row["odds_ratio"]],
[row["vertical_index"], row["vertical_index"]],
color="black",
linewidth="0.4",
)
plt.xlim([0, final_df3["odds_ratio"].max() + 1])
figure = plt.gcf()
figure.set_size_inches(12, 7)
plt.savefig(expanduser(file_path),
bbox_inches="tight",
format="PNG",
dpi=300)
