def make_debug_graph(num_nodes, graph_mat):
# Create factor graph
fg = graphs.FactorGraph()
# Create variable nodes
X = {}
F = {}
dist_fa = np.zeros([30, 2, 2])
for k in range(30):
dist_fa[k] = np.random.rand(2, 2)
for i in range(num_nodes):
X['x' + str(i + 1)] = nodes.VNode("x" + str(i + 1), rv.Discrete)
fg.set_nodes(X.values())
for i in range(len(graph_mat)):
edge = graph_mat[i]
nodez = [X["x" + str(edge[m])] for m in range(len(edge))]
F['f' + str(i + 1)] = nodes.FNode("f" + str(i + 1),
rv.Discrete(dist_fa[i], *nodez))
fg.set_nodes(F.values())
for i in range(len(graph_mat)):
node_name = graph_mat[i]
fg.set_edge(X['x' + str(node_name[0])], F['f' + str(i + 1)])
fg.set_edge(F['f' + str(i + 1)], X['x' + str(node_name[1])])
draw(fg, nx.circular_layout(fg))
plt.show()
print([attr["type"].value for (n, attr) in fg.nodes(data=True)])
belief = inference.loopy_belief_propagation(
fg, 1000, [*X.values()], order=[*F.values(), *X.values()])
print(X['x1'].belief())
print(X['x2'].belief())
print(X['x3'].belief())
def make_debug_graph_new():
fg = graphs.FactorGraph()
x1 = nodes.VNode('x1', rv.Discrete)
x2 = nodes.VNode('x2', rv.Discrete)
x3 = nodes.VNode('x3', rv.Discrete)
dist_fa = [[0.1, 0.7], [0.3, 0.2]]
dist_f2 = [0.3, 0.7]
f1 = nodes.FNode('f1', rv.Discrete(dist_f2, x1))
f2 = nodes.FNode('f2', rv.Discrete(dist_fa, x1, x2))
#f3 = nodes.FNode('f3', rv.Discrete(dist_fa, x1,x2 ))
f4 = nodes.FNode('f4', rv.Discrete(dist_fa, x2, x3))
print(f1.factor)
fg.set_nodes([x1, x2, x3])
fg.set_nodes([f1, f2, f4])
# Add edges to factor graph
fg.set_edge(f1, x1)
fg.set_edge(x1, f2)
fg.set_edge(f2, x2)
#fg.set_edge(x2, f3)
#fg.set_edge(f3, x1)
fg.set_edge(x2, f4)
fg.set_edge(x3, f4)
draw(fg, nx.circular_layout(fg))
plt.show()
belief = inference.loopy_belief_propagation(fg,
10, [x1, x2, x3],
order=[f1, f2, f4, x1, x2, x3])
def make_debug_graph():
# Create factor graph
fg = graphs.FactorGraph()
# Create variable nodes
x1 = nodes.VNode("x1", rv.Discrete)
x2 = nodes.VNode("x2", rv.Discrete)
x3 = nodes.VNode("x3", rv.Discrete)
x4 = nodes.VNode("x4", rv.Discrete)
# Create factor nodes
f12 = nodes.FNode("f12")
f234 = nodes.FNode("f234")
f3 = nodes.FNode("f3")
f4 = nodes.FNode("f4")
# Add nodes to factor graph
fg.set_nodes([x1, x2, x3, x4])
fg.set_nodes([f12, f234, f3, f4])
# Add edges to factor graph
fg.set_edge(x1, f12)
fg.set_edge(f12, x2)
fg.set_edge(x2, f234)
fg.set_edge(f234, x3)
fg.set_edge(f234, x4)
fg.set_edge(x3, f3)
fg.set_edge(x4, f4)
#add potential for f_3: p(x3)
dist_f3 = [0.5, 0.5]
f3.factor = rv.Discrete(dist_f3, x3)
#add potential for f_4: p(x4)
dist_f4 = [0.4, 0.6]
f4.factor = rv.Discrete(dist_f4, x4)
# add potential for f_{234}: p(x2, x3, x4) = p(x2|x3,x4) p(x3,x4)
px3x4 = np.outer(dist_f3, dist_f4)
px3x4 = np.reshape(px3x4, np.shape(px3x4) + (1, ))
px2_conditioned_x3x4 = [[
[0.2, 0.8],
[0.25, 0.75],
], [[0.7, 0.3], [0.3, 0.7]]]
dist_f234 = px3x4 * px2_conditioned_x3x4
f234.factor = rv.Discrete(dist_f234, x3, x4, x2)
# add potential for f_{12}: p (x1,x2) = p(x1 | x2) p(x2)
px1_conditioned_x2 = [[0.5, 0.5], [0.7, 0.3]]
px2 = np.sum(dist_f234, axis=(0, 1))
dist_f12 = px2[:, np.newaxis] * px1_conditioned_x2
f12.factor = rv.Discrete(dist_f12, x2, x1)
#########_____________ PROBLEM 2_____________############
fglib_beliefs = inference.belief_propagation(fg, query_node=x1)
return fglib_beliefs, fg, x1
def __call__(self, priorMean, priorVariance, userResponse):
# Create factor graph
fg = graphs.FactorGraph()
# Create variable nodes
x1 = nodes.VNode("x1", rv.Gaussian)
x2 = nodes.VNode("x2", rv.Gaussian)
# Create factor nodes (with joint distributions)
priorMean = 3;
priorVariance = 0.1;
priorPrecision = 1/priorVariance;
priorPrecisionMean = priorPrecision * priorMean;
responsePrecision = 1/self.responseVariance;
responsePrecisionMean = responsePrecision * userResponse;
fa = nodes.FNode( "fa", rv.Gaussian.inf_form( [priorPrecision], [priorPrecisionMean], x1) )
fb = nodes.FNode( "fb", rv.Gaussian.inf_form( [responsePrecision], [responsePrecisionMean], x1) )
# Add nodes to factor graph
fg.set_nodes([x1])
fg.set_nodes([fa, fb])
# Add edges to factor graph
fg.set_edge(fa, x1)
fg.set_edge(x1, fb)
# Perform sum-product algorithm on factor graph
# and request belief of variable node x4
belief = inference.sum_product(fg, x1)
# Print belief of variables
#Belief of variable node x1
variance = 1 / belief._W
mean = belief._Wm / belief._W
return [mean,variance]
"""The below will not work, because the procedure for
inverting the precision matrix checks that it has at
least 2 dimensions. Using the default constructor for
the Gaussian variable will not work for the same
reason.
"""
#print("Belief of variable node x1:")
#print(x1.belief())
#print("Belief of variable node x1:")
#print(x1.belief(normalize=True))
#print("Unnormalized belief of variable node x1:")
#print(x1.belief(normalize=False))
def make_arbit_graph(num_nodes, graph_mat):
# Create factor graph
fg = graphs.FactorGraph()
# Create variable nodes
X = {}
F = {}
dist_fa = np.zeros([len(graph_mat), 2, 2])
for k in range(len(graph_mat)):
dist_fa[k] = np.random.rand(2, 2)
for i in range(num_nodes):
X['x' + str(i + 1)] = nodes.VNode("x" + str(i + 1), rv.Discrete, P)
fg.set_nodes(X.values())
for i in range(len(graph_mat)):
edge = graph_mat[i]
nodez = [X["x" + str(edge[m])] for m in range(len(edge))]
F['f' + str(i + 1)] = nodes.FNode("f" + str(i + 1),
rv.Discrete(dist_fa[i], *nodez))
fg.set_nodes(F.values())
for i in range(len(graph_mat)):
node_name = graph_mat[i]
fg.set_edge(X['x' + str(node_name[0])], F['f' + str(i + 1)])
fg.set_edge(F['f' + str(i + 1)], X['x' + str(node_name[1])])
print([attr["type"].value for (n, attr) in fg.nodes(data=True)])
draw(fg, nx.spectral_layout(fg))
plt.show()
print([*F.values(), *X.values()])
#belief = inference.loopy_belief_propagation(fg, 1000, [*X.values()], order=[*F.values(), *X.values()])
grid = inference.nash_propagation(fg,
10,
epsilon,
1 / 10, [*X.values()],
order=[*F.values(), *X.values()])
## COmpute the mixed strategy
prob = []
prob_i = 0
print(len(grid.keys()))
length = 0
for i in grid.keys():
if (np.where(grid[str(i)] == 1) != []):
length = length + 1
prob_i = np.where(grid[str(i)] == 1)
print('new')
print(prob_i)
def make_graph():
G = graphs.FactorGraph()
x1 = nodes.VNode('x1', rv.Discrete, P)
x2 = nodes.VNode('x2', rv.Discrete, P)
x3 = nodes.VNode('x3', rv.Discrete, P)
x4 = nodes.VNode('x4', rv.Discrete, P)
x5 = nodes.VNode('x5', rv.Discrete, P)
dist_fa = np.array([[20, 10], [20, 80]])
dist_fb = np.array([[40, 30], [30, 50]])
dist_fc = np.array([[30, 50], [40, 30]])
dist_fd = np.array([[70, 10], [10, 20]])
dist_fe = np.array([[120, 50], [80, 100]])
dist_ff = np.array([[40, 100], [70, 30]])
dist_fg = np.array([[20, 10], [50, 30]])
fa = nodes.FNode('f1', rv.Discrete(dist_fa, x1, x2))
fb = nodes.FNode('f2', rv.Discrete(dist_fb, x2, x3))
fc = nodes.FNode('f3', rv.Discrete(dist_fc, x3, x4))
fd = nodes.FNode('f4', rv.Discrete(dist_fd, x4, x1))
fe = nodes.FNode('f5', rv.Discrete(dist_fe, x4, x5))
ff = nodes.FNode('f6', rv.Discrete(dist_ff, x5, x3))
fg = nodes.FNode('f7', rv.Discrete(dist_fg, x1, x3))
G.set_nodes([x1, x2, x3, x4, x5])
G.set_nodes([fa, fb, fc, fd, fe, ff, fg])
# Add edges to factor graph
G.set_edge(x1, fa)
G.set_edge(fa, x2)
G.set_edge(x2, fb)
G.set_edge(fb, x3)
G.set_edge(x3, fc)
G.set_edge(fc, x4)
G.set_edge(x4, fd)
G.set_edge(fd, x1)
G.set_edge(fe, x4)
G.set_edge(x5, fe)
G.set_edge(ff, x5)
G.set_edge(x3, ff)
G.set_edge(fg, x1)
G.set_edge(x3, fg)
draw(G, nx.spectral_layout(G))
plt.show()
inference.nash_propagation(
G,
20,
epsilon,
1 / 30, [x1, x2, x3, x4, x5],
order=[fa, fb, fc, fd, fe, ff, fg, x1, x2, x3, x4, x5])
def main():
fg = graphs.FactorGraph()
# Create variable nodes
x1 = nodes.VNode("x1", rv.Discrete) # with 2 states (Bernoulli)
x2 = nodes.VNode("x2", rv.Discrete) # with 3 states
x3 = nodes.VNode("x3", rv.Discrete)
x4 = nodes.VNode("x4", rv.Discrete)
# Create factor nodes (with joint distributions)
dist_fa = [[0.3, 0.2, 0.1],
[0.3, 0.0, 0.1]]
fa = nodes.FNode("fa", rv.Discrete(dist_fa, x1, x2))
dist_fb = [[0.3, 0.2],
[0.3, 0.0],
[0.1, 0.1]]
fb = nodes.FNode("fb", rv.Discrete(dist_fb, x2, x3))
dist_fc = [[0.3, 0.2],
[0.3, 0.0],
[0.1, 0.1]]
fc = nodes.FNode("fc", rv.Discrete(dist_fc, x2, x4))
# Add nodes to factor graph
fg.set_nodes([x1, x2, x3, x4])
fg.set_nodes([fa, fb, fc])
# Add edges to factor graph
fg.set_edge(x1, fa)
fg.set_edge(fa, x2)
fg.set_edge(x2, fb)
fg.set_edge(fb, x3)
fg.set_edge(x2, fc)
fg.set_edge(fc, x4)
sum_product(fg)
length = 0
for i in grid.keys():
if (np.where(grid[str(i)] == 1) != []):
length = length + 1
prob_i = np.where(grid[str(i)] == 1)
print('new')
print(prob_i)
## Now assign values to the factors ?
Num_Of_Players = 50
max_degree = 5
epsilon = 0.26 ## To be tuned for every experiement
tau = epsilon / (np.power(2,
(max_degree + 1) * max_degree * np.log(max_degree)))
# Initialize tables for each Node in the graph
fg = graphs.FactorGraph()
P = np.ones([10, 10])
## Below create the links of the matrix
Mat_link = []
for i in range(1, 9):
Mat_link.append((i, i % 9 + 1))
Mat_link.append((i, np.random.randint(i + 1, 10)))
print(Mat_link)
#make_arbit_graph(10,graph_mat=Mat_link)
make_graph()