def log_post_ratio(from_tree, to_tree, seqdist):
from_tree_seps = jtlib.separators(from_tree)
log_post1 = seqdist.log_likelihood_partial(from_tree.nodes(), from_tree_seps)
log_post1 -= jtlib.log_n_junction_trees(from_tree, from_tree_seps)
to_tree_seps = jtlib.separators(to_tree)
log_post2 = seqdist.log_likelihood_partial(to_tree.nodes(), to_tree_seps)
log_post2 -= jtlib.log_n_junction_trees(to_tree, to_tree_seps)
return log_post2 - log_post1
def test_logmu():
"""
Check so that logmu is equal to the example in Thomas & Green 2009.
"""
cliques = [frozenset([11, 12]), frozenset([9, 12, 17]), frozenset([3, 7, 17, 22]),
frozenset([9, 10]), frozenset([6]), frozenset([4]), frozenset([8, 17]),
frozenset([17, 21]), frozenset([3, 18, 19]), frozenset([2, 3, 18]),
frozenset([2, 3, 16]), frozenset([3, 20]), frozenset([2, 3, 18]), frozenset([1, 2, 3]),
frozenset([3, 5]), frozenset([13, 14, 15]), frozenset([13, 14, 23])]
edges = [(frozenset([11, 12]), frozenset([9, 12, 17])),
(frozenset([9, 12, 17]), frozenset([9, 10])),
(frozenset([9, 12, 17]), frozenset([3, 7, 17, 22])),
(frozenset([3, 7, 17, 22]), frozenset([6])),
(frozenset([3, 7, 17, 22]), frozenset([8, 17])),
(frozenset([3, 7, 17, 22]), frozenset([3, 18, 19])),
(frozenset([6]), frozenset([4])),
(frozenset([8, 17]), frozenset([17, 21])),
(frozenset([3, 18, 19]), frozenset([2, 3, 18])),
(frozenset([2, 3, 18]), frozenset([2, 3, 16])),
(frozenset([2, 3, 18]), frozenset([3, 20])),
(frozenset([2, 3, 18]), frozenset([1, 2, 3])),
(frozenset([1, 2, 3]), frozenset([3, 5])),
(frozenset([1, 2, 3]), frozenset([13, 14, 15])),
(frozenset([13, 14, 15]), frozenset([13, 14, 23]))]
g = nx.Graph()
g.add_nodes_from(cliques)
g.add_edges_from(edges)
S = libj.separators(g)
assert int(np.round(np.exp(libj.log_n_junction_trees(g, S)))) == 57802752
def test_logmu_monte_carlo():
p = 4
matspace = [range(2) for i in range(p * p)]
graphs = {}
graph_jtreps = {}
for adjmatvec in itertools.product(*matspace):
adjmat = np.matrix(adjmatvec).reshape(p, p)
if np.diag(adjmat).sum() == 0:
g = nx.from_numpy_matrix(adjmat)
if nx.is_chordal(g):
if check_symmetric(adjmat):
# print libg.mu(g)
graphs[adjmatvec] = trilearn.graph.decomposable.n_junction_trees(g)
jt = trilearn.graph.decomposable.junction_tree(g)
S = jt.get_separators()
graph_jtreps[adjmatvec] = {"graph": g,
"jts": set(),
"mu": np.exp(jtlib.log_n_junction_trees(jt, S))}
for i in range(100):
jtlib.randomize(jt)
graph_jtreps[adjmatvec]["jts"].add(jt.tuple())
#print graphs
#print "Exact number of chordal graphs: " + str(len(graph_jtreps))
#print "Exact number of junction trees: " + str(np.sum([val for key, val in graphs.iteritems()]))
sum = 0
for graph, val in graph_jtreps.items():
#print val["mu"], val["jts"]
#print val["mu"] - len(val["jts"])
sum += len(val["jts"])
assert np.abs(val["mu"] - len(val["jts"]) < 0.0000001)
print(sum)
def n_junction_trees(graph):
"""Count then number of junctino trees for graph.
Args:
graph (NetworkX graph): A decomposable graph.
Returns:
int: Number of junction trees for graph.
Example:
>>> g = dlib.sample_random_AR_graph(5,3)
>>> g.nodes
NodeView((0, 1, 2, 3, 4))
>>> g.edges
EdgeView([(0, 1), (0, 2), (1, 2), (2, 3), (3, 4)])
>>> dlib.separators(g)
{frozenset([2]): set([(frozenset([2, 3]), frozenset([0, 1, 2]))]), frozenset([3]): set([(frozenset([2, 3]), frozenset([3, 4]))])}
>>> lib.n_junction_trees(g)
1.0
"""
tree = junction_tree(graph)
seps = separators(graph)
return np.exp(libj.log_n_junction_trees(tree, seps))
def sample_trajectory(n_samples, randomize, sd):
graph = nx.Graph()
graph.add_nodes_from(range(sd.p))
jt = dlib.junction_tree(graph)
assert (jtlib.is_junction_tree(jt))
jt_traj = [None] * n_samples
graphs = [None] * n_samples
jt_traj[0] = jt
graphs[0] = jtlib.graph(jt)
log_prob_traj = [None] * n_samples
gtraj = mcmctraj.Trajectory()
gtraj.set_sampling_method({
"method": "mh",
"params": {
"samples": n_samples,
"randomize_interval": randomize
}
})
gtraj.set_sequential_distribution(sd)
log_prob_traj[0] = 0.0
log_prob_traj[0] = sd.log_likelihood(jtlib.graph(jt_traj[0]))
log_prob_traj[0] += -jtlib.log_n_junction_trees(
jt_traj[0], jtlib.separators(jt_traj[0]))
accept_traj = [0] * n_samples
MAP_graph = (graphs[0], log_prob_traj[0])
for i in tqdm(range(1, n_samples), desc="Metropolis-Hastings samples"):
if log_prob_traj[i - 1] > MAP_graph[1]:
MAP_graph = (graphs[i - 1], log_prob_traj[i - 1])
if i % randomize == 0:
jtlib.randomize(jt)
graphs[i] = jtlib.graph(jt) # TODO: Improve.
log_prob_traj[i] = sd.log_likelihood(
graphs[i]) - jtlib.log_n_junction_trees(
jt, jtlib.separators(jt))
r = np.random.randint(2) # Connect / disconnect move
num_seps = jt.size()
log_p1 = log_prob_traj[i - 1]
if r == 0:
# Connect move
num_cliques = jt.order()
conn = aglib.connect_move(
jt) # need to move to calculate posterior
seps_prop = jtlib.separators(jt)
log_p2 = sd.log_likelihood(
jtlib.graph(jt)) - jtlib.log_n_junction_trees(jt, seps_prop)
if not conn:
log_prob_traj[i] = log_prob_traj[i - 1]
graphs[i] = graphs[i - 1]
continue
C_disconn = conn[2] | conn[3] | conn[4]
if conn[0] == "a":
(case, log_q12, X, Y, S, CX_disconn, CY_disconn, XSneig,
YSneig) = conn
(NX_disconn, NY_disconn,
N_disconn) = aglib.disconnect_get_neighbors(
jt, C_disconn, X, Y) # TODO: could this be done faster?
log_q21 = aglib.disconnect_logprob_a(num_cliques - 1, X, Y, S,
N_disconn)
#print log_p2, log_q21, log_p1, log_q12
alpha = min(np.exp(log_p2 + log_q21 - log_p1 - log_q12), 1)
#print alpha
samp = np.random.choice(2, 1, p=[(1 - alpha), alpha])
if samp == 1:
# print "Accept"
accept_traj[i] = 1
log_prob_traj[i] = log_p2
graphs[i] = jtlib.graph(jt) # TODO: Improve.
else:
#print "Reject"
aglib.disconnect_a(jt, C_disconn, X, Y, CX_disconn,
CY_disconn, XSneig, YSneig)
log_prob_traj[i] = log_prob_traj[i - 1]
graphs[i] = graphs[i - 1]
continue
elif conn[0] == "b":
(case, log_q12, X, Y, S, CX_disconn, CY_disconn) = conn
log_q21 = aglib.disconnect_logprob_bcd(num_cliques, X, Y, S)
alpha = min(np.exp(log_p2 + log_q21 - log_p1 - log_q12), 1)
samp = np.random.choice(2, 1, p=[(1 - alpha), alpha])
if samp == 1:
#print "Accept"
accept_traj[i] = 1
log_prob_traj[i] = log_p2
graphs[i] = jtlib.graph(jt) # TODO: Improve.
else:
#print "Reject"
aglib.disconnect_b(jt, C_disconn, X, Y, CX_disconn,
CY_disconn)
log_prob_traj[i] = log_prob_traj[i - 1]
graphs[i] = graphs[i - 1]
continue
elif conn[0] == "c":
(case, log_q12, X, Y, S, CX_disconn, CY_disconn) = conn
log_q21 = aglib.disconnect_logprob_bcd(num_cliques, X, Y, S)
alpha = min(np.exp(log_p2 + log_q21 - log_p1 - log_q12), 1)
samp = np.random.choice(2, 1, p=[(1 - alpha), alpha])
if samp == 1:
accept_traj[i] = 1
#print "Accept"
log_prob_traj[i] = log_p2
graphs[i] = jtlib.graph(jt) # TODO: Improve.
else:
#print "Reject"
aglib.disconnect_c(jt, C_disconn, X, Y, CX_disconn,
CY_disconn)
log_prob_traj[i] = log_prob_traj[i - 1]
graphs[i] = graphs[i - 1]
continue
elif conn[0] == "d":
(case, log_q12, X, Y, S, CX_disconn, CY_disconn) = conn
log_q21 = aglib.disconnect_logprob_bcd(num_cliques + 1, X, Y,
S)
alpha = min(np.exp(log_p2 + log_q21 - log_p1 - log_q12), 1)
samp = np.random.choice(2, 1, p=[(1 - alpha), alpha])
if samp == 1:
accept_traj[i] = 1
#print "Accept"
log_prob_traj[i] = log_p2
graphs[i] = jtlib.graph(jt) # TODO: Improve.
else:
#print "Reject"
aglib.disconnect_d(jt, C_disconn, X, Y, CX_disconn,
CY_disconn)
log_prob_traj[i] = log_prob_traj[i - 1]
graphs[i] = graphs[i - 1]
continue
elif r == 1:
# Disconnect move
disconnect = aglib.disconnect_move(
jt) # need to move to calculate posterior
seps_prop = jtlib.separators(jt)
log_p2 = sd.log_likelihood(
jtlib.graph(jt)) - jtlib.log_n_junction_trees(jt, seps_prop)
#assert(jtlib.is_junction_tree(jt))
#print "disconnect"
if disconnect is not False:
if disconnect[0] == "a":
(case, log_q12, X, Y, S, CX_conn, CY_conn) = disconnect
log_q21 = aglib.connect_logprob(num_seps + 1, X, Y,
CX_conn, CY_conn)
alpha = min(np.exp(log_p2 + log_q21 - log_p1 - log_q12), 1)
samp = np.random.choice(2, 1, p=[(1 - alpha), alpha])
if samp == 1:
accept_traj[i] = 1
#print "Accept"
log_prob_traj[i] = log_p2
graphs[i] = jtlib.graph(jt) # TODO: Improve.
else:
#print "Reject"
aglib.connect_a(jt, S, X, Y, CX_conn, CY_conn)
log_prob_traj[i] = log_prob_traj[i - 1]
graphs[i] = graphs[i - 1]
continue
elif disconnect[0] == "b":
(case, log_q12, X, Y, S, CX_conn, CY_conn) = disconnect
log_q21 = aglib.connect_logprob(num_seps, X, Y, CX_conn,
CY_conn)
alpha = min(np.exp(log_p2 + log_q21 - log_p1 - log_q12), 1)
samp = np.random.choice(2, 1, p=[(1 - alpha), alpha])
if samp == 1:
accept_traj[i] = 1
#print "Accept"
log_prob_traj[i] = log_p2
graphs[i] = jtlib.graph(jt) # TODO: Improve.
else:
#print "Reject"
aglib.connect_b(jt, S, X, Y, CX_conn, CY_conn)
log_prob_traj[i] = log_prob_traj[i - 1]
graphs[i] = graphs[i - 1]
continue
elif disconnect[0] == "c":
(case, log_q12, X, Y, S, CX_conn, CY_conn) = disconnect
log_q21 = aglib.connect_logprob(num_seps, X, Y, CX_conn,
CY_conn)
alpha = min(np.exp(log_p2 + log_q21 - log_p1 - log_q12), 1)
samp = np.random.choice(2, 1, p=[(1 - alpha), alpha])
if samp == 1:
accept_traj[i] = 1
#print "Accept"
log_prob_traj[i] = log_p2
graphs[i] = jtlib.graph(jt) # TODO: Improve.
else:
#print "Reject"
aglib.connect_c(jt, S, X, Y, CX_conn, CY_conn)
log_prob_traj[i] = log_prob_traj[i - 1]
graphs[i] = graphs[i - 1]
continue
elif disconnect[0] == "d":
(case, log_q12, X, Y, S, CX_conn, CY_conn) = disconnect
log_q21 = aglib.connect_logprob(num_seps - 1, X, Y,
CX_conn, CY_conn)
alpha = min(np.exp(log_p2 + log_q21 - log_p1 - log_q12), 1)
samp = np.random.choice(2, 1, p=[(1 - alpha), alpha])
if samp == 1:
#print "Accept"
accept_traj[i] = 1
log_prob_traj[i] = log_p2
graphs[i] = jtlib.graph(jt) # TODO: Improve.
else:
#print "Reject"
aglib.connect_d(jt, S, X, Y, CX_conn, CY_conn)
log_prob_traj[i] = log_prob_traj[i - 1]
graphs[i] = graphs[i - 1]
continue
else:
log_prob_traj[i] = log_prob_traj[i - 1]
graphs[i] = graphs[i - 1]
continue
#print(np.mean(accept_traj[:i]))
gtraj.set_trajectory(graphs)
gtraj.logl = log_prob_traj
return gtraj