def sample(order, alpha=0.5, beta=0.5):
""" Generates a random decomposable graph using the Christmas tree algorithm.
Args:
internal_nodes (list): list of internal nodes in the generated graph.
alpha (float): Subtree kernel parameter
beta (float): Subtree kernel parameter
directory (string): Path to where the plots should be saved.
Returns:
NetworkX graph: A decomposable graph.
Example:
>>> g = dlib.sample_dec_graph(5)
>>> g.edges
EdgeView([(0, 1), (0, 3), (1, 3), (2, 3)])
>>> g.nodes
NodeView((0, 1, 2, 3, 4))
"""
if type(order) is int:
nodes = range(order) # OBS. Python 2.7
random.shuffle(nodes)
tree = libj.sample(nodes, alpha, beta)
return jtlib.graph(tree)
elif type(order) is list:
tree = libj.sample(order, alpha, beta)
return jtlib.graph(tree)
def mh(alpha, beta, traj_length, seq_dist,
jt_traj=None, debug=False):
""" A Metropolis-Hastings implementation for approximating distributions over
junction trees.
Args:
traj_length (int): Number of Gibbs iterations (samples)
alpha (float): sparsity parameter for the Christmas tree algorithm
beta (float): sparsity parameter for the Christmas tree algorithm
seq_dist (SequentialJTDistributions): the distribution to be sampled from
Returns:
mcmctraj.Trajectory: Markov chain of teh underlying graphs of the junction trees sampled by M-H.
"""
graph_traj = mcmctraj.Trajectory()
graph_traj.set_sequential_distribution(seq_dist)
prev_tree = None
for i in tqdm(range(traj_length), desc="Metropolis-Hastings samples"):
tree = None
start_time = time.time()
if i == 0:
tree = jtlib.sample(seq_dist.p, alpha, beta)
else:
# Sample backwards trajectories
tree = trans_sample(prev_tree, alpha, beta, seq_dist)
# Sample T from T_1..p
end_time = time.time()
graph_traj.add_sample(jtlib.graph(tree), end_time - start_time)
prev_tree = tree
return graph_traj
def smc_ggm_graphs(N, alpha, beta, radius, X, D, delta):
cache = {}
seq_dist = seqdist.GGMJTPosterior()
seq_dist.init_model(X, D, delta, cache)
(trees, log_w) = approximate(N, alpha, beta, radius, seq_dist)
log_w_rescaled = np.array(log_w.T)[seq_dist.p - 1] - \
max(np.array(log_w.T)[seq_dist.p - 1])
norm_w = np.exp(log_w_rescaled) / sum(np.exp(log_w_rescaled))
graphs = [jtlib.graph(tree) for tree in trees]
return (graphs, norm_w)
def est_log_norm_consts(order,
n_particles,
sequential_distribution,
alpha=0.5,
beta=0.5,
n_smc_estimates=1,
debug=False):
log_consts = np.zeros(n_smc_estimates * (order)).reshape(
n_smc_estimates, (order))
def estimate_norm_const(order, weights):
log_consts = np.zeros(order)
for n in range(1, order):
log_consts[n] = log_consts[n - 1] + np.log(np.mean(weights[:, n]))
return log_consts
for t in tqdm(range(n_smc_estimates), desc="Const estimates"):
(trees, log_w) = approximate(n_particles, alpha, beta,
sequential_distribution.p,
sequential_distribution)
w = np.exp(log_w)
log_consts[t, :] = estimate_norm_const(order, w)
if debug:
unique_trees = set()
for tree in trees:
tree_alt = (frozenset(tree.nodes()),
frozenset([frozenset(e) for e in tree.edges()]))
unique_trees.add(tree_alt)
print("Sampled unique junction trees: " + str(len(unique_trees)))
unique_graphs = set(
[glib.hash_graph(jtlib.graph(tree)) for tree in trees])
print(
"Sampled unique chordal graphs: {n_unique_chordal_graphs}".
format(n_unique_chordal_graphs=len(unique_graphs)), )
if n_smc_estimates == 1:
log_consts = log_consts.flatten()
return log_consts
def sample_dec_graph(internal_nodes, alpha=0.5, beta=0.5, directory='.'):
""" Generates a random decomposable graph using the Christmas tree algorithm.
Args:
internal_nodes (list): list of internal nodes in the generated graph.
alpha (float): Subtree kernel parameter
beta (float): Subtree kernel parameter
directory (string): Path to where the plots should be saved.
Returns:
NetworkX graph: A decomposable graph.
Example:
>>> g = dlib.sample_dec_graph(5)
>>> g.edges
EdgeView([(0, 1), (0, 3), (1, 3), (2, 3)])
>>> g.nodes
NodeView((0, 1, 2, 3, 4))
"""
T = libj.sample(internal_nodes, alpha=alpha, beta=beta)
return libj.graph(T)
def sample_trajectory(smc_N,
alpha,
beta,
radius,
n_samples,
seq_dist,
jt_traj=None,
debug=False,
reset_cache=True):
""" A particle Gibbs implementation for approximating distributions over
junction trees.
Args:
smc_N (int): Number of particles in SMC in each Gibbs iteration
n_samples (int): Number of Gibbs iterations (samples)
alpha (float): sparsity parameter for the Christmas tree algorithm
beta (float): sparsity parameter for the Christmas tree algorithm
radius (float): defines the radius within which ned nodes are selected
seq_dist (SequentialJTDistributions): the distribution to be sampled from
Returns:
Trajectory: Markov chain of the underlying graphs of the junction trees sampled by pgibbs.
"""
graph_traj = mcmctraj.Trajectory()
graph_traj.set_sampling_method({
"method": "pgibbs",
"params": {
"N": smc_N,
"alpha": alpha,
"beta": beta,
"radius": radius
}
})
graph_traj.set_sequential_distribution(seq_dist)
neig_set_cache = {}
(trees, log_w) = (None, None)
prev_tree = None
for i in tqdm(range(n_samples), desc="Particle Gibbs samples"):
if reset_cache is True:
seq_dist.cache = {}
start_time = time.time()
if i == 0:
#start_graph = nx.Graph()
#start_graph.add_nodes_from(range(seqdist.p))
#start_tree = dlib.junction_tree(start_graph)
(trees, log_w) = approximate(smc_N,
alpha,
beta,
radius,
seq_dist,
neig_set_cache=neig_set_cache)
else:
# Sample backwards trajectories
perm_traj = sp.backward_perm_traj_sample(seq_dist.p, radius)
T_traj = trilearn.graph.junction_tree_collapser.backward_jt_traj_sample(
perm_traj, prev_tree)
(trees, log_w,
Is) = approximate_cond(smc_N,
alpha,
beta,
radius,
seq_dist,
T_traj,
perm_traj,
neig_set_cache=neig_set_cache)
# Sample T from T_1..p
log_w_array = np.array(log_w.T)[seq_dist.p - 1]
log_w_rescaled = log_w_array - max(log_w_array)
w_rescaled = np.exp(log_w_rescaled)
norm_w = w_rescaled / sum(w_rescaled)
I = np.random.choice(smc_N, size=1, p=norm_w)[0]
T = trees[I]
prev_tree = T
graph = jtlib.graph(T)
end_time = time.time()
graph_traj.add_sample(graph, end_time - start_time)
return graph_traj
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
def uniform_dec_samples(order, n_particles, alpha=0.5, beta=0.5, debug=False):
sd = seqdist.CondUniformJTDistribution(order)
(trees, log_w) = approximate(n_particles, alpha, beta, sd.p, sd)
graphs = [jtlib.graph(tree) for tree in trees]
return graphs