def do_experiment(num_clusters, num_nodes):
tm = TreeMixture(num_clusters, num_nodes)
tm.simulate_pi(seed_val)
tm.simulate_trees(seed_val)
tm.sample_mixtures(2000, seed_val=seed_val)
samples = tm.samples
em = EM_Algorithm(samples, num_clusters, seed_val=seed_val)
em.initialize(1, 2)
loglikelihoods, topology_list, theta_list = em.optimize(max_num_iter=100)
real_likelyhood = tm.likelihood_dataset(samples)
learned_likelyhood = em.tree_mixture.likelihood_dataset(samples)
print("Real likelyhood: " + str(real_likelyhood) + ", learned " +
str(learned_likelyhood))
plt.title('Actual likelihood: ' + str(real_likelyhood) +
', inferred likelyhood: ' + str(learned_likelyhood))
plt.plot(range(len(loglikelihoods)),
loglikelihoods,
label=str(num_clusters) + ' clusters, ' + str(num_nodes) +
' nodes')
plt.legend()
plt.show()
def em_algorithm(seed_val, samples, num_clusters, max_num_iter=100):
"""
This function is for the EM algorithm.
:param seed_val: Seed value for reproducibility. Type: int
:param samples: Observed x values. Type: numpy array. Dimensions: (num_samples, num_nodes)
:param num_clusters: Number of clusters. Type: int
:param max_num_iter: Maximum number of EM iterations. Type: int
:return: loglikelihood: Array of log-likelihood of each EM iteration. Type: numpy array.
Dimensions: (num_iterations, ) Note: num_iterations does not have to be equal to max_num_iter.
:return: topology_list: A list of tree topologies. Type: numpy array. Dimensions: (num_clusters, num_nodes)
:return: theta_list: A list of tree CPDs. Type: numpy array. Dimensions: (num_clusters, num_nodes, 2)
You can change the function signature and add new parameters. Add them as parameters with some default values.
i.e.
Function template: def em_algorithm(seed_val, samples, k, max_num_iter=10):
You can change it to: def em_algorithm(seed_val, samples, k, max_num_iter=10, new_param_1=[], new_param_2=123):
"""
# Set the seed
np.random.seed(seed_val)
# TODO: Implement EM algorithm here.
# Start: Example Code Segment. Delete this segment completely before you implement the algorithm.
print("Running EM algorithm...")
loglikelihood = []
for iter_ in range(max_num_iter):
loglikelihood.append(np.log((1 + iter_) / max_num_iter))
from Tree import TreeMixture
tm = TreeMixture(num_clusters=num_clusters, num_nodes=samples.shape[1])
tm.simulate_pi(seed_val=seed_val)
tm.simulate_trees(seed_val=seed_val)
tm.sample_mixtures(num_samples=samples.shape[0], seed_val=seed_val)
topology_list = []
theta_list = []
for i in range(num_clusters):
topology_list.append(tm.clusters[i].get_topology_array())
theta_list.append(tm.clusters[i].get_theta_array())
loglikelihood = np.array(loglikelihood)
topology_list = np.array(topology_list)
theta_list = np.array(theta_list)
# End: Example Code Segment
###
return loglikelihood, topology_list, theta_list
def initialize(self, sieving_tries=100, sieving_train=10):
"""Initializes the TreeMixtures using sieving.
Parameters:
sieving_tries -- Number of random initializations
sieving_train -- Number of iterations for each initialization
"""
print("Initializing EM ...")
best_tree_mix = None
best_likelihood = -float('inf')
for t in tqdm(range(sieving_tries)):
tree_mix = TreeMixture(self.num_clusters, self.num_nodes)
tree_mix.simulate_trees(self.seed_val)
tree_mix.simulate_pi(self.seed_val)
tm, likelihoods = self.__iter_optimize(sieving_train, tree_mix=tree_mix, display_progress=False)
if likelihoods[-1] > best_likelihood:
best_likelihood = likelihoods[-1]
best_tree_mix = tm
self.tree_mixture = best_tree_mix
def em_algorithm(seed_val, samples, num_clusters, max_num_iter=10, tm=None):
"""
This function is for the EM algorithm.
:param seed_val: Seed value for reproducibility. Type: int
:param samples: Observed x values. Type: numpy array. Dimensions: (num_samples, num_nodes)
:param num_clusters: Number of clusters. Type: int
:param max_num_iter: Maximum number of EM iterations. Type: int
:return: loglikelihood: Array of log-likelihood of each EM iteration. Type: numpy array.
Dimensions: (num_iterations, ) Note: num_iterations does not have to be equal to max_num_iter.
:return: topology_list: A list of tree topologies. Type: numpy array. Dimensions: (num_clusters, num_nodes)
:return: theta_list: A list of tree CPDs. Type: numpy array. Dimensions: (num_clusters, num_nodes, 2)
This is a suggested template. Feel free to code however you want.
"""
# Set the seed
np.random.seed(seed_val)
# TODO: Implement EM algorithm here.
N = len(samples)
K = num_clusters
V = samples.shape[1]
if tm == None:
tm = TreeMixture(num_clusters=num_clusters, num_nodes=samples.shape[1])
tm.simulate_pi(seed_val=seed_val)
tm.simulate_trees(seed_val=seed_val)
log_hoods = []
for iteration in range(max_num_iter):
#STEP 1
R = np.zeros(shape=(N, K))
for n in range(N):
for k in range(K):
nth_sample = samples[n]
kth_tree = tm.clusters[k]
hood = tree_sample_likelihood(kth_tree, nth_sample)
R[n, k] = tm.pi[k] * hood
R = normalize(R, axis=1, norm='l1')
#STEP 2
new_pi = np.zeros(shape=(K))
for k in range(K):
suma = 0
for n in range(N):
suma += R[n, k]
new_pi[k] = suma / N
tm.pi = new_pi
for k in range(K):
#STEP 3
Qstab = np.zeros(shape=(V, V, 2,
2)) #Xs x Xt x (0 or 1) x (0 or 1)
Nstab = np.zeros(shape=(V, V, 2,
2)) #Xs x Xt x (0 or 1) x (0 or 1)
#2 vertex relation
for Xs in range(V): #foreach vertex pair
for Xt in range(V):
if Xs == Xt:
continue
for n in range(N):
a = samples[n][Xs]
b = samples[n][Xt]
r_nk = R[n, k]
Nstab[Xs, Xt, a, b] += r_nk
for Xs in range(V): #foreach vertex pair
for Xt in range(V):
if Xs == Xt:
continue
denom = sum(R[:, k])
for a in range(2): #for each observation (0 or 1)
for b in range(2):
num = Nstab[Xs, Xt, a, b]
Qstab[Xs, Xt, a, b] = num / denom
#1 vertex relation
Qsa = np.zeros(shape=(V, 2))
Nsa = np.zeros(shape=(V, 2))
for Xs in range(V): # foreach vertex
for n in range(N):
a = samples[n][Xs]
r_nk = R[n, k]
Nsa[Xs, a] += r_nk
for Xs in range(V):
for a in range(2):
num = Nsa[Xs, a]
denom = sum(Nsa[Xs, :])
Qsa[Xs, a] = num / denom
#mutual information
Info = np.zeros(shape=(V, V)) #information between vertices
for Xs in range(V): #foreach vertex pair
for Xt in range(V):
if Xs == Xt:
continue
for a in range(2):
for b in range(2):
qab = Qstab[Xs, Xt, a, b]
qa = Qsa[Xs, a]
qb = Qsa[Xt, b]
if qab / (qa * qb) != 0:
Info[Xs, Xt] += qab * log(qab / (qa * qb))
else:
Info[Xs, Xt] += 0
#conditional information (for step 5)
Qcond_stab = np.zeros(shape=(V, V, 2, 2))
for Xs in range(V): #foreach vertex pair
for Xt in range(V):
if Xs == Xt:
continue
for a in range(2):
for b in range(2):
num = Nstab[Xs, Xt, a, b]
denom = sum(Nstab[Xs, Xt, a, :])
Qcond_stab[Xs, Xt, a,
b] = num / denom #p(Xt=b|Xs=a)
#STEP 4
g = Graph(V)
for Xs in range(V): #foreach vertex pair
for Xt in range(V):
if Xs == Xt:
continue
g.addEdge(Xs, Xt, Info[Xs, Xt])
mst = g.maximum_spanning_tree() #this is an array
mst = sorted(mst, key=lambda x: x[0])
#STEP 5
topology_array = [np.nan for i in range(V)]
theta_array = [None for i in range(V)] #placeholder
topology_array = np.array(topology_array)
theta_array = np.array(theta_array)
#root
root = 0
theta_array[0] = Qsa[root, :]
MST = {}
for u, v, w in mst:
if u not in MST:
MST[u] = []
MST[u].append(v)
if v not in MST:
MST[v] = []
MST[v].append(u)
VISITED = []
def dfs(curr, prior):
VISITED.append(curr)
if prior != -1:
cat = Qcond_stab[prior, curr]
theta_array[curr] = cat
topology_array[curr] = prior
for child in MST[curr]:
if child in VISITED:
continue
dfs(child, curr)
dfs(root, -1)
new_tree = Tree()
#print(topology_array)
#print(theta_array)
new_tree.load_tree_from_direct_arrays(topology_array, theta_array)
tm.clusters[k] = new_tree
#print("End iteration ", iteration)
log_hood = tm_likelihood(tm, samples, N, num_clusters)
#print(log_hood)
log_hoods.append(log_hood)
loglikelihood_list = np.array(log_hoods)
return loglikelihood_list, tm
def case3():
real = TreeMixture(2, 5)
real.simulate_pi()
real.simulate_trees(seed_val=123)
real.sample_mixtures(30, seed_val=123)
real.save_mixture("q2_4/case3.pkl")
def case1():
real = TreeMixture(7, 4)
real.simulate_pi()
real.simulate_trees(seed_val=123)
real.sample_mixtures(100, seed_val=123)
real.save_mixture("q2_4/case1.pkl")
def main():
print("Hello World!")
seed_val = 123
#sample_filename = "q2_4/q2_4_tree_mixture.pkl_samples.txt"
#real_values_filename = "q2_4/q2_4_tree_mixture.pkl"
#sample_filename = "q2_4/case1.pkl_samples.txt"
#real_values_filename = "q2_4/case1.pkl"
#sample_filename = "q2_4/case2.pkl_samples.txt"
#real_values_filename = "q2_4/case2.pkl"
sample_filename = "q2_4/case3.pkl_samples.txt"
real_values_filename = "q2_4/case3.pkl"
num_clusters = 2 #need to change this fpr each case!
samples = np.loadtxt(sample_filename, delimiter="\t", dtype=np.int32)
loglikelihood, my_tm = sieving(seed_val,
samples,
num_clusters=num_clusters)
plt.figure(figsize=(8, 3))
plt.subplot(121)
plt.plot(np.exp(loglikelihood), label='Estimated')
plt.ylabel("Likelihood of Mixture")
plt.xlabel("Iterations")
plt.subplot(122)
plt.plot(loglikelihood, label='Estimated')
plt.ylabel("Log-Likelihood of Mixture")
plt.xlabel("Iterations")
plt.legend(loc=(1.04, 0))
plt.show()
if real_values_filename != "":
real = TreeMixture(0, 0)
real.load_mixture(real_values_filename)
print("\t4.1. Make the Robinson-Foulds distance analysis.\n")
tns = dendropy.TaxonNamespace()
real_trees = [i.newick for i in real.clusters]
my_trees = [i.newick for i in my_tm.clusters]
print(my_trees)
i = 0
for real_tree in real_trees:
real_den = dendropy.Tree.get(data=real_tree,
schema="newick",
taxon_namespace=tns)
j = 0
for my_tree in my_trees:
my_den = dendropy.Tree.get(data=my_tree,
schema="newick",
taxon_namespace=tns)
print(
"RF distance: $<", i, j, ">$\t=",
dendropy.calculate.treecompare.symmetric_difference(
real_den, my_den), "\\\\")
j += 1
i += 1
print("4.2. Make the likelihood comparison.\n")
real_log_hood = tm_likelihood(real, samples, len(samples),
num_clusters)
print("Real: ", real_log_hood)
print("Infered: ", loglikelihood)
def em_algorithm(seed_val, samples, num_clusters, max_num_iter=30):
best_likelihood = -100000000.0
best_seed = 0
for seedno in range(100):
np.random.seed(seedno)
#print("Running EM algorithm...")
tm = TreeMixture(num_clusters=num_clusters, num_nodes=samples.shape[1])
tm.simulate_pi(seedno)
tm.simulate_trees(seedno)
tm.sample_mixtures(num_samples=samples.shape[0], seed_val=seedno)
topology_list = []
theta_list = []
for k in range(num_clusters):
topology_list.append(tm.clusters[k].get_topology_array())
theta_list.append(tm.clusters[k].get_theta_array())
topology_list = np.array(topology_list)
theta_list = np.array(theta_list)
loglikelihood = np.zeros(max_num_iter)
pi = tm.pi
for it in range(max_num_iter):
#print("start iteration",it)
#1: compute responsibilities
resp = responsibilities(num_clusters, samples, theta_list,
topology_list, pi)
#print(resp)
#2: set pi' = sum(r[n,k]/N)
pi = np.zeros(num_clusters)
pi_newdenom = np.sum(resp)
for k in range(num_clusters):
pi[k] = np.sum(resp[:, k]) / pi_newdenom
#print(pi)
#3: calculate mutual information between x[s] and x[t]
N_ind1, q_denom1 = q_parts1(num_clusters, samples, resp)
N_ind0, q_denom0 = q_parts0(num_clusters, samples, resp)
#4: set Tau'[k] as maximum spanning tree in G[k]
##PACKAGE NETWORKX USED TO CONVERT MAXIMUM SPANNING TREE TO TOPOLOGY
trees = [
Graph(samples.shape[1]),
Graph(samples.shape[1]),
Graph(samples.shape[1]),
Graph(samples.shape[1])
]
weights = np.zeros(
(num_clusters, samples.shape[1], samples.shape[1]))
MST = [
Graph(samples.shape[1]),
Graph(samples.shape[1]),
Graph(samples.shape[1]),
Graph(samples.shape[1])
]
for k in range(num_clusters):
for s in range(samples.shape[1]):
for t in range(samples.shape[1]):
weights[k, s,
t] = I_Info(k, s, t, N_ind1, N_ind0, q_denom0,
q_denom1, num_clusters, samples)
#print(weights)
trees[k].addEdge(s, t, weights[k, s, t])
MST[k] = trees[k].maximum_spanning_tree()
tree_graphs = [nx.Graph(), nx.Graph(), nx.Graph(), nx.Graph()]
treearray = [nx.Graph(), nx.Graph(), nx.Graph(), nx.Graph()]
for k in range(num_clusters):
for u_of_edge, v_of_edge, weight in MST[k]:
tree_graphs[k].add_edge(u_of_edge=u_of_edge,
v_of_edge=v_of_edge)
treearray[k] = list(nx.bfs_edges(G=tree_graphs[k], source=0))
tau_new = topology_list
for k in range(num_clusters):
for s in range(0, len(treearray[k])):
parent = treearray[k][s][0]
child = treearray[k][s][1]
tau_new[k][child] = parent
#5: set Theta'[k](X[r])
theta_new = theta_list
for k in range(num_clusters):
theta_new[k][0][:] = [
q0(k, 0, 0, N_ind0, q_denom0),
q0(k, 0, 1, N_ind0, q_denom0)
]
for s in range(1, samples.shape[1]):
for a in range(0, 2):
for b in range(0, 2):
theta_new[k][s][a][b] = q_parts1cond(
s, int(tau_new[k][s]), a, b, samples, resp[:,
k])
#6: calculate log-likelihood
theta_list = theta_new
topology_list = tau_new
loglikelihood[it] = log_likelihood(num_clusters, samples,
theta_list, topology_list, pi)
#print("best_likelihood = ",best_likelihood, "loglikelihood = ",loglikelihood[9])
if best_likelihood < loglikelihood[25]:
print(best_likelihood, ">", loglikelihood[25])
best_likelihood = loglikelihood[25]
best_seed = seedno
print("seed val = ", best_seed)
"repeat algorithm after finding best seed"
np.random.seed(best_seed)
#print("Running EM algorithm...")
# TODO: Implement EM algorithm here.
tm = TreeMixture(num_clusters=num_clusters, num_nodes=samples.shape[1])
tm.simulate_pi(best_seed)
tm.simulate_trees(best_seed)
tm.sample_mixtures(num_samples=samples.shape[0], seed_val=best_seed)
topology_list = []
theta_list = []
for k in range(num_clusters):
topology_list.append(tm.clusters[k].get_topology_array())
theta_list.append(tm.clusters[k].get_theta_array())
#loglikelihood = np.array(loglikelihood)
topology_list = np.array(topology_list)
theta_list = np.array(theta_list)
#start iterations
loglikelihood = np.zeros(max_num_iter)
pi = tm.pi
for it in range(max_num_iter):
#print("start iteration",it)
#1: compute responsibilities
resp = responsibilities(num_clusters, samples, theta_list,
topology_list, pi)
#print(resp)
#2: set pi' = sum(r[n,k]/N)
pi = np.zeros(num_clusters)
pi_newdenom = np.sum(resp)
for k in range(num_clusters):
pi[k] = np.sum(resp[:, k]) / pi_newdenom
#print(pi)
#3: calculate mutual information between x[s] and x[t]
N_ind1, q_denom1 = q_parts1(num_clusters, samples, resp)
N_ind0, q_denom0 = q_parts0(num_clusters, samples, resp)
#4: set Tau'[k] as maximum spanning tree in G[k]
trees = [
Graph(samples.shape[1]),
Graph(samples.shape[1]),
Graph(samples.shape[1]),
Graph(samples.shape[1])
]
weights = np.zeros((num_clusters, samples.shape[1], samples.shape[1]))
MST = [
Graph(samples.shape[1]),
Graph(samples.shape[1]),
Graph(samples.shape[1]),
Graph(samples.shape[1])
]
for k in range(num_clusters):
for s in range(samples.shape[1]):
for t in range(samples.shape[1]):
weights[k, s,
t] = I_Info(k, s, t, N_ind1, N_ind0, q_denom0,
q_denom1, num_clusters, samples)
trees[k].addEdge(s, t, weights[k, s, t])
MST[k] = trees[k].maximum_spanning_tree()
##PACKAGE NETWORKX USED TO CONVERT MAXIMUM SPANNING TREE TO TOPOLOGY
tree_graphs = [nx.Graph(), nx.Graph(), nx.Graph(), nx.Graph()]
treearray = [nx.Graph(), nx.Graph(), nx.Graph(), nx.Graph()]
for k in range(num_clusters):
for u_of_edge, v_of_edge, weight in MST[k]:
tree_graphs[k].add_edge(u_of_edge=u_of_edge,
v_of_edge=v_of_edge)
treearray[k] = list(nx.bfs_edges(G=tree_graphs[k], source=0))
tau_new = topology_list
for k in range(num_clusters):
for s in range(0, len(treearray[k])):
parent = treearray[k][s][0]
child = treearray[k][s][1]
tau_new[k][child] = parent
#5: set Theta'[k](X[r])
theta_new = theta_list
for k in range(num_clusters):
theta_new[k][0][:] = [
q0(k, 0, 0, N_ind0, q_denom0),
q0(k, 0, 1, N_ind0, q_denom0)
]
for s in range(1, samples.shape[1]):
for a in range(0, 2):
for b in range(0, 2):
theta_new[k][s][a][b] = q_parts1cond(
s, int(tau_new[k][s]), a, b, samples, resp[:, k])
#6: calculate log-likelihood
theta_list = theta_new
topology_list = tau_new
loglikelihood[it] = log_likelihood(num_clusters, samples, theta_list,
topology_list, pi)
print("topology_list = ", topology_list)
print(loglikelihood)
return loglikelihood, np.array(topology_list), theta_list
def main():
# Code to process command line arguments
parser = argparse.ArgumentParser(
description='EM algorithm for likelihood of a tree GM.')
parser.add_argument(
'sample_filename',
type=str,
help=
'Specify the name of the sample file (i.e data/example_samples.txt)')
parser.add_argument(
'output_filename',
type=str,
help=
'Specify the name of the output file (i.e data/example_results.txt)')
parser.add_argument('num_clusters',
type=int,
help='Specify the number of clusters (i.e 3)')
parser.add_argument(
'--seed_val',
type=int,
default=42,
help='Specify the seed value for reproducibility (i.e 42)')
parser.add_argument(
'--real_values_filename',
type=str,
default="",
help=
'Specify the name of the real values file (i.e data/example_tree_mixture.pkl)'
)
# You can add more default parameters if you want.
print("Hello World!")
print(
"This file demonstrates the flow of function templates of question 2.5."
)
print("\n0. Load the parameters from command line.\n")
args = parser.parse_args()
print("\tArguments are: ", args)
print("\n1. Load samples from txt file.\n")
samples = np.loadtxt(args.sample_filename, delimiter="\t", dtype=np.int32)
sample_filename = args.sample_filename
customData = False
if sample_filename == "data/q_2_5_tm_20node_20sample_4clusters.pkl_samples.txt":
pi_file = 'data/q_2_5_tm_20node_20sample_4clusters.pkl_pi.npy'
tree0 = 'data/q_2_5_tm_20node_20sample_4clusters.pkl_tree_0_topology.npy'
tree1 = 'data/q_2_5_tm_20node_20sample_4clusters.pkl_tree_1_topology.npy'
tree2 = 'data/q_2_5_tm_20node_20sample_4clusters.pkl_tree_2_topology.npy'
tree3 = 'data/q_2_5_tm_20node_20sample_4clusters.pkl_tree_3_topology.npy'
theta0 = 'data/q_2_5_tm_20node_20sample_4clusters.pkl_tree_0_theta.npy'
theta1 = 'data/q_2_5_tm_20node_20sample_4clusters.pkl_tree_1_theta.npy'
theta2 = 'data/q_2_5_tm_20node_20sample_4clusters.pkl_tree_2_theta.npy'
theta3 = 'data/q_2_5_tm_20node_20sample_4clusters.pkl_tree_3_theta.npy'
elif sample_filename == "data/q_2_5_tm_10node_50sample_4clusters.pkl_samples.txt":
pi_file = 'data/q_2_5_tm_10node_50sample_4clusters.pkl_pi.npy'
tree0 = 'data/q_2_5_tm_10node_50sample_4clusters.pkl_tree_0_topology.npy'
tree1 = 'data/q_2_5_tm_10node_50sample_4clusters.pkl_tree_1_topology.npy'
tree2 = 'data/q_2_5_tm_10node_50sample_4clusters.pkl_tree_2_topology.npy'
tree3 = 'data/q_2_5_tm_10node_50sample_4clusters.pkl_tree_3_topology.npy'
theta0 = 'data/q_2_5_tm_10node_50sample_4clusters.pkl_tree_0_theta.npy'
theta1 = 'data/q_2_5_tm_10node_50sample_4clusters.pkl_tree_1_theta.npy'
theta2 = 'data/q_2_5_tm_10node_50sample_4clusters.pkl_tree_2_theta.npy'
theta3 = 'data/q_2_5_tm_10node_50sample_4clusters.pkl_tree_3_theta.npy'
elif sample_filename == "data/q_2_5_tm_10node_20sample_4clusters.pkl_samples.txt":
pi_file = 'data/q_2_5_tm_10node_20sample_4clusters.pkl_pi.npy'
tree0 = 'data/q_2_5_tm_10node_20sample_4clusters.pkl_tree_0_topology.npy'
tree1 = 'data/q_2_5_tm_10node_20sample_4clusters.pkl_tree_1_topology.npy'
tree2 = 'data/q_2_5_tm_10node_20sample_4clusters.pkl_tree_2_topology.npy'
tree3 = 'data/q_2_5_tm_10node_20sample_4clusters.pkl_tree_3_topology.npy'
theta0 = 'data/q_2_5_tm_10node_20sample_4clusters.pkl_tree_0_theta.npy'
theta1 = 'data/q_2_5_tm_10node_20sample_4clusters.pkl_tree_1_theta.npy'
theta2 = 'data/q_2_5_tm_10node_20sample_4clusters.pkl_tree_2_theta.npy'
theta3 = 'data/q_2_5_tm_10node_20sample_4clusters.pkl_tree_3_theta.npy'
else:
print(
'Testing with Custom File. Please provide true mixture for likelihood and RF Comparisiom'
)
customData = True
num_samples, num_nodes = samples.shape
print("\tnum_samples: ", num_samples, "\tnum_nodes: ", num_nodes)
print("\tSamples: \n", samples)
print("\n2. Run EM Algorithm.\n")
sieving = np.random.randint(20, 999, size=10)
good_seed = sieving[0]
bestFit = -np.Infinity
for sieve in sieving:
loglikelihood, topology_array, theta_array = em_algorithm(
sieve, samples, args.num_clusters, 10)
# print(loglikelihood)
thisFit = loglikelihood[-1]
if (thisFit > bestFit):
bestFit = thisFit
good_seed = sieve
loglikelihood, topology_array, theta_array = em_algorithm(
good_seed, samples, num_clusters=args.num_clusters)
print("\n3. Save, print and plot the results.\n")
num_clusters = args.num_clusters
save_results(loglikelihood, topology_array, theta_array,
args.output_filename)
for i in range(args.num_clusters):
print("\n\tCluster: ", i)
print("\tTopology: \t", topology_array[i])
print("\tTheta: \t", theta_array[i])
plt.figure(figsize=(8, 3))
plt.subplot(121)
plt.plot(np.exp(loglikelihood), label='Estimated')
plt.ylabel("Likelihood of Mixture")
plt.xlabel("Iterations")
plt.subplot(122)
plt.title(sample_filename)
plt.plot(loglikelihood, label='Estimated')
plt.ylabel("Log-Likelihood of Mixture")
plt.xlabel("Iterations")
plt.legend(loc=(1.04, 0))
plt.show()
print("\n4. Retrieve real results and compare.\n")
if args.real_values_filename != "" or True:
if customData == False:
print("\tComparing the results with real values...")
print("\t4.1. Make the Robinson-Foulds distance analysis.\n")
# TODO: Do RF Comparison
t0 = Tree()
t1 = Tree()
t2 = Tree()
t3 = Tree()
true_pi = np.load(pi_file)
t0.load_tree_from_arrays(tree0, theta0)
t1.load_tree_from_arrays(tree1, theta1)
t2.load_tree_from_arrays(tree2, theta2)
t3.load_tree_from_arrays(tree3, theta3)
tns = dendropy.TaxonNamespace()
t0_rf = dendropy.Tree.get(data=t0.get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t1_rf = dendropy.Tree.get(data=t1.get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t2_rf = dendropy.Tree.get(data=t2.get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t3_rf = dendropy.Tree.get(data=t3.get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t0_infer = Tree()
t1_infer = Tree()
t2_infer = Tree()
t3_infer = Tree()
t0_infer.load_tree_from_direct_arrays(topology_array[0],
theta_array[0])
t1_infer.load_tree_from_direct_arrays(topology_array[1],
theta_array[1])
t2_infer.load_tree_from_direct_arrays(topology_array[2],
theta_array[2])
t3_infer.load_tree_from_direct_arrays(topology_array[3],
theta_array[3])
t0_infer_rf = dendropy.Tree.get(data=t0_infer.get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t1_infer_rf = dendropy.Tree.get(data=t1_infer.get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t2_infer_rf = dendropy.Tree.get(data=t2_infer.get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t3_infer_rf = dendropy.Tree.get(data=t3_infer.get_tree_newick(),
schema="newick",
taxon_namespace=tns)
print('File:', sample_filename)
print('------Robinson-Foulds Distance------')
rfTree0 = [
RfDist(t0_infer_rf, t0_rf),
RfDist(t0_infer_rf, t1_rf),
RfDist(t0_infer_rf, t2_rf),
RfDist(t0_infer_rf, t3_rf)
]
rfTree1 = [
RfDist(t1_infer_rf, t0_rf),
RfDist(t1_infer_rf, t1_rf),
RfDist(t1_infer_rf, t2_rf),
RfDist(t1_infer_rf, t3_rf)
]
rfTree2 = [
RfDist(t2_infer_rf, t0_rf),
RfDist(t2_infer_rf, t1_rf),
RfDist(t2_infer_rf, t2_rf),
RfDist(t2_infer_rf, t3_rf)
]
rfTree3 = [
RfDist(t3_infer_rf, t0_rf),
RfDist(t3_infer_rf, t1_rf),
RfDist(t3_infer_rf, t2_rf),
RfDist(t3_infer_rf, t3_rf)
]
print('------Real Trees------')
print(t0.get_tree_newick())
print(t1.get_tree_newick())
print(t2.get_tree_newick())
print(t3.get_tree_newick())
print('------Inferred Trees------')
print(t0_infer.get_tree_newick())
print(t1_infer.get_tree_newick())
print(t2_infer.get_tree_newick())
print(t3_infer.get_tree_newick())
print()
print('RF Distance of Inferred Tree 0 with each Tree(true):',
rfTree0)
print('RF Distance of Inferred Tree 1 with each Tree(true):',
rfTree1)
print('RF Distance of Inferred Tree 2 with each Tree(true):',
rfTree2)
print('RF Distance of Inferred Tree 3 with each Tree(true):',
rfTree3)
print('------Robinson-Foulds Distance------')
print("\t4.2. Make the likelihood comparison.\n")
# TODO: Do Likelihood Comparison
print('Log Likelihood of real mixture: ' + str(
truelikelihood([t0, t1, t2, t3], samples, num_samples,
num_clusters, true_pi)))
print('Log Likelihood of inferred mixture: ' +
str(loglikelihood[-1]))
else:
print('Testing with Custom Data')
tns = dendropy.TaxonNamespace()
if sample_filename == "newData/Data1/Dataset1.pkl_samples.txt":
num_clusters = 5
num_nodes = 30
tm = TreeMixture(num_clusters, num_nodes)
seed_val = 12
tm.simulate_pi(seed_val=seed_val)
tm.simulate_trees(seed_val)
seed_val = 12
num_samples = 20
tm.sample_mixtures(num_samples, seed_val=seed_val)
t0_rf = dendropy.Tree.get(
data=tm.clusters[0].get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t1_rf = dendropy.Tree.get(
data=tm.clusters[1].get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t2_rf = dendropy.Tree.get(
data=tm.clusters[2].get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t3_rf = dendropy.Tree.get(
data=tm.clusters[3].get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t4_rf = dendropy.Tree.get(
data=tm.clusters[4].get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t0_infer = Tree()
t1_infer = Tree()
t2_infer = Tree()
t3_infer = Tree()
t4_infer = Tree()
t0_infer.load_tree_from_direct_arrays(topology_array[0],
theta_array[0])
t1_infer.load_tree_from_direct_arrays(topology_array[1],
theta_array[1])
t2_infer.load_tree_from_direct_arrays(topology_array[2],
theta_array[2])
t3_infer.load_tree_from_direct_arrays(topology_array[3],
theta_array[3])
t4_infer.load_tree_from_direct_arrays(topology_array[4],
theta_array[4])
t0_infer_rf = dendropy.Tree.get(
data=t0_infer.get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t1_infer_rf = dendropy.Tree.get(
data=t1_infer.get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t2_infer_rf = dendropy.Tree.get(
data=t2_infer.get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t3_infer_rf = dendropy.Tree.get(
data=t3_infer.get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t4_infer_rf = dendropy.Tree.get(
data=t4_infer.get_tree_newick(),
schema="newick",
taxon_namespace=tns)
print('File:', sample_filename)
print('------Robinson-Foulds Distance------')
rfTree0 = [
RfDist(t0_infer_rf, t0_rf),
RfDist(t0_infer_rf, t1_rf),
RfDist(t0_infer_rf, t2_rf),
RfDist(t0_infer_rf, t3_rf)
]
rfTree1 = [
RfDist(t1_infer_rf, t0_rf),
RfDist(t1_infer_rf, t1_rf),
RfDist(t1_infer_rf, t2_rf),
RfDist(t1_infer_rf, t3_rf)
]
rfTree2 = [
RfDist(t2_infer_rf, t0_rf),
RfDist(t2_infer_rf, t1_rf),
RfDist(t2_infer_rf, t2_rf),
RfDist(t2_infer_rf, t3_rf)
]
rfTree3 = [
RfDist(t3_infer_rf, t0_rf),
RfDist(t3_infer_rf, t1_rf),
RfDist(t3_infer_rf, t2_rf),
RfDist(t3_infer_rf, t3_rf)
]
rfTree4 = [
RfDist(t4_infer_rf, t0_rf),
RfDist(t4_infer_rf, t1_rf),
RfDist(t4_infer_rf, t2_rf),
RfDist(t4_infer_rf, t4_rf)
]
print('------Real Trees------')
print(tm.clusters[0].get_tree_newick())
print(tm.clusters[1].get_tree_newick())
print(tm.clusters[2].get_tree_newick())
print(tm.clusters[3].get_tree_newick())
print(tm.clusters[4].get_tree_newick())
print('------Inferred Trees------')
print(t0_infer.get_tree_newick())
print(t1_infer.get_tree_newick())
print(t2_infer.get_tree_newick())
print(t3_infer.get_tree_newick())
print(t4_infer.get_tree_newick())
print()
print('RF Distance of Inferred Tree 0 with each Tree(true):',
rfTree0)
print('RF Distance of Inferred Tree 1 with each Tree(true):',
rfTree1)
print('RF Distance of Inferred Tree 2 with each Tree(true):',
rfTree2)
print('RF Distance of Inferred Tree 3 with each Tree(true):',
rfTree3)
print('RF Distance of Inferred Tree 4 with each Tree(true):',
rfTree4)
print('------Robinson-Foulds Distance------')
print("\t4.2. Make the likelihood comparison.\n")
print('Log Likelihood of real mixture: ' + str(
truelikelihood([
tm.clusters[0], tm.clusters[1], tm.clusters[2],
tm.clusters[3], tm.clusters[4]
], samples, num_samples, num_clusters, tm.pi)))
print('Log Likelihood of inferred mixture: ' +
str(loglikelihood[-1]))
elif sample_filename == "newData/Data2/Dataset2.pkl_samples.txt":
num_clusters = 3
num_nodes = 50
tm = TreeMixture(num_clusters, num_nodes)
seed_val = 123
tm.simulate_pi(seed_val=seed_val)
tm.simulate_trees(seed_val)
seed_val = 12
num_samples = 100
tm.sample_mixtures(num_samples, seed_val=seed_val)
t0_rf = dendropy.Tree.get(
data=tm.clusters[0].get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t1_rf = dendropy.Tree.get(
data=tm.clusters[1].get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t2_rf = dendropy.Tree.get(
data=tm.clusters[2].get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t0_infer = Tree()
t1_infer = Tree()
t2_infer = Tree()
t0_infer.load_tree_from_direct_arrays(topology_array[0],
theta_array[0])
t1_infer.load_tree_from_direct_arrays(topology_array[1],
theta_array[1])
t2_infer.load_tree_from_direct_arrays(topology_array[2],
theta_array[2])
t0_infer_rf = dendropy.Tree.get(
data=t0_infer.get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t1_infer_rf = dendropy.Tree.get(
data=t1_infer.get_tree_newick(),
schema="newick",
taxon_namespace=tns)
t2_infer_rf = dendropy.Tree.get(
data=t2_infer.get_tree_newick(),
schema="newick",
taxon_namespace=tns)
print('File:', sample_filename)
print('------Robinson-Foulds Distance------')
rfTree0 = [
RfDist(t0_infer_rf, t0_rf),
RfDist(t0_infer_rf, t1_rf),
RfDist(t0_infer_rf, t2_rf)
]
rfTree1 = [
RfDist(t1_infer_rf, t0_rf),
RfDist(t1_infer_rf, t1_rf),
RfDist(t1_infer_rf, t2_rf)
]
rfTree2 = [
RfDist(t2_infer_rf, t0_rf),
RfDist(t2_infer_rf, t1_rf),
RfDist(t2_infer_rf, t2_rf)
]
print('------Real Trees------')
print(tm.clusters[0].get_tree_newick())
print(tm.clusters[1].get_tree_newick())
print(tm.clusters[2].get_tree_newick())
print('------Inferred Trees------')
print(t0_infer.get_tree_newick())
print(t1_infer.get_tree_newick())
print(t2_infer.get_tree_newick())
print()
print('RF Distance of Inferred Tree 0 with each Tree(true):',
rfTree0)
print('RF Distance of Inferred Tree 1 with each Tree(true):',
rfTree1)
print('RF Distance of Inferred Tree 2 with each Tree(true):',
rfTree2)
print('------Robinson-Foulds Distance------')
print("\t4.2. Make the likelihood comparison.\n")
print('Log Likelihood of real mixture: ' + str(
truelikelihood(
[tm.clusters[0], tm.clusters[1], tm.clusters[2]],
samples, num_samples, num_clusters, tm.pi)))
print('Log Likelihood of inferred mixture: ' +
str(loglikelihood[-1]))
def em_algorithm(seed_val, samples, num_clusters, max_num_iter=100):
"""
This function is for the EM algorithm.
:param seed_val: Seed value for reproducibility. Type: int
:param samples: Observed x values. Type: numpy array. Dimensions: (num_samples, num_nodes)
:param num_clusters: Number of clusters. Type: int
:param max_num_iter: Maximum number of EM iterations. Type: int
:return: loglikelihood: Array of log-likelihood of each EM iteration. Type: numpy array.
Dimensions: (num_iterations, ) Note: num_iterations does not have to be equal to max_num_iter.
:return: topology_list: A list of tree topologies. Type: numpy array. Dimensions: (num_clusters, num_nodes)
:return: theta_list: A list of tree CPDs. Type: numpy array. Dimensions: (num_clusters, num_nodes, 2)
You can change the function signature and add new parameters. Add them as parameters with some default values.
i.e.
Function template: def em_algorithm(seed_val, samples, k, max_num_iter=10):
You can change it to: def em_algorithm(seed_val, samples, k, max_num_iter=10, new_param_1=[], new_param_2=123):
"""
print("Running EM algorithm...")
# Set threshold for convergence
THRES = 1e-4
num_sieving = 10
num_samples = np.size(samples, 0)
num_nodes = np.size(samples, 1)
np.random.seed(seed_val)
seeds = np.random.randint(0, 100000000, num_sieving)
last_loglikelihoods = []
tms = []
for seed in seeds:
np.random.seed(seed)
tm = TreeMixture(num_clusters=num_clusters, num_nodes=num_nodes)
tm.simulate_pi(seed_val=seed)
tm.simulate_trees(seed_val=seed)
tm_loglikelihood, tm = em_helper(tm,
samples,
num_clusters,
max_num_iter=10)
last_loglikelihoods.append(tm_loglikelihood[-1])
tms.append(tm)
print("=> Sieving finished")
seed = seeds[last_loglikelihoods.index(max(last_loglikelihoods))]
# tm = tms[last_loglikelihoods.index(max(last_loglikelihoods))]
tm = TreeMixture(num_clusters=num_clusters, num_nodes=num_nodes)
tm.simulate_pi(seed_val=seed)
tm.simulate_trees(seed_val=seed)
loglikelihood, tm = em_helper(tm,
samples,
num_clusters,
max_num_iter=max_num_iter)
print("=> EM finished")
topology_list = []
theta_list = []
for t in tm.clusters:
topology_list.append(t.get_topology_array())
theta_list.append(t.get_theta_array())
loglikelihood = np.array(loglikelihood)
topology_list = np.array(topology_list)
# theta_list = np.array(theta_list)
return loglikelihood, topology_list, theta_list, tm
def main():
# Code to process command line arguments
parser = argparse.ArgumentParser(
description='EM algorithm for likelihood of a tree GM.')
parser.add_argument(
'--sample_filename',
type=str,
default='data/q_2_5_tm_20node_20sample_4clusters.pkl_samples.txt',
help=
'Specify the name of the sample file (i.e data/example_samples.txt)')
parser.add_argument(
'--real_values_filename',
type=str,
default='data/q_2_5_tm_20node_20sample_4clusters.pkl',
help=
'Specify the name of the real values file (i.e data/example_tree_mixture.pkl)'
)
parser.add_argument(
'--output_filename',
type=str,
default='q_2_5_tm_20node_20sample_4clusters_result.txt',
help=
'Specify the name of the output file (i.e data/example_results.txt)')
parser.add_argument('--num_nodes',
type=int,
default=10,
help='Specify the number of nodes of trees (i.e 10)')
parser.add_argument('--num_clusters',
type=int,
default=10,
help='Specify the number of clusters (i.e 3)')
parser.add_argument(
'--seed_val',
type=int,
default=123,
help='Specify the seed value for reproducibility (i.e 42)')
parser.add_argument(
'--if_simulate',
type=bool,
default=True,
help='Specify whether the sampling is enabled (i.e False)')
parser.add_argument(
'--num_samples',
type=int,
default=50,
help='Specify the number of samples if sampling is enabled (i.e 1000)')
# You can add more default parameters if you want.
print("Hello World!")
print(
"This file demonstrates the flow of function templates of question 2.5."
)
print("\n0. Load the parameters from command line.\n")
args = parser.parse_args()
print("\tArguments are: ", args)
if args.if_simulate:
print("\n1. Make new tree and sample.\n")
tm_truth = TreeMixture(num_clusters=args.num_clusters,
num_nodes=args.num_nodes)
tm_truth.simulate_pi(seed_val=args.seed_val)
tm_truth.simulate_trees(seed_val=args.seed_val)
tm_truth.sample_mixtures(args.num_samples, seed_val=args.seed_val)
else:
print("\n1. Load true tree from file.\n")
tm_truth = TreeMixture(0, 0)
tm_truth.load_mixture(args.real_values_filename)
print("Load samples.")
samples = tm_truth.samples
num_samples, num_nodes = samples.shape
print("\tnum_samples: ", num_samples, "\tnum_nodes: ", num_nodes)
print("\tSamples: \n", samples)
print("\n2. Run EM Algorithm.\n")
loglikelihood, topology_array, theta_array, tm = em_algorithm(
args.seed_val, samples, num_clusters=args.num_clusters)
print("\n3. Save, print and plot the results.\n")
# save_results(loglikelihood, topology_array, theta_array, args.output_filename)
for i in range(args.num_clusters):
print("\n\tCluster: ", i)
print("\tTopology: \t", topology_array[i])
print("\tTheta: \t", theta_array[i])
plt.figure(figsize=(8, 3))
plt.subplot(121)
plt.plot(np.exp(loglikelihood), label='Estimated')
plt.ylabel("Likelihood of Mixture")
plt.xlabel("Iterations")
plt.subplot(122)
plt.plot(loglikelihood, label='Estimated')
plt.ylabel("Log-Likelihood of Mixture")
plt.xlabel("Iterations")
plt.legend(loc=(1.04, 0))
plt.show()
print("\n4. Retrieve real results and compare.\n")
if args.real_values_filename != "":
print(
"\n=> Compare trees and print Robinson-Foulds (RF) distance (result v.s truth):\n"
)
N = len(samples)
K = tm_truth.num_clusters
tns = dendropy.TaxonNamespace()
print("\\hline")
for k in range(K):
print(k, end=" & ")
for j in range(K):
t_0 = tm.clusters[k]
t_0.get_tree_newick()
t_0 = dendropy.Tree.get(data=t_0.newick,
schema="newick",
taxon_namespace=tns)
t_t = tm_truth.clusters[j]
t_t.get_tree_newick()
t_t = dendropy.Tree.get(data=t_t.newick,
schema="newick",
taxon_namespace=tns)
print(dendropy.calculate.treecompare.symmetric_difference(
t_0, t_t),
end=" & ")
print("\\\\")
print("\n=> Compare log-likelihood (result v.s truth):\n")
posterior = np.ones((N, K))
prior = np.ones(N)
for n, x in enumerate(samples):
for k, tree in enumerate(tm_truth.clusters):
visit_list = [tree.root]
while len(visit_list) != 0:
cur_node = visit_list[0]
visit_list = visit_list[1:]
visit_list = visit_list + cur_node.descendants
if cur_node.ancestor is None:
posterior[n, k] *= cur_node.cat[x[int(cur_node.name)]]
else:
posterior[n, k] *= cur_node.cat[x[int(
cur_node.ancestor.name)]][x[int(cur_node.name)]]
prior[n] *= np.sum(posterior[n] * tm_truth.pi)
loglikelihood_truth = np.sum(np.log(prior))
print("%f : %f" % (loglikelihood[-1], loglikelihood_truth))
def main():
# Code to process command line arguments
parser = argparse.ArgumentParser(
description='EM algorithm for likelihood of a tree GM.')
parser.add_argument(
'sample_filename',
type=str,
help=
'Specify the name of the sample file (i.e data/example_samples.txt)')
parser.add_argument(
'output_filename',
type=str,
help=
'Specify the name of the output file (i.e data/example_results.txt)')
parser.add_argument('num_clusters',
type=int,
help='Specify the number of clusters (i.e 3)')
parser.add_argument(
'--seed_val',
type=int,
default=42,
help='Specify the seed value for reproducibility (i.e 42)')
parser.add_argument(
'--real_values_filename',
type=str,
default="",
help=
'Specify the name of the real values file (i.e data/example_tree_mixture.pkl)'
)
# You can add more default parameters if you want.
print("Hello World!")
print(
"This file demonstrates the flow of function templates of question 2.5."
)
print("\n0. Load the parameters from command line.\n")
args = parser.parse_args()
print("\tArguments are: ", args)
print("\n1. Load samples from txt file.\n")
samples = np.loadtxt(args.sample_filename, delimiter="\t", dtype=np.int32)
num_samples, num_nodes = samples.shape
print("\tnum_samples: ", num_samples, "\tnum_nodes: ", num_nodes)
print("\tSamples: \n", samples)
print("\n2. Run EM Algorithm.\n")
loglikelihood, topology_array, theta_array = em_algorithm(
args.seed_val, samples, num_clusters=args.num_clusters)
print("\n3. Save, print and plot the results.\n")
save_results(loglikelihood, topology_array, theta_array,
args.output_filename)
for i in range(args.num_clusters):
print("\n\tCluster: ", i)
print("\tTopology: \t", topology_array[i])
print("\tTheta: \t", theta_array[i])
plt.figure(figsize=(8, 3))
plt.subplot(121)
plt.plot(np.exp(loglikelihood), label='Estimated')
plt.ylabel("Likelihood of Mixture")
plt.xlabel("Iterations")
plt.subplot(122)
plt.plot(loglikelihood, label='Estimated')
plt.ylabel("Log-Likelihood of Mixture")
plt.xlabel("Iterations")
plt.legend(loc=(1.04, 0))
plt.show()
print("\n4. Retrieve real results and compare.\n")
if args.real_values_filename != "":
print("\tComparing the results with real values...")
actual_tm = TreeMixture(args.num_clusters, num_nodes)
actual_tm.load_mixture(args.real_values_filename)
inferred_tm = TreeMixture(args.num_clusters, num_nodes)
inferred_tm.load_mixture(args.output_filename)
print("\t4.1. Make the Robinson-Foulds distance analysis.\n")
diff = compute_tree_mix_diff(actual_tm, inferred_tm)
print("Total Robinson-Foulds distance: " + str(diff))
print("\t4.2. Make the likelihood comparison.\n")
actual_lik = actual_tm.likelihood_dataset(samples)
inferred_lik = inferred_tm.likelihood_dataset(samples)
print("Log-Likelihood of actual tree: " + str(actual_lik) +
", inferred tree: " + str(inferred_lik))
def em_algorithm(seed_val, samples, num_clusters, max_num_iter, tm=None):
num_samples = samples.shape[0]
num_nodes = samples.shape[1]
loglikelihood = []
if tm is None:
tm = TreeMixture(num_clusters=num_clusters, num_nodes=num_nodes)
tm.simulate_pi(None)
tm.simulate_trees(None)
#samples = tm.samples
for iter_ in range(max_num_iter):
# 1. Compute responsibilities for all trees
sample_likelihoods = np.array([[sample_likelihood(tm.clusters[ii], samples[jj,:]\
, tm.pi[ii]) for ii in range(num_clusters)] for jj in range(num_samples)])
sum_over_trees_likelihoods = np.reshape(
np.sum(sample_likelihoods, axis=1), (num_samples, 1))
Responsibilities = np.divide(sample_likelihoods,
sum_over_trees_likelihoods)
# Computing loglikelihood
ll = np.sum(np.log(np.sum(sample_likelihoods, axis=1)), axis=None)
loglikelihood.append(ll)
tm.loglikelihood.append(ll)
# 2. Updating pi for all trees
tm.pi = np.sum(Responsibilities, axis=0) / num_samples
vertices = list(range(num_nodes))
# 3. Updating each tree
for i in range(num_clusters):
tree = tm.clusters[i]
responsibilities = Responsibilities[:, i]
# Creating the symmetric mutual information matrix
mutual_information_matrix = np.asarray([[mutual_information(responsibilities, samples, s_idx, t_idx) \
for s_idx in vertices] for t_idx in vertices])
# Computing the graph
graph = create_graph(num_nodes, responsibilities, samples,
mutual_information_matrix, vertices)
# Finding the maximum spanning tree
MST = maximum_spanning_tree(graph)
# Choosing the root as 0
root_name = 0
# Finding the order of nodes in the tree
ordered_nodes, I_sum_tree = create_ordered_nodes(MST, root_name)
# Getting attributes for tree to enable update
topology_array, theta_array = create_tree_attributes1(
ordered_nodes, root_name, samples, responsibilities, num_nodes)
# Updating the tree
tree.load_tree_from_direct_arrays(topology_array, theta_array)
# -------------------------------------------
topology_list = []
theta_list = []
for i in range(num_clusters):
topology_list.append(tm.clusters[i].get_topology_array())
theta_list.append(tm.clusters[i].get_theta_array())
loglikelihood = np.array(loglikelihood)
topology_list = np.array(topology_list)
theta_list = np.array(theta_list)
return loglikelihood, topology_list, theta_list, tm
def main():
num_clusters = 3
new_tm = TreeMixture(num_clusters=num_clusters, num_nodes=3)
new_tm.simulate_pi(None)
new_tm.simulate_trees(None)
new_tm.sample_mixtures(100)
new_samples = new_tm.samples
#samples = tm.samples
seed_val = None
directory = '/Users/filipbergentoft/Desktop/Github/DD2434/Assignment 2/2_4/'
sample_filename = directory + "data/q2_4/q2_4_tree_mixture.pkl_samples.txt"
output_filename = directory + "data/q2_4/q2_4_own_results"
real_values_filename = directory + "data/q2_4/q2_4_tree_mixture.pkl"
samples = np.loadtxt(sample_filename, delimiter="\t", dtype=np.int32)
np.random.shuffle(samples)
best_tm = sieving(n_first_mixtures=50,
n_second_mixtures=10,
n_first_iterations=10,
n_second_iterations=100,
samples=samples,
num_clusters=num_clusters)
real_tm = TreeMixture(num_clusters=3, num_nodes=5)
real_tm.load_mixture(real_values_filename)
print('best tree', mixture_likelihood(best_tm, samples))
print('best tree', best_tm.pi)
print('real tree', mixture_likelihood(real_tm, samples))
print('real tree', real_tm.pi)
print(RF_comparison(best_tm, real_tm))
for tree in new_tm.clusters:
print('Real tree topology')
print(tree.get_topology_array())
for tree in best_tm.clusters:
print('Inferred tree topology')
print(tree.get_topology_array())
sns.set_style('darkgrid')
"""
plt.subplot(121)
plt.plot(np.exp(best_tm.loglikelihood), label='Estimated')
plt.ylabel("Likelihood of Mixture")
plt.xlabel("Iterations")
plt.subplot(122)
"""
plt.plot(best_tm.loglikelihood, label='Estimated')
plt.ylabel("Log-Likelihood of Mixture")
plt.xlabel("Iterations")
plt.legend()
plt.show()
def em_algorithm(seed_val, samples, num_clusters, max_num_iter=100):
"""
This function is for the EM algorithm.
:param seed_val: Seed value for reproducibility. Type: int
:param samples: Observed x values. Type: numpy array. Dimensions: (num_samples, num_nodes)
:param num_clusters: Number of clusters. Type: int
:param max_num_iter: Maximum number of EM iterations. Type: int
:return: loglikelihood: Array of log-likelihood of each EM iteration. Type: numpy array.
Dimensions: (num_iterations, ) Note: num_iterations does not have to be equal to max_num_iter.
:return: topology_list: A list of tree topologies. Type: numpy array. Dimensions: (num_clusters, num_nodes)
:return: theta_list: A list of tree CPDs. Type: numpy array. Dimensions: (num_clusters, num_nodes, 2)
You can change the function signature and add new parameters. Add them as parameters with some default values.
i.e.
Function template: def em_algorithm(seed_val, samples, k, max_num_iter=10):
You can change it to: def em_algorithm(seed_val, samples, k, max_num_iter=10, new_param_1=[], new_param_2=123):
"""
# Set the seed
np.random.seed(seed_val)
# TODO: Implement EM algorithm here.
# Start: Example Code Segment. Delete this segment completely before you implement the algorithm.
print("Running EM algorithm...")
from Kruskal_v1 import Graph
# return result in the method
import sys
tm = TreeMixture(num_clusters=num_clusters, num_nodes=samples.shape[1])
tm.simulate_pi(seed_val=seed_val)
tm.simulate_trees(seed_val=seed_val)
tm.sample_mixtures(num_samples=samples.shape[0], seed_val=seed_val)
eps = sys.float_info.min
topology_list = []
theta_list = []
loglikelihood = []
num_samples = samples.shape[0]
num_nodes = samples.shape[1]
for iter in range(max_num_iter):
r = np.ones((num_samples, num_clusters))
for i, sample in enumerate(samples):
for j, t in enumerate(tm.clusters):
visitedNodes = [t.root]
r[i, j] *= tm.pi[j]
while len(visitedNodes) != 0:
presentNode = visitedNodes[0]
visitedNodes = visitedNodes[1:]
if len(presentNode.descendants) != 0:
visitedNodes = visitedNodes + presentNode.descendants
if presentNode.ancestor == None: #root node
r[i,
j] *= presentNode.cat[sample[int(presentNode.name)]]
else:
r[i, j] *= presentNode.cat[sample[int(
presentNode.ancestor.name)]][sample[int(
presentNode.name)]]
r += eps
rn = np.sum(r, axis=1).reshape(num_samples, 1)
r /= rn
loglikelihood.append(np.sum(np.log(rn)))
tm.pi = np.sum(r, axis=0) / num_samples
den = np.sum(r, axis=0)
NominatorQk = np.zeros((num_nodes, num_nodes, 2, 2, num_clusters))
for s in range(num_nodes):
for t in range(num_nodes):
for a in range(2):
for b in range(2):
matched_index = np.where(
(samples[:, (s, t)] == [a, b]).all(1))[0]
NominatorQk[s, t, a,
b] = np.sum(r[matched_index], axis=0) / den
DenominatorQk = np.zeros((num_nodes, 2, num_clusters))
for s in range(num_nodes):
for a in range(2):
matched_index = np.where((samples[:, s] == a))
DenominatorQk[s, a] = np.sum(r[matched_index], axis=0) / den
Iqst = np.zeros((num_nodes, num_nodes, num_clusters))
for s in range(num_nodes):
for t in range(num_nodes):
for a in range(2):
for b in range(2):
if (np.all(NominatorQk[s, t, a, b, :] > 0)):
Iqst[s, t] += NominatorQk[s, t, a, b] * np.log(
(NominatorQk[s, t, a, b] /
(DenominatorQk[s, a])) / DenominatorQk[t, b])
else:
Iqst[s, t] += 0
for k in range(num_clusters):
g = Graph(num_nodes)
for s in range(num_nodes):
for t in range(s + 1, num_nodes):
g.addEdge(s, t, Iqst[s, t, k])
mst_edges = np.array(g.maximum_spanning_tree())[:, [0, 1]]
topology_array = np.zeros(num_nodes)
topology_array[0] = np.nan
visitedNodes = [0]
while len(visitedNodes) != 0:
presentNode = visitedNodes[0]
visitedNodes = visitedNodes[1:]
child_edges = np.array(np.where(mst_edges == [presentNode])).T
for ind in child_edges:
child = mst_edges[ind[0]][1 - ind[1]]
topology_array[int(child)] = presentNode
visitedNodes.append(child)
if np.size(child_edges) != 0:
mst_edges = np.delete(mst_edges, child_edges[:, 0], 0)
new_tree = Tree()
new_tree.load_tree_from_direct_arrays(topology_array)
new_tree.alpha = [1.0] * 2
new_tree.k = 2
visitedNodes = [new_tree.root]
while len(visitedNodes) != 0:
presentNode = visitedNodes[0]
visitedNodes = visitedNodes[1:]
if len(presentNode.descendants) != 0:
visitedNodes = visitedNodes + presentNode.descendants
if presentNode.ancestor == None:
presentNode.cat = DenominatorQk[int(presentNode.name), :,
k].tolist()
else:
presentNode.cat = NominatorQk[
int(presentNode.ancestor.name),
int(presentNode.name), :, :, k]
presentNode.cat[0] = presentNode.cat[0] / np.sum(
presentNode.cat[0])
presentNode.cat[1] = presentNode.cat[1] / np.sum(
presentNode.cat[1])
presentNode.cat = [presentNode.cat[0], presentNode.cat[1]]
tm.clusters[k] = new_tree
for j, t in enumerate(tm.clusters):
topology_list.append(t.get_topology_array())
theta_list.append(t.get_theta_array())
loglikelihood = np.array(loglikelihood)
topology_list = np.array(topology_list)
theta_list = np.array(theta_list)
return loglikelihood, topology_list, theta_list
from Tree import TreeMixture
import Exercise2_5
import argparse
# This file has the pupose of creating new samples for testing exercise 5
parser = argparse.ArgumentParser()
parser.add_argument("seed",
help="Introduce the seed to generate trees",
type=int)
parser.add_argument("samples",
help="Introduce the number of samples",
type=int)
parser.add_argument("nodes", help="Introduce the number of nodes", type=int)
parser.add_argument("clusters",
help="Introduce the number of clusters",
type=int)
args = parser.parse_args()
print("Generating tree with seed:", args.seed, "\tsamples:", args.samples,
"\tnodes:", args.nodes, "\tclusters:", args.clusters)
tm = TreeMixture(num_clusters=args.clusters, num_nodes=args.nodes)
tm.simulate_pi(seed_val=args.seed)
tm.simulate_trees(seed_val=args.seed)
tm.sample_mixtures(num_samples=args.samples, seed_val=args.seed)
path = 'data/q_2_5_tm_' + str(args.nodes) + 'node_' + str(
args.samples) + 'sample_' + str(args.clusters) + 'clusters.pkl'
tm.save_mixture(path, True)
def em_algorithm(seed_val, samples, num_clusters, max_num_iter):
# Initialize the needed variables
sieving = 100
max_log = float("-inf")
best_seed = 0
# Get the best seed for likelihood
for siev in tqdm(range(sieving)):
# Set the seed
aux_seed = seed_val + siev # Try with all seeds from @param:seed_val to @param:seed_val + sieving
np.random.seed(aux_seed)
# Generate tree mixture
tm = TreeMixture(num_clusters=num_clusters, num_nodes=samples.shape[1])
tm.simulate_pi(seed_val=aux_seed)
tm.simulate_trees(seed_val=aux_seed)
topology_list = []
theta_list = []
for i in range(num_clusters):
topology_list.append(tm.clusters[i].get_topology_array())
theta_list.append(tm.clusters[i].get_theta_array())
# Run 10 iterations according to this mixture
loglikelihood = computationsEM(10, samples, num_clusters, tm, topology_list, theta_list)
aux = loglikelihood[-1]
if (aux > max_log):
max_log = aux
best_seed = aux_seed
# -------------------- End of sieving -------------------- #
# Variable initialization
np.random.seed(best_seed)
topology_list = [] # Dimensions: (num_clusters, num_nodes)
theta_list = [] # Dimensions: (num_clusters, num_nodes, 2)
tm = TreeMixture(num_clusters = num_clusters, num_nodes = samples.shape[1])
tm.simulate_pi(seed_val = best_seed)
tm.simulate_trees(seed_val = best_seed)
for k in range(num_clusters):
topology_list.append(tm.clusters[k].get_topology_array())
theta_list.append(tm.clusters[k].get_theta_array())
# Beginning of iterations
pi = tm.pi
loglikelihood = computationsEM(max_num_iter, samples, num_clusters, tm, topology_list, theta_list)
return loglikelihood, topology_list, theta_list
def em_algorithm(seed_val, samples, num_clusters, max_num_iter=100):
print("Running EM algorithm...")
# Set threshold for convergence
THRES = 1e-4
# Set rounds for sieving
num_sieving = 10
# Get the dimension of the data
num_samples = np.size(samples, 0)
num_nodes = np.size(samples, 1)
# Sieving
np.random.seed(seed_val)
seeds = np.random.randint(0, 100000000, num_sieving)
last_loglikelihoods = []
tms = []
for seed in seeds:
np.random.seed(seed)
tm = TreeMixture(num_clusters=num_clusters, num_nodes=num_nodes)
tm.simulate_pi(seed_val=seed)
tm.simulate_trees(seed_val=seed)
tm_loglikelihood, tm = em_helper(tm,
samples,
num_clusters,
max_num_iter=10)
last_loglikelihoods.append(tm_loglikelihood[-1])
tms.append(tm)
# Main procedure for EM algorithm
print("=> Sieving finished")
seed = seeds[last_loglikelihoods.index(max(last_loglikelihoods))]
tm = TreeMixture(num_clusters=num_clusters, num_nodes=num_nodes)
tm.simulate_pi(seed_val=seed)
tm.simulate_trees(seed_val=seed)
loglikelihood, tm = em_helper(tm,
samples,
num_clusters,
max_num_iter=max_num_iter)
print("=> EM finished")
topology_list = []
theta_list = []
for t in tm.clusters:
topology_list.append(t.get_topology_array())
theta_list.append(t.get_theta_array())
loglikelihood = np.array(loglikelihood)
topology_list = np.array(topology_list)
theta_list = np.array(theta_list)
return loglikelihood, topology_list, theta_list, tm
