def objective_and_gradient(scene, X):
delta = 1e-8
distn, kappa, tau, rates = unpack(X)
scene['tree']['edge_rate_scaling_factors'] = rates.tolist()
log_likelihood_request = {'property' : 'snnlogl'}
derivatives_request = {'property' : 'sdnderi'}
# Get the log likelihood and per-edge derivatives.
# Note that the edge derivatives are of the log likelihood
# with respect to logs of edge rates, and we will eventually
# multiply them by -1 to get the gradient of the cost function
# which we want to minimize rather than the log likelihood function
# which we want to maximize.
process_defn, root_prior = get_process_defn_and_prior(distn, kappa, tau)
scene['root_prior'] = root_prior
scene['process_definitions'] = [process_defn]
j_in = {
'scene' : scene,
'requests' : [log_likelihood_request, derivatives_request]
}
j_out = jsonctmctree.interface.process_json_in(j_in)
log_likelihood, edge_gradient = j_out['responses']
cost = -log_likelihood
# For each non-edge-specific parameter get finite-differences
# approximation of the gradient.
nedges = len(scene['tree']['row_nodes'])
nparams = len(X) - nedges
gradient = []
for i in range(nparams):
W = np.copy(X)
W[i] += delta
distn, kappa, tau, rates = unpack(W)
process_defn, root_prior = get_process_defn_and_prior(distn, kappa, tau)
scene['root_prior'] = root_prior
scene['process_definitions'] = [process_defn]
j_in = {
'scene' : scene,
'requests' : [log_likelihood_request]
}
j_out = jsonctmctree.interface.process_json_in(j_in)
ll = j_out['responses'][0]
c = -ll
slope = (c - cost) / delta
gradient.append(slope)
gradient.extend([-x for x in edge_gradient])
gradient = np.array(gradient)
# Return cost and gradient.
return cost, gradient
def objective(scene, X):
distn, kappa, tau, rates = unpack(X)
scene['root_prior']['probabilities'] = distn.tolist()
scene['tree']['edge_rate_scaling_factors'] = rates.tolist()
triples = list(gen_transitions(distn, kappa, tau))
rows, cols, transition_rates = zip(*triples)
process_definition = {
'row_states' : [list(x) for x in rows],
'column_states' : [list(x) for x in cols],
'transition_rates' : list(transition_rates)
}
scene['process_definitions'] = [process_definition]
request = {'property' : 'snnlogl'}
j_in = {'scene' : scene, 'requests' : [request]}
j_out = jsonctmctree.interface.process_json_in(j_in)
log_likelihood = j_out['responses'][0]
cost = -log_likelihood
return cost
def main():
name_to_node = {
'tamarin' : 0,
'macaque' : 1,
'orangutan' : 2,
'chimpanzee' : 3,
'gorilla' : 4}
paralog_to_variable = {
'ecp' : 0,
'edn' : 1}
nodes = []
variables = []
rows = []
with open('paralogs.fasta') as fin:
while True:
line = fin.readline().strip().lower()
if not line:
break
name = line[1:-3]
paralog = line[-3:]
seq = fin.readline().strip()
row = ['ACGT'.index(x) for x in seq]
nodes.append(name_to_node[name])
variables.append(paralog_to_variable[paralog])
rows.append(row)
columns = [list(x) for x in zip(*rows)]
distn = [0.25, 0.25, 0.25, 0.25]
rates = [1, 1, 1, 1, 1, 1, 1, 1]
kappa = 2.0
tau = 3.0
process_defn, root_prior = get_process_defn_and_prior(distn, kappa, tau)
scene = {
"node_count" : 9,
"process_count" : 1,
"state_space_shape" : [4, 4],
"tree" : {
"row_nodes" : [5, 5, 6, 6, 7, 7, 8, 8],
"column_nodes" : [0, 6, 1, 7, 2, 8, 3, 4],
"edge_rate_scaling_factors" : rates,
"edge_processes" : [0, 0, 0, 0, 0, 0, 0, 0]
},
"root_prior" : root_prior,
"process_definition" : process_defn,
"observed_data" : {
"nodes" : nodes,
"variables" : variables,
"iid_observations" : columns
}
}
X = pack(distn, kappa, tau, rates)
f = functools.partial(objective_and_gradient, scene)
result = minimize(f, X, jac=True, method='L-BFGS-B')
print('final value of objective function:', result.fun)
distn, kappa, tau, rates = unpack(result.x)
print('nucleotide distribution:')
for nt, p in zip('ACGT', distn):
print(' ', nt, ':', p)
print('kappa:', kappa)
print('tau:', tau)
print('edge rate scaling factors:')
for r in rates:
print(' ', r)
def main():
name_to_node = {
'tamarin' : 0,
'macaque' : 1,
'orangutan' : 2,
'chimpanzee' : 3,
'gorilla' : 4}
paralog_to_variable = {
'ecp' : 0,
'edn' : 1}
nodes = []
variables = []
rows = []
with open('paralogs.fasta') as fin:
while True:
line = fin.readline().strip().lower()
if not line:
break
name = line[1:-3]
paralog = line[-3:]
seq = fin.readline().strip()
row = ['ACGT'.index(x) for x in seq]
nodes.append(name_to_node[name])
variables.append(paralog_to_variable[paralog])
rows.append(row)
columns = [list(x) for x in zip(*rows)]
print('number of sites in the alignment:', len(columns))
print('number of sequences:', len(nodes))
# Compute the empirical distribution of the nucleotides.
counts = np.zeros(4)
for k in np.ravel(columns):
counts[k] += 1
empirical_pi = counts / counts.sum()
distn = empirical_pi
rates = [1, 1, 1, 1, 1, 1, 1, 1]
scene = {
"node_count" : 9,
"process_count" : 1,
"state_space_shape" : [4, 4],
"tree" : {
"row_nodes" : [5, 5, 6, 6, 7, 7, 8, 8],
"column_nodes" : [0, 6, 1, 7, 2, 8, 3, 4],
"edge_rate_scaling_factors" : rates,
"edge_processes" : [0, 0, 0, 0, 0, 0, 0, 0]
},
"root_prior" : {
"states" : [[0, 0], [1, 1], [2, 2], [3, 3]],
"probabilities" : distn
},
"observed_data" : {
"nodes" : nodes,
"variables" : variables,
"iid_observations" : columns
}
}
X = pack(distn, 2.0, 3.0, rates)
f = functools.partial(objective, scene)
result = minimize(f, X, method='L-BFGS-B')
print('final value of objective function:', result.fun)
distn, kappa, tau, rates = unpack(result.x)
print('nucleotide distribution:')
for nt, p in zip('ACGT', distn):
print(' ', nt, ':', p)
print('kappa:', kappa)
print('tau:', tau)
print('edge rate scaling factors:')
for r in rates:
print(' ', r)
def custom_unpack(rate_expansion, X):
distn, kappa, tau, rates = unpack(X)
return distn, kappa, tau, hardcoded_rate_expand(rate_expansion, rates)
