table 4.3 JC69ΒΆ
Although incomplete ambiguity of observations is not supported, it is possible to emulate these types of observations using an expanded multivariate state space.
In this example, we expand a univariate 4-state nucleotide process to a \(2 \times 2 \times 2 \times 2\) multivariate process. The edge rate scaling factors are estimated using expectation maximization to find the log likelihood of -6,262.01 reported in Ziheng Yang’s 2014 textbook.
The output includes the results of 8 iterations of EM.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 | from __future__ import print_function, division, absolute_import
import copy
import json
import pyparsing
import numpy as np
from numpy.testing import assert_equal
import jsonctmctree.interface
s_tree = """(kiwi_fruit, ((((agave, garlic), rice), black_pepper),
((cabbage, cotton), (cucumber, walnut))), (sunflower, (tomato, tobacco)))"""
def _help_build_tree(parent, root, node, name_to_node, edges):
if parent is not None:
edges.append((parent, node))
neo = node + 1
if isinstance(root, basestring):
name_to_node[root] = node
else:
for element in root:
neo = _help_build_tree(node, element, neo, name_to_node, edges)
return neo
def get_tree_info():
# Return a dictionary mapping name to node index,
# and return a list of edges as ordered pairs of node indices.
tree = s_tree.replace(',', ' ')
nestedItems = pyparsing.nestedExpr(opener='(', closer=')')
tree = (nestedItems + pyparsing.stringEnd).parseString(tree).asList()[0]
name_to_node = {}
edges = []
_help_build_tree(None, tree, 0, name_to_node, edges)
return name_to_node, edges
def get_nucleotide_alignment_info(name_to_node):
# Return an ordered list of observable node indices,
# and return the array of iid observations.
# An observed state of -1 means completely missing data.
nt_to_state = {
'A' : [1, 0, 0, 0],
'C' : [0, 1, 0, 0],
'G' : [0, 0, 1, 0],
'T' : [0, 0, 0, 1],
'?' : [-1, -1, -1, -1],
'-' : [-1, -1, -1, -1],
'N' : [-1, -1, -1, -1],
'M' : [-1, -1, 0, 0],
'R' : [-1, 0, -1, 0],
'W' : [-1, 0, 0, -1],
'S' : [0, -1, -1, 0],
'Y' : [0, -1, 0, -1],
'K' : [0, 0, -1, -1],
}
sequences = []
nodes = []
variables = []
with open('vegetables.rbcL.txt') as fin:
lines = fin.readlines()
header = lines[0]
for line in lines[1:]:
name, sequence = line.strip().split()
node = name_to_node[name]
nodes.extend([node]*4)
sequences.append([nt_to_state[c] for c in sequence])
variables.extend([0, 1, 2, 3])
# arr[node, site, variable]
arr = np.array(sequences, dtype=int)
arr = np.transpose(arr, (1, 0, 2))
iid_observations = np.reshape(arr, (arr.shape[0], -1))
iid_observations = iid_observations.tolist()
return nodes, variables, iid_observations
def main():
# Read the tree.
name_to_node, edges = get_tree_info()
edge_count = len(edges)
node_count = edge_count + 1
# Read the alignment.
info = get_nucleotide_alignment_info(name_to_node)
nodes, variables, iid_observations = info
# Define the tree component of the scene
row_nodes, column_nodes = zip(*edges)
tree = dict(
row_nodes = list(row_nodes),
column_nodes = list(column_nodes),
edge_rate_scaling_factors = [0.01] * edge_count,
edge_processes = [0] * edge_count)
# Define the Jukes-Cantor process.
# Rates are scaled so that the exit rate is 1 from every state.
row_states = []
column_states = []
rates = []
ident = np.identity(4, dtype=int).tolist()
for i in range(4):
for j in range(4):
if i != j:
row_states.append(ident[i])
column_states.append(ident[j])
rates.append(1/3)
process_definition = dict(
row_states = row_states,
column_states = column_states,
transition_rates = rates)
# Define the root distribution.
root_prior = dict(
states = ident,
probabilities = [0.25, 0.25, 0.25, 0.25])
# Define the observed data.
observed_data = dict(
nodes = nodes,
variables = variables,
iid_observations = iid_observations)
# Assemble the scene.
scene = dict(
node_count = node_count,
process_count = 1,
state_space_shape = [2, 2, 2, 2],
tree = tree,
root_prior = root_prior,
process_definitions = [process_definition],
observed_data = observed_data)
# Define some requests.
# These include the log likelihood
# and the sum of transition count expectations.
requests = [
{"property" : "SNNLOGL"},
{
"property" : "SDNTRAN",
"transition_reduction" : {
"row_states" : row_states,
"column_states" : column_states,
"weights" : [1] * len(row_states)
}
}]
# Request some stuff.
j_in = {
"scene" : scene,
"requests" : requests
}
arr = []
j_out = None
nsites = len(iid_observations)
for i in range(8):
if j_out is None:
j_out = jsonctmctree.interface.process_json_in(j_in)
else:
ll, trans_counts = j_out['responses']
edge_rates = [t/nsites for t in trans_counts]
j_in['scene']['tree']['edge_rate_scaling_factors'] = edge_rates
j_out = jsonctmctree.interface.process_json_in(j_in)
arr.append(copy.deepcopy(j_out))
print(json.dumps(arr, indent=4))
main()
|
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{
"status": "feasible",
"responses": [
-6749.528980298121,
[
38.54275388560657,
12.037458550453508,
40.25804994338261,
38.6294765231242,
30.956776009282507,
37.905224291636515,
27.076723254699374,
98.91403030760839,
72.57833339446896,
10.915565332307388,
19.818530425852366,
75.4194698042263,
45.878226215070306,
18.55467221991212,
50.8147692090247,
34.95460442071937,
19.535805753716325,
64.19946564149734,
57.14875533831474,
12.279596433719373,
6.273710329493812
]
]
},
{
"status": "feasible",
"responses": [
-6269.538919189791,
[
42.36745935386131,
8.343051121349692,
39.80229475456449,
33.82736183847302,
25.38361434935728,
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68.51605179424939,
59.457459696833936,
12.732578296702457,
5.408973242355975
]
]
},
{
"status": "feasible",
"responses": [
-6262.648537452265,
[
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7.377407685404555,
39.452290914705884,
31.803358090339447,
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69.29635966845777,
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12.872426981591603,
5.266804842862319
]
]
},
{
"status": "feasible",
"responses": [
-6262.0766288079885,
[
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69.47714143694492,
59.88886885322965,
12.897759415300118,
5.242207596873577
]
]
},
{
"status": "feasible",
"responses": [
-6262.021218360713,
[
43.4666592227035,
7.007028544921212,
39.43300881628473,
30.973573921125244,
21.882814323238073,
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69.51751060338685,
59.91492303942013,
12.901981436535692,
5.238133741051998
]
]
},
{
"status": "feasible",
"responses": [
-6262.015269165555,
[
43.46765103953117,
6.975135058680808,
39.446628514616236,
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69.52528735443195,
59.9212734954846,
12.902794402731823,
5.237339200662891
]
]
},
{
"status": "feasible",
"responses": [
-6262.014562740338,
[
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6.962854386714466,
39.45297358636966,
30.908049315202256,
21.729304846744984,
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5.2370679723310225
]
]
},
{
"status": "feasible",
"responses": [
-6262.0144698716895,
[
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]
]
}
]
|