We will assume one observation at node x4. The program generates samples and
then illustrates how to compute the needed kernel matrices and pre-computed
solutions to the linear systems to be solved by Kernel-BP. All matrices are
stored in separate files. In addition, a graph definition file is created, which
can be loaded by the provided line reader of our Graphlab Kernel-BP
implementation. See documentation for details.
"""
from numpy.random import randint
from src.GaussianKernel import GaussianKernel
from src.PrecomputeDenseMatrixKernelBP import PrecomputeDenseMatrixKernelBP
from src.ToyModel import ToyModel
model=ToyModel()
graph=model.get_moralised_graph()
# one observation at node 4
observations={4:0.0}
# directed edges for kernel BP implementation
edges=model.extract_edges(observations)
print "graph:", graph
print "observations:", observations
print "edges:", edges
# sample data, random number of samples for each edge
n_min=5
n_max=6
data={}
def fixed_data(self):
"""
Uses some fixed data from the ToyModel and pre-computes all matrices.
Results are asserted to be correct (against Matlab implementation) and
output files can be used to test the KernelBP implementation.
"""
model = ToyModel()
graph = model.get_moralised_graph()
# one observation at node 4
observations = {4: 0.0}
# directed edges for kernel BP implementation
edges = model.extract_edges(observations)
print "graph:", graph
print "observations:", observations
print "edges:", edges
# we sample the data jointly, so edges will share data along vertices
joint_data = {}
joint_data[1] = [-0.274722354853981, 0.044011207316815, 0.073737451640458]
joint_data[2] = [-0.173264814517908, 0.213918664844409, 0.123246012188621]
joint_data[3] = [-0.348879413536605, -0.081766464397055, -0.117171083361484]
joint_data[4] = [-0.014012058355118, -0.145789276405117, -0.317649695308685]
joint_data[5] = [-0.291794859908481, 0.260902212951398, -0.276258182225143]
# generate data in format that works for the dense matrix class, i.e., a pair of
# points for every edge
data = {}
for edge in edges:
# only sample once per undirected edge
inverse_edge = (edge[1], edge[0])
data[edge] = (joint_data[edge[0]], joint_data[edge[1]])
data[inverse_edge] = (joint_data[edge[1]], joint_data[edge[0]])
# Gaussian kernel used in matlab files
kernel = GaussianKernel(sigma=sqrt(0.15))
# use the example class for dense matrix data that can be stored in memory
precomputer = PrecomputeDenseMatrixKernelBP(
graph, edges, data, observations, kernel, reg_lambda=0.1, output_filename=self.output_filename
)
precomputer.precompute()
# go through all the files and make sure they contain the correct matrices
# files created by matlab implementation
filenames = [
"1->2->3_non_obs_kernel.txt",
"1->2->4_non_obs_kernel.txt",
"1->3->2_non_obs_kernel.txt",
"1->3->4_non_obs_kernel.txt",
"1->3->5_non_obs_kernel.txt",
"2->1->3_non_obs_kernel.txt",
"2->3->1_non_obs_kernel.txt",
"2->3->4_non_obs_kernel.txt",
"2->3->5_non_obs_kernel.txt",
"2->4->3_non_obs_kernel.txt",
"3->1->2_non_obs_kernel.txt",
"3->2->1_non_obs_kernel.txt",
"3->2->4_non_obs_kernel.txt",
"3->4->2_non_obs_kernel.txt",
"4->2->1_non_obs_kernel.txt",
"4->2->3_non_obs_kernel.txt",
"4->3->1_non_obs_kernel.txt",
"4->3->2_non_obs_kernel.txt",
"4->3->5_non_obs_kernel.txt",
"5->3->1_non_obs_kernel.txt",
"5->3->2_non_obs_kernel.txt",
"5->3->4_non_obs_kernel.txt",
"3->4_obs_kernel.txt",
"2->4_obs_kernel.txt",
"1->2_L_s.txt",
"1->3_L_s.txt",
"2->1_L_s.txt",
"2->3_L_s.txt",
"2->4_L_s.txt",
"2->4_L_t.txt",
"3->1_L_s.txt",
"3->2_L_s.txt",
"3->4_L_s.txt",
"3->4_L_t.txt",
"3->5_L_s.txt",
"5->3_L_s.txt",
]
# from matlab implementation
matrices = {
"2->1->3_non_obs_kernel.txt": asarray(
[[1.000000, 0.712741, 0.667145], [0.712741, 1.000000, 0.997059], [0.667145, 0.997059, 1.000000]]
),
"3->1->2_non_obs_kernel.txt": asarray(
[[1.000000, 0.712741, 0.667145], [0.712741, 1.000000, 0.997059], [0.667145, 0.997059, 1.000000]]
),
"1->2->3_non_obs_kernel.txt": asarray(
[[1.000000, 0.606711, 0.745976], [0.606711, 1.000000, 0.972967], [0.745976, 0.972967, 1.000000]]
),
"1->2->4_non_obs_kernel.txt": asarray(
[[1.000000, 0.606711, 0.745976], [0.606711, 1.000000, 0.972967], [0.745976, 0.972967, 1.000000]]
),
"3->2->1_non_obs_kernel.txt": asarray(
[[1.000000, 0.606711, 0.745976], [0.606711, 1.000000, 0.972967], [0.745976, 0.972967, 1.000000]]
),
"3->2->4_non_obs_kernel.txt": asarray(
[[1.000000, 0.606711, 0.745976], [0.606711, 1.000000, 0.972967], [0.745976, 0.972967, 1.000000]]
),
"4->2->1_non_obs_kernel.txt": asarray(
[[1.000000, 0.606711, 0.745976], [0.606711, 1.000000, 0.972967], [0.745976, 0.972967, 1.000000]]
),
"4->2->3_non_obs_kernel.txt": asarray(
[[1.000000, 0.606711, 0.745976], [0.606711, 1.000000, 0.972967], [0.745976, 0.972967, 1.000000]]
),
"1->3->2_non_obs_kernel.txt": asarray(
[[1.000000, 0.788336, 0.836137], [0.788336, 1.000000, 0.995830], [0.836137, 0.995830, 1.000000]]
),
"1->3->4_non_obs_kernel.txt": asarray(
[[1.000000, 0.788336, 0.836137], [0.788336, 1.000000, 0.995830], [0.836137, 0.995830, 1.000000]]
),
"1->3->5_non_obs_kernel.txt": asarray(
[[1.000000, 0.788336, 0.836137], [0.788336, 1.000000, 0.995830], [0.836137, 0.995830, 1.000000]]
),
"2->3->1_non_obs_kernel.txt": asarray(
[[1.000000, 0.788336, 0.836137], [0.788336, 1.000000, 0.995830], [0.836137, 0.995830, 1.000000]]
),
"2->3->4_non_obs_kernel.txt": asarray(
[[1.000000, 0.788336, 0.836137], [0.788336, 1.000000, 0.995830], [0.836137, 0.995830, 1.000000]]
),
"2->3->5_non_obs_kernel.txt": asarray(
[[1.000000, 0.788336, 0.836137], [0.788336, 1.000000, 0.995830], [0.836137, 0.995830, 1.000000]]
),
"4->3->1_non_obs_kernel.txt": asarray(
[[1.000000, 0.788336, 0.836137], [0.788336, 1.000000, 0.995830], [0.836137, 0.995830, 1.000000]]
),
"4->3->2_non_obs_kernel.txt": asarray(
[[1.000000, 0.788336, 0.836137], [0.788336, 1.000000, 0.995830], [0.836137, 0.995830, 1.000000]]
),
"4->3->5_non_obs_kernel.txt": asarray(
[[1.000000, 0.788336, 0.836137], [0.788336, 1.000000, 0.995830], [0.836137, 0.995830, 1.000000]]
),
"5->3->1_non_obs_kernel.txt": asarray(
[[1.000000, 0.788336, 0.836137], [0.788336, 1.000000, 0.995830], [0.836137, 0.995830, 1.000000]]
),
"5->3->2_non_obs_kernel.txt": asarray(
[[1.000000, 0.788336, 0.836137], [0.788336, 1.000000, 0.995830], [0.836137, 0.995830, 1.000000]]
),
"5->3->4_non_obs_kernel.txt": asarray(
[[1.000000, 0.788336, 0.836137], [0.788336, 1.000000, 0.995830], [0.836137, 0.995830, 1.000000]]
),
"2->4->3_non_obs_kernel.txt": asarray(
[[1.000000, 0.943759, 0.735416], [0.943759, 1.000000, 0.906238], [0.735416, 0.906238, 1.000000]]
),
"3->4->2_non_obs_kernel.txt": asarray(
[[1.000000, 0.943759, 0.735416], [0.943759, 1.000000, 0.906238], [0.735416, 0.906238, 1.000000]]
),
"2->4_obs_kernel.txt": asarray([[0.999346], [0.931603], [0.714382]]),
"2->4_L_s.txt": asarray(
[[1.048809, 0.000000, 0.000000], [0.578476, 0.874852, 0.000000], [0.711260, 0.641846, 0.426782]]
),
"2->4_L_t.txt": asarray(
[[1.048809, 0.000000, 0.000000], [0.899839, 0.538785, 0.000000], [0.701191, 0.510924, 0.589311]]
),
"3->4_obs_kernel.txt": asarray([[0.999346], [0.931603], [0.714382]]),
"3->4_L_s.txt": asarray(
[[1.048809, 0.000000, 0.000000], [0.751649, 0.731453, 0.000000], [0.797226, 0.542204, 0.412852]]
),
"3->4_L_t.txt": asarray(
[[1.048809, 0.000000, 0.000000], [0.899839, 0.538785, 0.000000], [0.701191, 0.510924, 0.589311]]
),
"2->1_L_s.txt": asarray(
[[1.048809, 0.000000, 0.000000], [0.578476, 0.874852, 0.000000], [0.711260, 0.641846, 0.426782]]
),
"3->1_L_s.txt": asarray(
[[1.048809, 0.000000, 0.000000], [0.751649, 0.731453, 0.000000], [0.797226, 0.542204, 0.412852]]
),
"1->2_L_s.txt": asarray(
[[1.048809, 0.000000, 0.000000], [0.679572, 0.798863, 0.000000], [0.636098, 0.706985, 0.442211]]
),
"3->2_L_s.txt": asarray(
[[1.048809, 0.000000, 0.000000], [0.751649, 0.731453, 0.000000], [0.797226, 0.542204, 0.412852]]
),
"1->3_L_s.txt": asarray(
[[1.048809, 0.000000, 0.000000], [0.679572, 0.798863, 0.000000], [0.636098, 0.706985, 0.442211]]
),
"2->3_L_s.txt": asarray(
[[1.048809, 0.000000, 0.000000], [0.578476, 0.874852, 0.000000], [0.711260, 0.641846, 0.426782]]
),
"5->3_L_s.txt": asarray(
[[1.048809, 0.000000, 0.000000], [0.344417, 0.990645, 0.000000], [0.952696, 0.054589, 0.435191]]
),
"3->5_L_s.txt": asarray(
[[1.048809, 0.000000, 0.000000], [0.751649, 0.731453, 0.000000], [0.797226, 0.542204, 0.412852]]
),
}
assert len(filenames) == len(matrices)
for filename in filenames:
self.assertTrue(self.assert_file_matrix(self.output_folder + filename, matrices[filename]))
