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#! /usr/bin/env python
# Last Change: Wed Dec 06 09:00 PM 2006 J
import copy
import sys
from numpy.testing import *
import numpy as N
from numpy.random import seed
set_package_path()
from pyem import GM, GMM
from pyem.online_em import OnGMM, OnGMM1d
restore_path()
# #Optional:
# set_local_path()
# # import modules that are located in the same directory as this file.
# restore_path()
# Error precision allowed (nb of decimals)
AR_AS_PREC = 12
KM_ITER = 5
class OnlineEmTest(NumpyTestCase):
def _create_model(self, d, k, mode, nframes, emiter):
#+++++++++++++++++++++++++++++++++++++++++++++++++
# Generate a model with k components, d dimensions
#+++++++++++++++++++++++++++++++++++++++++++++++++
w, mu, va = GM.gen_param(d, k, mode, spread = 1.5)
gm = GM.fromvalues(w, mu, va)
# Sample nframes frames from the model
data = gm.sample(nframes)
#++++++++++++++++++++++++++++++++++++++++++
# Approximate the models with classical EM
#++++++++++++++++++++++++++++++++++++++++++
# Init the model
lgm = GM(d, k, mode)
gmm = GMM(lgm, 'kmean')
gmm.init(data, niter = KM_ITER)
self.gm0 = copy.copy(gmm.gm)
# The actual EM, with likelihood computation
for i in range(emiter):
g, tgd = gmm.sufficient_statistics(data)
gmm.update_em(data, g)
self.data = data
self.gm = lgm
class test_on_off_eq(OnlineEmTest):
def check_1d(self, level = 1):
d = 1
k = 2
mode = 'diag'
nframes = int(1e2)
emiter = 3
seed(1)
self._create_model(d, k, mode, nframes, emiter)
self._check(d, k, mode, nframes, emiter)
def check_2d(self, level = 1):
d = 2
k = 2
mode = 'diag'
nframes = int(1e2)
emiter = 3
seed(1)
self._create_model(d, k, mode, nframes, emiter)
self._check(d, k, mode, nframes, emiter)
def check_5d(self, level = 5):
d = 5
k = 2
mode = 'diag'
nframes = int(1e2)
emiter = 3
seed(1)
self._create_model(d, k, mode, nframes, emiter)
self._check(d, k, mode, nframes, emiter)
def _check(self, d, k, mode, nframes, emiter):
#++++++++++++++++++++++++++++++++++++++++
# Approximate the models with online EM
#++++++++++++++++++++++++++++++++++++++++
# Learn the model with Online EM
ogm = GM(d, k, mode)
ogmm = OnGMM(ogm, 'kmean')
init_data = self.data
ogmm.init(init_data, niter = KM_ITER)
# Check that online kmean init is the same than kmean offline init
ogm0 = copy.copy(ogm)
assert_array_equal(ogm0.w, self.gm0.w)
assert_array_equal(ogm0.mu, self.gm0.mu)
assert_array_equal(ogm0.va, self.gm0.va)
# Forgetting param
lamb = N.ones((nframes, 1))
lamb[0] = 0
nu0 = 1.0
nu = N.zeros((len(lamb), 1))
nu[0] = nu0
for i in range(1, len(lamb)):
nu[i] = 1./(1 + lamb[i] / nu[i-1])
# object version of online EM: the p* arguments are updated only at each
# epoch, which is equivalent to on full EM iteration on the
# classic EM algorithm
ogmm.pw = ogmm.cw.copy()
ogmm.pmu = ogmm.cmu.copy()
ogmm.pva = ogmm.cva.copy()
for e in range(emiter):
for t in range(nframes):
ogmm.compute_sufficient_statistics_frame(self.data[t], nu[t])
ogmm.update_em_frame()
# Change pw args only a each epoch
ogmm.pw = ogmm.cw.copy()
ogmm.pmu = ogmm.cmu.copy()
ogmm.pva = ogmm.cva.copy()
# For equivalence between off and on, we allow a margin of error,
# because of round-off errors.
print " Checking precision of equivalence with offline EM trainer "
maxtestprec = 18
try :
for i in range(maxtestprec):
assert_array_almost_equal(self.gm.w, ogmm.pw, decimal = i)
assert_array_almost_equal(self.gm.mu, ogmm.pmu, decimal = i)
assert_array_almost_equal(self.gm.va, ogmm.pva, decimal = i)
print "\t !! Precision up to %d decimals !! " % i
except AssertionError:
if i < AR_AS_PREC:
print """\t !!NOT OK: Precision up to %d decimals only,
outside the allowed range (%d) !! """ % (i, AR_AS_PREC)
raise AssertionError
else:
print "\t !!OK: Precision up to %d decimals !! " % i
class test_on(OnlineEmTest):
def check_consistency(self):
d = 1
k = 2
mode = 'diag'
nframes = int(5e2)
emiter = 4
self._create_model(d, k, mode, nframes, emiter)
self._run_pure_online(d, k, mode, nframes)
def check_1d_imp(self):
d = 1
k = 2
mode = 'diag'
nframes = int(5e2)
emiter = 4
self._create_model(d, k, mode, nframes, emiter)
gmref = self._run_pure_online(d, k, mode, nframes)
gmtest = self._run_pure_online_1d(d, k, mode, nframes)
assert_array_almost_equal(gmref.w, gmtest.w, AR_AS_PREC)
assert_array_almost_equal(gmref.mu, gmtest.mu, AR_AS_PREC)
assert_array_almost_equal(gmref.va, gmtest.va, AR_AS_PREC)
def _run_pure_online_1d(self, d, k, mode, nframes):
#++++++++++++++++++++++++++++++++++++++++
# Approximate the models with online EM
#++++++++++++++++++++++++++++++++++++++++
ogm = GM(d, k, mode)
ogmm = OnGMM1d(ogm, 'kmean')
init_data = self.data[0:nframes / 20, :]
ogmm.init(init_data[:, 0])
# Forgetting param
ku = 0.005
t0 = 200
lamb = 1 - 1/(N.arange(-1, nframes-1) * ku + t0)
nu0 = 0.2
nu = N.zeros((len(lamb), 1))
nu[0] = nu0
for i in range(1, len(lamb)):
nu[i] = 1./(1 + lamb[i] / nu[i-1])
# object version of online EM
for t in range(nframes):
# the assert are here to check we do not create copies
# unvoluntary for parameters
a, b, c = ogmm.compute_sufficient_statistics_frame(self.data[t, 0], nu[t])
ogmm.update_em_frame(a, b, c)
ogmm.gm.set_param(ogmm.cw, ogmm.cmu[:, N.newaxis], ogmm.cva[:, N.newaxis])
return ogmm.gm
def _run_pure_online(self, d, k, mode, nframes):
#++++++++++++++++++++++++++++++++++++++++
# Approximate the models with online EM
#++++++++++++++++++++++++++++++++++++++++
ogm = GM(d, k, mode)
ogmm = OnGMM(ogm, 'kmean')
init_data = self.data[0:nframes / 20, :]
ogmm.init(init_data)
# Forgetting param
ku = 0.005
t0 = 200
lamb = 1 - 1/(N.arange(-1, nframes-1) * ku + t0)
nu0 = 0.2
nu = N.zeros((len(lamb), 1))
nu[0] = nu0
for i in range(1, len(lamb)):
nu[i] = 1./(1 + lamb[i] / nu[i-1])
# object version of online EM
for t in range(nframes):
# the assert are here to check we do not create copies
# unvoluntary for parameters
assert ogmm.pw is ogmm.cw
assert ogmm.pmu is ogmm.cmu
assert ogmm.pva is ogmm.cva
ogmm.compute_sufficient_statistics_frame(self.data[t], nu[t])
ogmm.update_em_frame()
ogmm.gm.set_param(ogmm.cw, ogmm.cmu, ogmm.cva)
return ogmm.gm
if __name__ == "__main__":
NumpyTest().run()
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