def _do_mstep(self, stats, params):
posteriors = np.vstack(stats['posteriors'])
obs = np.vstack(stats['obs'])
if 't' in params:
if self.reversible_type == 'mle':
counts = np.maximum(
stats['trans'] + self.transmat_prior - 1.0, 1e-20).astype(np.float64)
self.transmat_, self.populations_ = _reversibility.reversible_transmat(counts)
elif self.reversible_type == 'transpose':
revcounts = np.maximum(
self.transmat_prior - 1.0 + stats['trans'] + stats['trans'].T, 1e-20)
populations = np.sum(revcounts, axis=0)
self.populations_ = populations / np.sum(populations)
self.transmat_ = revcounts / np.sum(revcounts, axis=1)[:, np.newaxis]
else:
raise ValueError('Invalid value for reversible_type: %s '
'Must be either "mle" or "transpose"'
% self.reversible_type)
self.startprob_ = self.populations_
if 'm' in params:
self._fitmeans(posteriors, obs, out=self._means_)
if 'k' in params:
self._fitkappas(posteriors, obs, self._means_)
def _do_mstep(self, stats, params):
posteriors = np.vstack(stats['posteriors'])
obs = np.vstack(stats['obs'])
if 't' in params:
if self.reversible_type == 'mle':
counts = np.maximum(stats['trans'] + self.transmat_prior - 1.0,
1e-20).astype(np.float64)
self.transmat_, self.populations_ = _reversibility.reversible_transmat(
counts)
elif self.reversible_type == 'transpose':
revcounts = np.maximum(
self.transmat_prior - 1.0 + stats['trans'] +
stats['trans'].T, 1e-20)
populations = np.sum(revcounts, axis=0)
self.populations_ = populations / np.sum(populations)
self.transmat_ = revcounts / np.sum(revcounts,
axis=1)[:, np.newaxis]
else:
raise ValueError('Invalid value for reversible_type: %s '
'Must be either "mle" or "transpose"' %
self.reversible_type)
self.startprob_ = self.populations_
if 'm' in params:
self._fitmeans(posteriors, obs, out=self._means_)
if 'k' in params:
self._fitkappas(posteriors, obs, self._means_)
def test_reversible_mle():
import scipy.sparse.linalg
C = 1.0 * np.array([[6, 3, 7], [4, 6, 9], [2, 6, 7]])
# generated with msmbuilder
result = np.array([[0.37499995, 0.2370208, 0.38797925],
[0.16882446, 0.31578918, 0.51538636],
[0.18615565, 0.34717763, 0.46666672]])
T, pi = _reversibility.reversible_transmat(C)
np.testing.assert_array_almost_equal(T, result)
u, v = scipy.sparse.linalg.eigs(T.T, k=1)
np.testing.assert_array_almost_equal(np.real(v / v.sum()).flatten(), pi)
def test_reversible_mle():
import scipy.sparse.linalg
C = 1.0*np.array([[6, 3, 7], [4, 6, 9], [2, 6, 7]])
# generated with msmbuilder
result = np.array([[ 0.37499995, 0.2370208, 0.38797925],
[ 0.16882446, 0.31578918, 0.51538636],
[ 0.18615565, 0.34717763, 0.46666672]])
T, pi = _reversibility.reversible_transmat(C)
np.testing.assert_array_almost_equal(T, result)
u, v = scipy.sparse.linalg.eigs(T.T, k=1)
np.testing.assert_array_almost_equal(np.real(v / v.sum()).flatten(), pi)
def _do_mstep(self, stats, params):
if 't' in params:
if self.reversible_type == 'mle':
counts = np.maximum(
stats['trans'] + self.transmat_prior - 1.0, 1e-20).astype(np.float64)
self.transmat_, self.populations_ = _reversibility.reversible_transmat(
counts)
elif self.reversible_type == 'transpose':
revcounts = np.maximum(
self.transmat_prior - 1.0 + stats['trans'] + stats['trans'].T, 1e-20)
populations = np.sum(revcounts, axis=0)
self.populations_ = populations / np.sum(populations)
self.transmat_ = revcounts / np.sum(revcounts, axis=1)[:, np.newaxis]
else:
raise ValueError('Invalid value for reversible_type: %s '
'Must be either "mle" or "transpose"'
% self.reversible_type)
difference_cutoff = 1e-10
# we don't want denom to be zero, because then the new value of the means
# will be nan/inf. so padd it up by a very small constant. This particular
# padding is following the sklearn mixture model m_step code from
# https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/mixture/gmm.py#L496
denom = (stats['post'][:, np.newaxis] + 10 * EPS)
def getdiff(means):
diff = np.zeros((self.n_features, self.n_states, self.n_states))
for i in range(self.n_features):
diff[i] = np.maximum(
np.abs(np.subtract.outer(means[:, i], means[:, i])), difference_cutoff)
return diff
if 'm' in params:
means = stats['obs'] / denom # unregularized means
if self.fusion_prior > 0 and self.n_lqa_iter > 0:
# adaptive regularization strength
strength = self.fusion_prior / getdiff(means)
rhs = stats['obs'] / self.vars_
for i in range(self.n_features):
np.fill_diagonal(strength[i], 0)
break_lqa = False
for s in range(self.n_lqa_iter):
diff = getdiff(means)
if np.all(diff <= difference_cutoff) or break_lqa:
break
offdiagonal = -strength / diff
diagonal_penalty = np.sum(strength / diff, axis=2)
for f in range(self.n_features):
if np.all(diff[f] <= difference_cutoff):
continue
ridge_approximation = np.diag(
stats['post'] / self.vars_[:, f] + diagonal_penalty[f]) + offdiagonal[f]
try:
means[:, f] = np.linalg.solve(ridge_approximation, rhs[:, f])
except np.linalg.LinAlgError:
# I'm not really sure what exactly causes the ridge
# approximation to be non-solvable, but it probably
# means we're too close to the merging. Maybe 1e-10
# is cutting it too close. ANyways, just break now and
# use the last valid value of the means.
break_lqa = True
for i in range(self.n_features):
for k, j in zip(*np.triu_indices(self.n_states)):
if diff[i, k, j] <= difference_cutoff:
means[k, i] = means[j, i]
self.means_ = means
if 'v' in params:
vars_prior = self.vars_prior
vars_weight = self.vars_weight
if vars_prior is None:
vars_weight = 0
vars_prior = 0
var_num = (stats['obs**2']
- 2 * self.means_ * stats['obs']
+ self.means_ ** 2 * denom)
var_denom = max(vars_weight - 1, 0) + denom
self.vars_ = (vars_prior + var_num) / var_denom
def _transmat_update(self, stats):
counts = np.maximum(stats['trans'] + self.transmat_prior - 1.0,
1e-20).astype(np.float64)
self.transmat_, self.populations_ = _reversibility.reversible_transmat(
counts)
def _do_mstep(self, stats, params):
if 't' in params:
if self.reversible_type == 'mle':
counts = np.maximum(stats['trans'] + self.transmat_prior - 1.0,
1e-20).astype(np.float64)
self.transmat_, self.populations_ = _reversibility.reversible_transmat(
counts)
elif self.reversible_type == 'transpose':
revcounts = np.maximum(
self.transmat_prior - 1.0 + stats['trans'] +
stats['trans'].T, 1e-20)
populations = np.sum(revcounts, axis=0)
self.populations_ = populations / np.sum(populations)
self.transmat_ = revcounts / np.sum(revcounts,
axis=1)[:, np.newaxis]
else:
raise ValueError('Invalid value for reversible_type: %s '
'Must be either "mle" or "transpose"' %
self.reversible_type)
difference_cutoff = 1e-10
# we don't want denom to be zero, because then the new value of the means
# will be nan/inf. so padd it up by a very small constant. This particular
# padding is following the sklearn mixture model m_step code from
# https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/mixture/gmm.py#L496
denom = (stats['post'][:, np.newaxis] + 10 * EPS)
def getdiff(means):
diff = np.zeros((self.n_features, self.n_states, self.n_states))
for i in range(self.n_features):
diff[i] = np.maximum(
np.abs(np.subtract.outer(means[:, i], means[:, i])),
difference_cutoff)
return diff
if 'm' in params:
means = stats['obs'] / denom # unregularized means
if self.fusion_prior > 0 and self.n_lqa_iter > 0:
strength = self.fusion_prior / getdiff(
means) # adaptive regularization strength
rhs = stats['obs'] / self.vars_
for i in range(self.n_features):
np.fill_diagonal(strength[i], 0)
break_lqa = False
for s in range(self.n_lqa_iter):
diff = getdiff(means)
if np.all(diff <= difference_cutoff) or break_lqa:
break
offdiagonal = -strength / diff
diagonal_penalty = np.sum(strength / diff, axis=2)
for f in range(self.n_features):
if np.all(diff[f] <= difference_cutoff):
continue
ridge_approximation = np.diag(
stats['post'] / self.vars_[:, f] +
diagonal_penalty[f]) + offdiagonal[f]
try:
means[:,
f] = np.linalg.solve(ridge_approximation,
rhs[:, f])
except np.linalg.LinAlgError:
# I'm not really sure what exactly causes the ridge
# approximation to be non-solvable, but it probably
# means we're too close to the merging. Maybe 1e-10
# is cutting it too close. ANyways, just break now and
# use the last valid value of the means.
break_lqa = True
for i in range(self.n_features):
for k, j in zip(*np.triu_indices(self.n_states)):
if diff[i, k, j] <= difference_cutoff:
means[k, i] = means[j, i]
self.means_ = means
if 'v' in params:
vars_prior = self.vars_prior
vars_weight = self.vars_weight
if vars_prior is None:
vars_weight = 0
vars_prior = 0
var_num = (stats['obs**2'] - 2 * self.means_ * stats['obs'] +
self.means_**2 * denom)
var_denom = max(vars_weight - 1, 0) + denom
self.vars_ = (vars_prior + var_num) / var_denom
def _transmat_update(self, stats):
counts = np.maximum(stats['trans'] + self.transmat_prior - 1.0, 1e-20).astype(np.float64)
self.transmat_, self.populations_ = _reversibility.reversible_transmat(counts)
