def test_dirichlet_expectation():
"""Test Cython version of Dirichlet expectation calculation."""
x = np.logspace(-100, 10, 10000)
expectation = np.empty_like(x)
_dirichlet_expectation_1d(x, 0, expectation)
assert_allclose(expectation, np.exp(psi(x) - psi(np.sum(x))),
atol=1e-19)
x = x.reshape(100, 100)
assert_allclose(_dirichlet_expectation_2d(x),
psi(x) - psi(np.sum(x, axis=1)[:, np.newaxis]),
rtol=1e-11, atol=3e-9)
def test_dirichlet_expectation():
"""Test Cython version of Dirichlet expectation calculation."""
x = np.logspace(-100, 10, 10000)
expectation = np.empty_like(x)
_dirichlet_expectation_1d(x, 0, expectation)
assert_allclose(expectation, np.exp(psi(x) - psi(np.sum(x))),
atol=1e-19)
x = x.reshape(100, 100)
assert_allclose(_dirichlet_expectation_2d(x),
psi(x) - psi(np.sum(x, axis=1)[:, np.newaxis]),
rtol=1e-11, atol=3e-9)
def _update_doc_distribution(X, exp_topic_word_distr, doc_topic_prior,
max_iters, mean_change_tol, cal_sstats,
random_state):
"""E-step: update document-topic distribution.
Parameters
----------
X : array-like or sparse matrix, shape=(n_samples, n_features)
Document word matrix.
exp_topic_word_distr : dense matrix, shape=(n_topics, n_features)
Exponential value of expection of log topic word distribution.
In the literature, this is `exp(E[log(beta)])`.
doc_topic_prior : float
Prior of document topic distribution `theta`.
max_iters : int
Max number of iterations for updating document topic distribution in
the E-step.
mean_change_tol : float
Stopping tolerance for updating document topic distribution in E-setp.
cal_sstats : boolean
Parameter that indicate to calculate sufficient statistics or not.
Set `cal_sstats` to `True` when we need to run M-step.
random_state : RandomState instance or None
Parameter that indicate how to initialize document topic distribution.
Set `random_state` to None will initialize document topic distribution
to a constant number.
Returns
-------
(doc_topic_distr, suff_stats) :
`doc_topic_distr` is unnormalized topic distribution for each document.
In the literature, this is `gamma`. we can calculate `E[log(theta)]`
from it.
`suff_stats` is expected sufficient statistics for the M-step.
When `cal_sstats == False`, this will be None.
"""
is_sparse_x = sp.issparse(X)
n_samples, n_features = X.shape
n_topics = exp_topic_word_distr.shape[0]
if random_state:
doc_topic_distr = random_state.gamma(100., 0.01, (n_samples, n_topics))
else:
doc_topic_distr = np.ones((n_samples, n_topics))
# In the literature, this is `exp(E[log(theta)])`
exp_doc_topic = np.exp(_dirichlet_expectation_2d(doc_topic_distr))
# diff on `component_` (only calculate it when `cal_diff` is True)
suff_stats = np.zeros(exp_topic_word_distr.shape) if cal_sstats else None
if is_sparse_x:
X_data = X.data
X_indices = X.indices
X_indptr = X.indptr
for idx_d in xrange(n_samples):
if is_sparse_x:
ids = X_indices[X_indptr[idx_d]:X_indptr[idx_d + 1]]
cnts = X_data[X_indptr[idx_d]:X_indptr[idx_d + 1]]
else:
ids = np.nonzero(X[idx_d, :])[0]
cnts = X[idx_d, ids]
doc_topic_d = doc_topic_distr[idx_d, :]
# The next one is a copy, since the inner loop overwrites it.
exp_doc_topic_d = exp_doc_topic[idx_d, :].copy()
#exp_topic_word_d = exp_topic_word_distr[:, ids]
exp_topic_word_d = np.repeat(exp_topic_word_distr[:, ids],
cnts,
axis=1)
# Iterate between `doc_topic_d` and `norm_phi` until convergence
for _ in xrange(0, max_iters):
last_d = doc_topic_d
# The optimal phi_{dwk} is proportional to
# exp(E[log(theta_{dk})]) * exp(E[log(beta_{dw})]).
norm_phi = np.dot(exp_doc_topic_d, exp_topic_word_d) + EPS
doc_topic_d = (exp_doc_topic_d *
np.dot(1.0 / norm_phi, exp_topic_word_d.T))
# Note: adds doc_topic_prior to doc_topic_d, in-place.
_dirichlet_expectation_1d(doc_topic_d, doc_topic_prior,
exp_doc_topic_d)
if mean_change(last_d, doc_topic_d) < mean_change_tol:
break
doc_topic_distr[idx_d, :] = doc_topic_d
# Contribution of document d to the expected sufficient
# statistics for the M step.
if cal_sstats:
norm_phi = np.dot(exp_doc_topic_d, exp_topic_word_d) + EPS
suff_stats[:, ids] += np.outer(exp_doc_topic_d, 1.0 / norm_phi)
return (doc_topic_distr, suff_stats)