def test_logsumexp():
x = np.abs(np.random.normal(1e-42, size=100000))
logx = np.log(x)
assert np.allclose(np.exp(logsumexp(logx)), x.sum())
X = np.vstack([x, x])
logX = np.vstack([logx, logx])
assert np.allclose(np.exp(logsumexp(logX, axis=0)), X.sum(axis=0))
assert np.allclose(np.exp(logsumexp(logX, axis=1)), X.sum(axis=1))
def test_logsumexp():
x = np.abs(np.random.normal(1e-42, size=100000))
logx = np.log(x)
assert np.allclose(np.exp(logsumexp(logx)), x.sum())
X = np.vstack([x, x])
logX = np.vstack([logx, logx])
assert np.allclose(np.exp(logsumexp(logX, axis=0)), X.sum(axis=0))
assert np.allclose(np.exp(logsumexp(logX, axis=1)), X.sum(axis=1))
def test_decode(self):
_logprob, state_sequence = self.hmm.decode(self.framelogprob)
n_samples, n_components = self.framelogprob.shape
norm = logsumexp(self.framelogprob, axis=1)[:, np.newaxis]
gmmposteriors = np.exp(self.framelogprob -
np.tile(norm, (1, n_components)))
gmmstate_sequence = gmmposteriors.argmax(axis=1)
assert np.allclose(state_sequence, gmmstate_sequence)
def test_decode(self):
_logprob, state_sequence = self.hmm.decode(self.framelogprob)
n_samples, n_components = self.framelogprob.shape
norm = logsumexp(self.framelogprob, axis=1)[:, np.newaxis]
gmmposteriors = np.exp(self.framelogprob -
np.tile(norm, (1, n_components)))
gmmstate_sequence = gmmposteriors.argmax(axis=1)
assert np.allclose(state_sequence, gmmstate_sequence)
def test_score_samples(self):
logprob, hmmposteriors = self.hmm.score_samples(self.framelogprob)
n_samples, n_components = self.framelogprob.shape
assert np.allclose(hmmposteriors.sum(axis=1), np.ones(n_samples))
norm = logsumexp(self.framelogprob, axis=1)[:, np.newaxis]
gmmposteriors = np.exp(self.framelogprob
- np.tile(norm, (1, n_components)))
assert np.allclose(hmmposteriors, gmmposteriors)
def test_score_samples(self):
logprob, hmmposteriors = self.hmm.score_samples(self.framelogprob)
n_samples, n_components = self.framelogprob.shape
assert np.allclose(hmmposteriors.sum(axis=1), np.ones(n_samples))
norm = logsumexp(self.framelogprob, axis=1)[:, np.newaxis]
gmmposteriors = np.exp(self.framelogprob
- np.tile(norm, (1, n_components)))
assert np.allclose(hmmposteriors, gmmposteriors)
def test_hmm_decode_consistent_with_gmm(self):
n_components = 8
nobs = 10
h = StubHMM(n_components)
# Add dummy observations to stub.
framelogprob = np.log(self.prng.rand(nobs, n_components))
h.framelogprob = framelogprob
# If startprob and transmat are uniform across all states (the
# default), the transitions are uninformative - the model
# reduces to a GMM with uniform mixing weights (in terms of
# posteriors, not likelihoods).
h.startprob_ = np.ones(n_components) / n_components
h.transmat_ = np.ones((n_components, n_components)) / n_components
viterbi_ll, state_sequence = h.decode(framelogprob)
norm = logsumexp(framelogprob, axis=1)[:, np.newaxis]
gmmposteriors = np.exp(framelogprob - np.tile(norm, (1, n_components)))
gmmstate_sequence = gmmposteriors.argmax(axis=1)
assert_array_equal(state_sequence, gmmstate_sequence)
def test_hmm_decode_consistent_with_gmm(self):
n_components = 8
nobs = 10
h = StubHMM(n_components)
# Add dummy observations to stub.
framelogprob = np.log(self.prng.rand(nobs, n_components))
h.framelogprob = framelogprob
# If startprob and transmat are uniform across all states (the
# default), the transitions are uninformative - the model
# reduces to a GMM with uniform mixing weights (in terms of
# posteriors, not likelihoods).
h.startprob_ = np.ones(n_components) / n_components
h.transmat_ = np.ones((n_components, n_components)) / n_components
viterbi_ll, state_sequence = h.decode(framelogprob)
norm = logsumexp(framelogprob, axis=1)[:, np.newaxis]
gmmposteriors = np.exp(framelogprob - np.tile(norm, (1, n_components)))
gmmstate_sequence = gmmposteriors.argmax(axis=1)
assert np.allclose(state_sequence, gmmstate_sequence)
def test_hmm_score_samples_consistent_with_gmm(self):
n_components = 8
nobs = 10
h = StubHMM(n_components)
# Add dummy observations to stub.
framelogprob = np.log(self.prng.rand(nobs, n_components))
h.framelogprob = framelogprob
# If startprob and transmat are uniform across all states (the
# default), the transitions are uninformative - the model
# reduces to a GMM with uniform mixing weights (in terms of
# posteriors, not likelihoods).
h.startprob_ = np.ones(n_components) / n_components
h.transmat_ = np.ones((n_components, n_components)) / n_components
logprob, hmmposteriors = h.score_samples(framelogprob)
assert_array_almost_equal(hmmposteriors.sum(axis=1), np.ones(nobs))
norm = logsumexp(framelogprob, axis=1)[:, np.newaxis]
gmmposteriors = np.exp(framelogprob - np.tile(norm, (1, n_components)))
assert_array_almost_equal(hmmposteriors, gmmposteriors)
def test_hmm_score_samples_consistent_with_gmm(self):
n_components = 8
nobs = 10
h = StubHMM(n_components)
# Add dummy observations to stub.
framelogprob = np.log(self.prng.rand(nobs, n_components))
h.framelogprob = framelogprob
# If startprob and transmat are uniform across all states (the
# default), the transitions are uninformative - the model
# reduces to a GMM with uniform mixing weights (in terms of
# posteriors, not likelihoods).
h.startprob_ = np.ones(n_components) / n_components
h.transmat_ = np.ones((n_components, n_components)) / n_components
logprob, hmmposteriors = h.score_samples(framelogprob)
assert_array_almost_equal(hmmposteriors.sum(axis=1), np.ones(nobs))
norm = logsumexp(framelogprob, axis=1)[:, np.newaxis]
gmmposteriors = np.exp(framelogprob - np.tile(norm, (1, n_components)))
assert_array_almost_equal(hmmposteriors, gmmposteriors)