def test_lds():
l = LinearDynamicalSystem(2, 3)
l.parameters.data[:] = np.random.random(l.parameters.data.shape)
nll = -l.exprs['log_likelihood'].mean()
f = l.function(['inpt'], nll, mode='FAST_COMPILE')
f(np.random.random((10, 1, 2)))
def test_lds():
l = LinearDynamicalSystem(2, 3)
l.parameters.data[:] = np.random.random(l.parameters.data.shape)
nll = -l.exprs['log_likelihood'].mean()
f = l.function(['inpt'], nll, mode='FAST_COMPILE')
f(np.random.random((10, 1, 2)))
def test_lds_shapes():
raise SkipTest()
n_inpt = 2
n_hidden = 3
inpt = T.tensor3('inpt')
inpt.tag.test_value = np.random.random((10, 2, n_inpt))
transition = T.matrix('transitions')
transition.tag.test_value = np.random.random((n_hidden, n_hidden))
emission = T.matrix('emissions')
emission.tag.test_value = np.random.random((n_hidden, n_inpt))
visible_noise_mean = T.vector('visible_noise_mean')
visible_noise_mean.tag.test_value = np.random.random(n_inpt)
visible_noise_cov = T.matrix('visible_noise_cov')
visible_noise_cov.tag.test_value = np.random.random((n_inpt, n_inpt))
hidden_noise_mean = T.vector('hidden_noise_mean')
hidden_noise_mean.tag.test_value = np.random.random(n_hidden)
hidden_noise_cov = T.matrix('hidden_noise_cov')
hidden_noise_cov.tag.test_value = np.random.random((n_hidden, n_hidden))
hidden_mean_initial = T.vector('hidden_mean_initial')
hidden_mean_initial.tag.test_value = np.random.random(n_hidden)
hidden_cov_initial = T.matrix('hidden_cov_initial')
hidden_cov_initial.tag.test_value = np.random.random((n_hidden, n_hidden))
LinearDynamicalSystem.make_exprs(
inpt, transition, emission,
visible_noise_mean, visible_noise_cov,
hidden_noise_mean, hidden_noise_cov,
hidden_mean_initial, hidden_cov_initial)
theano.config.compute_test_value = 'off'
def test_lds_shapes():
raise SkipTest()
n_inpt = 2
n_hidden = 3
inpt = T.tensor3('inpt')
inpt.tag.test_value = np.random.random((10, 2, n_inpt))
transition = T.matrix('transitions')
transition.tag.test_value = np.random.random((n_hidden, n_hidden))
emission = T.matrix('emissions')
emission.tag.test_value = np.random.random((n_hidden, n_inpt))
visible_noise_mean = T.vector('visible_noise_mean')
visible_noise_mean.tag.test_value = np.random.random(n_inpt)
visible_noise_cov = T.matrix('visible_noise_cov')
visible_noise_cov.tag.test_value = np.random.random((n_inpt, n_inpt))
hidden_noise_mean = T.vector('hidden_noise_mean')
hidden_noise_mean.tag.test_value = np.random.random(n_hidden)
hidden_noise_cov = T.matrix('hidden_noise_cov')
hidden_noise_cov.tag.test_value = np.random.random((n_hidden, n_hidden))
hidden_mean_initial = T.vector('hidden_mean_initial')
hidden_mean_initial.tag.test_value = np.random.random(n_hidden)
hidden_cov_initial = T.matrix('hidden_cov_initial')
hidden_cov_initial.tag.test_value = np.random.random((n_hidden, n_hidden))
LinearDynamicalSystem.make_exprs(inpt, transition, emission,
visible_noise_mean, visible_noise_cov,
hidden_noise_mean, hidden_noise_cov,
hidden_mean_initial, hidden_cov_initial)
theano.config.compute_test_value = 'off'
def test_lds_values():
# The following test values were generated with David Barber's LDS
# implementation coming along with his book 'Bayesian Reasoning and
# machine learning'.
l = LinearDynamicalSystem(2, 3)
l.parameters['transition'] = np.arange(1, 10).reshape((3, 3)).T
l.parameters['emission'] = np.arange(1, 7).reshape((3, 2))
l.parameters['visible_noise_mean'] = np.array((-1, 1))
cov_block = np.arange(1, 5).reshape((2, 2))
l.parameters['visible_noise_cov'] = (
np.dot(cov_block, cov_block.T) * 0.2 + np.eye(2) * 100)
l.parameters['hidden_noise_mean'] = np.array((1, 2, 3))
cov_block = np.arange(1, 10).reshape((3, 3))
l.parameters['hidden_noise_cov'] = (
np.dot(cov_block, cov_block.T) + np.eye(3) * 10)
l.parameters['hidden_mean_initial'] = -np.array((.1, .2, .3))
l.parameters['hidden_cov_initial'] = (
np.dot(cov_block, cov_block.T) * 0.2 + np.eye(3) * 10)
f_forward = l.function(
['inpt'],
['filtered_means', 'filtered_covs', 'log_likelihood'],
mode='FAST_COMPILE')
f_backward = l.function(
['filtered_means', 'filtered_covs'],
['smoothed_means', 'smoothed_covs'],
mode='FAST_COMPILE')
X = np.array([
[1, 1.5],
[2, 2.5],
[3, 3.5],
[4, 4.5]])
X.shape = 4, 1, 2
f, F, ll = f_forward(X)
f_desired = np.array([
[[-0.0395, 0.0649, 0.1694]],
[[0.5087, 0.2911, 0.0734]],
[[0.5593, 0.3754, 0.1914]],
[[0.8622, 0.5272, 0.1921]]])
F_desired = np.zeros((4, 1, 3, 3))
F_desired[0, 0] = [
[9.4992, -1.0806, -1.6604],
[-1.0806, 7.5570, -3.8054],
[-1.6604, -3.8054, 4.0497],
]
F_desired[1, 0] = [
[16.0466, 0.6834, -4.6797],
[0.6834, 8.0361, -4.6112],
[-4.6797, -4.6112, 5.4574],
]
F_desired[2, 0] = [
[18.8713, 1.4414, -5.9885],
[1.4414, 8.2395, -4.9624],
[-5.9885, -4.9624, 6.0637],
]
F_desired[3, 0] = [
[19.7744, 1.6837, -6.4070],
[1.6837, 8.3045, -5.0747],
[-6.4070, -5.0747, 6.2577],
]
assert roughly(f, f_desired, 1E-4), 'filtered means not correct'
assert roughly(F, F_desired, 1E-4), 'filtered covs not correct'
assert roughly(ll, [-38.3636], 1E-4), 'log likelihood calculated wrong: %f' % ll
s, S = f_backward(f, F)
s_desired = np.array([
[-0.2173, 0.1706, -0.5076, 0.8622],
[-0.0597, 0.0528, -0.0275, 0.5272],
[0.0978, -0.0651, 0.4526, 0.1921]]).T
S_desired = np.zeros((4, 1, 3, 3))
S_desired[0, 0] = np.array([[5.5498, -2.5166, -0.583],
[-2.5166, 6.9683, -3.5468],
[-0.583, -3.5468, 3.4894]])
S_desired[1, 0] = np.array([[7.3348, -2.1811, -1.697],
[-2.1811, 7.0324, -3.7542],
[-1.697, -3.7542, 4.1886]])
S_desired[2, 0] = np.array([[9.8391, -1.7404, -3.3199],
[-1.7404, 7.11, -4.0396],
[-3.3199, -4.0396, 5.2407]])
S_desired[3, 0] = np.array([[19.7744, 1.6837, -6.407],
[1.6837, 8.3045, -5.0747],
[-6.407, -5.0747, 6.2577]])
assert roughly(s[:, 0, :], s_desired, 1E-4), 'smooooothed means not correct'
assert roughly(S, S_desired, 1E-4), 'smooooothed covs not correct'
def test_lds_values():
# The following test values were generated with David Barber's LDS
# implementation coming along with his book 'Bayesian Reasoning and
# machine learning'.
l = LinearDynamicalSystem(2, 3)
l.parameters['transition'] = np.arange(1, 10).reshape((3, 3)).T
l.parameters['emission'] = np.arange(1, 7).reshape((3, 2))
l.parameters['visible_noise_mean'] = np.array((-1, 1))
cov_block = np.arange(1, 5).reshape((2, 2))
l.parameters['visible_noise_cov'] = (np.dot(cov_block, cov_block.T) * 0.2 +
np.eye(2) * 100)
l.parameters['hidden_noise_mean'] = np.array((1, 2, 3))
cov_block = np.arange(1, 10).reshape((3, 3))
l.parameters['hidden_noise_cov'] = (np.dot(cov_block, cov_block.T) +
np.eye(3) * 10)
l.parameters['hidden_mean_initial'] = -np.array((.1, .2, .3))
l.parameters['hidden_cov_initial'] = (
np.dot(cov_block, cov_block.T) * 0.2 + np.eye(3) * 10)
f_forward = l.function(
['inpt'], ['filtered_means', 'filtered_covs', 'log_likelihood'],
mode='FAST_COMPILE')
f_backward = l.function(['filtered_means', 'filtered_covs'],
['smoothed_means', 'smoothed_covs'],
mode='FAST_COMPILE')
X = np.array([[1, 1.5], [2, 2.5], [3, 3.5], [4, 4.5]])
X.shape = 4, 1, 2
f, F, ll = f_forward(X)
f_desired = np.array([[[-0.0395, 0.0649, 0.1694]],
[[0.5087, 0.2911,
0.0734]], [[0.5593, 0.3754, 0.1914]],
[[0.8622, 0.5272, 0.1921]]])
F_desired = np.zeros((4, 1, 3, 3))
F_desired[0, 0] = [
[9.4992, -1.0806, -1.6604],
[-1.0806, 7.5570, -3.8054],
[-1.6604, -3.8054, 4.0497],
]
F_desired[1, 0] = [
[16.0466, 0.6834, -4.6797],
[0.6834, 8.0361, -4.6112],
[-4.6797, -4.6112, 5.4574],
]
F_desired[2, 0] = [
[18.8713, 1.4414, -5.9885],
[1.4414, 8.2395, -4.9624],
[-5.9885, -4.9624, 6.0637],
]
F_desired[3, 0] = [
[19.7744, 1.6837, -6.4070],
[1.6837, 8.3045, -5.0747],
[-6.4070, -5.0747, 6.2577],
]
# Tolerances might seem too tolerant, but that happens when float32 is used.
assert np.allclose(f, f_desired, 1e-1), 'filtered means not correct'
assert np.allclose(F, F_desired, .3), 'filtered covs not correct'
assert np.allclose(ll, [-38.3636],
.2), 'log likelihood calculated wrong: %f' % ll
s, S = f_backward(f, F)
s_desired = np.array([[-0.2173, 0.1706, -0.5076, 0.8622],
[-0.0597, 0.0528, -0.0275, 0.5272],
[0.0978, -0.0651, 0.4526, 0.1921]]).T
S_desired = np.zeros((4, 1, 3, 3))
S_desired[0, 0] = np.array([[5.5498, -2.5166, -0.583],
[-2.5166, 6.9683, -3.5468],
[-0.583, -3.5468, 3.4894]])
S_desired[1, 0] = np.array([[7.3348, -2.1811, -1.697],
[-2.1811, 7.0324, -3.7542],
[-1.697, -3.7542, 4.1886]])
S_desired[2, 0] = np.array([[9.8391, -1.7404, -3.3199],
[-1.7404, 7.11, -4.0396],
[-3.3199, -4.0396, 5.2407]])
S_desired[3, 0] = np.array([[19.7744, 1.6837, -6.407],
[1.6837, 8.3045, -5.0747],
[-6.407, -5.0747, 6.2577]])
assert np.allclose(s[:, 0, :], s_desired,
.2), 'smooooothed means not correct'
assert np.allclose(S, S_desired, .3), 'smooooothed covs not correct'