def __init__(self,
initial_dist,
transition_dist,
observation_dist,
validate_args=None):
assert isinstance(initial_dist, torch.distributions.MultivariateNormal)
assert isinstance(transition_dist,
torch.distributions.MultivariateNormal)
assert isinstance(observation_dist,
torch.distributions.MultivariateNormal)
hidden_dim = initial_dist.event_shape[0]
assert transition_dist.event_shape[0] == hidden_dim + hidden_dim
obs_dim = observation_dist.event_shape[0] - hidden_dim
shape = broadcast_shape(initial_dist.batch_shape + (1, ),
transition_dist.batch_shape,
observation_dist.batch_shape)
batch_shape, time_shape = shape[:-1], shape[-1:]
event_shape = time_shape + (obs_dim, )
super(GaussianMRF, self).__init__(batch_shape,
event_shape,
validate_args=validate_args)
self.hidden_dim = hidden_dim
self.obs_dim = obs_dim
self._init = mvn_to_gaussian(initial_dist)
self._trans = mvn_to_gaussian(transition_dist)
self._obs = mvn_to_gaussian(observation_dist)
def test_gaussian_mrf_log_prob(sample_shape, batch_shape, num_steps,
hidden_dim, obs_dim):
init_dist = random_mvn(batch_shape, hidden_dim)
trans_dist = random_mvn(batch_shape + (num_steps, ),
hidden_dim + hidden_dim)
obs_dist = random_mvn(batch_shape + (num_steps, ), hidden_dim + obs_dim)
d = dist.GaussianMRF(init_dist, trans_dist, obs_dist)
data = obs_dist.sample(sample_shape)[..., hidden_dim:]
assert data.shape == sample_shape + d.shape()
actual_log_prob = d.log_prob(data)
# Compare against hand-computed density.
# We will construct enormous unrolled joint gaussians with shapes:
# t | 0 1 2 3 1 2 3 T = 3 in this example
# ------+-----------------------------------------
# init | H
# trans | H H H H H = hidden
# obs | H H H O O O O = observed
# and then combine these using gaussian_tensordot().
T = num_steps
init = mvn_to_gaussian(init_dist)
trans = mvn_to_gaussian(trans_dist)
obs = mvn_to_gaussian(obs_dist)
unrolled_trans = reduce(
operator.add,
[
trans[..., t].event_pad(left=t * hidden_dim,
right=(T - t - 1) * hidden_dim)
for t in range(T)
],
)
unrolled_obs = reduce(
operator.add,
[
obs[..., t].event_pad(left=t * obs.dim(),
right=(T - t - 1) * obs.dim())
for t in range(T)
],
)
# Permute obs from HOHOHO to HHHOOO.
perm = torch.cat(
[torch.arange(hidden_dim) + t * obs.dim() for t in range(T)] +
[torch.arange(obs_dim) + hidden_dim + t * obs.dim() for t in range(T)])
unrolled_obs = unrolled_obs.event_permute(perm)
unrolled_data = data.reshape(data.shape[:-2] + (T * obs_dim, ))
assert init.dim() == hidden_dim
assert unrolled_trans.dim() == (1 + T) * hidden_dim
assert unrolled_obs.dim() == T * (hidden_dim + obs_dim)
logp_h = gaussian_tensordot(init, unrolled_trans, hidden_dim)
logp_oh = gaussian_tensordot(logp_h, unrolled_obs, T * hidden_dim)
logp_h += unrolled_obs.marginalize(right=T * obs_dim)
expected_log_prob = logp_oh.log_density(
unrolled_data) - logp_h.event_logsumexp()
assert_close(actual_log_prob, expected_log_prob)
def test_matrix_and_mvn_to_gaussian_2(sample_shape, batch_shape, x_dim, y_dim):
matrix = torch.randn(batch_shape + (x_dim, y_dim))
y_mvn = random_mvn(batch_shape, y_dim)
x_mvn = random_mvn(batch_shape, x_dim)
Mx_cov = matrix.transpose(-2, -1).matmul(
x_mvn.covariance_matrix).matmul(matrix)
Mx_loc = matrix.transpose(-2,
-1).matmul(x_mvn.loc.unsqueeze(-1)).squeeze(-1)
mvn = dist.MultivariateNormal(Mx_loc + y_mvn.loc,
Mx_cov + y_mvn.covariance_matrix)
expected = mvn_to_gaussian(mvn)
actual = gaussian_tensordot(mvn_to_gaussian(x_mvn),
matrix_and_mvn_to_gaussian(matrix, y_mvn),
dims=x_dim)
assert_close_gaussian(expected, actual)
def test_mvn_to_gaussian(sample_shape, batch_shape, dim):
mvn = random_mvn(batch_shape, dim)
gaussian = mvn_to_gaussian(mvn)
value = mvn.sample(sample_shape)
actual_log_prob = gaussian.log_density(value)
expected_log_prob = mvn.log_prob(value)
assert_close(actual_log_prob, expected_log_prob)
def test_rsample_shape(sample_shape, batch_shape, dim):
mvn = random_mvn(batch_shape, dim)
g = mvn_to_gaussian(mvn)
expected = mvn.rsample(sample_shape)
actual = g.rsample(sample_shape)
assert actual.dtype == expected.dtype
assert actual.shape == expected.shape
def test_gaussian_hmm_log_prob(diag, sample_shape, batch_shape, num_steps, hidden_dim, obs_dim):
init_dist = random_mvn(batch_shape, hidden_dim)
trans_mat = torch.randn(batch_shape + (num_steps, hidden_dim, hidden_dim))
trans_dist = random_mvn(batch_shape + (num_steps,), hidden_dim)
obs_mat = torch.randn(batch_shape + (num_steps, hidden_dim, obs_dim))
obs_dist = random_mvn(batch_shape + (num_steps,), obs_dim)
if diag:
scale = obs_dist.scale_tril.diagonal(dim1=-2, dim2=-1)
obs_dist = dist.Normal(obs_dist.loc, scale).to_event(1)
d = dist.GaussianHMM(init_dist, trans_mat, trans_dist, obs_mat, obs_dist)
if diag:
obs_mvn = dist.MultivariateNormal(obs_dist.base_dist.loc,
scale_tril=obs_dist.base_dist.scale.diag_embed())
else:
obs_mvn = obs_dist
data = obs_dist.sample(sample_shape)
assert data.shape == sample_shape + d.shape()
actual_log_prob = d.log_prob(data)
# Compare against hand-computed density.
# We will construct enormous unrolled joint gaussians with shapes:
# t | 0 1 2 3 1 2 3 T = 3 in this example
# ------+-----------------------------------------
# init | H
# trans | H H H H H = hidden
# obs | H H H O O O O = observed
# and then combine these using gaussian_tensordot().
T = num_steps
init = mvn_to_gaussian(init_dist)
trans = matrix_and_mvn_to_gaussian(trans_mat, trans_dist)
obs = matrix_and_mvn_to_gaussian(obs_mat, obs_mvn)
unrolled_trans = reduce(operator.add, [
trans[..., t].event_pad(left=t * hidden_dim, right=(T - t - 1) * hidden_dim)
for t in range(T)
])
unrolled_obs = reduce(operator.add, [
obs[..., t].event_pad(left=t * obs.dim(), right=(T - t - 1) * obs.dim())
for t in range(T)
])
# Permute obs from HOHOHO to HHHOOO.
perm = torch.cat([torch.arange(hidden_dim) + t * obs.dim() for t in range(T)] +
[torch.arange(obs_dim) + hidden_dim + t * obs.dim() for t in range(T)])
unrolled_obs = unrolled_obs.event_permute(perm)
unrolled_data = data.reshape(data.shape[:-2] + (T * obs_dim,))
assert init.dim() == hidden_dim
assert unrolled_trans.dim() == (1 + T) * hidden_dim
assert unrolled_obs.dim() == T * (hidden_dim + obs_dim)
logp = gaussian_tensordot(init, unrolled_trans, hidden_dim)
logp = gaussian_tensordot(logp, unrolled_obs, T * hidden_dim)
expected_log_prob = logp.log_density(unrolled_data)
assert_close(actual_log_prob, expected_log_prob)
def test_matrix_and_mvn_to_gaussian(sample_shape, batch_shape, x_dim, y_dim):
matrix = torch.randn(batch_shape + (x_dim, y_dim))
y_mvn = random_mvn(batch_shape, y_dim)
xy_mvn = random_mvn(batch_shape, x_dim + y_dim)
gaussian = matrix_and_mvn_to_gaussian(matrix,
y_mvn) + mvn_to_gaussian(xy_mvn)
xy = torch.randn(sample_shape + (1, ) * len(batch_shape) +
(x_dim + y_dim, ))
x, y = xy[..., :x_dim], xy[..., x_dim:]
y_pred = x.unsqueeze(-2).matmul(matrix).squeeze(-2)
actual_log_prob = gaussian.log_density(xy)
expected_log_prob = xy_mvn.log_prob(xy) + y_mvn.log_prob(y - y_pred)
assert_close(actual_log_prob, expected_log_prob)
def test_rsample_distribution(batch_shape, dim):
num_samples = 20000
mvn = random_mvn(batch_shape, dim)
g = mvn_to_gaussian(mvn)
expected = mvn.rsample((num_samples, ))
actual = g.rsample((num_samples, ))
def get_moments(x):
mean = x.mean(0)
x = x - mean
cov = (x.unsqueeze(-1) * x.unsqueeze(-2)).mean(0)
std = cov.diagonal(dim1=-1, dim2=-2).sqrt()
corr = cov / (std.unsqueeze(-1) * std.unsqueeze(-2))
return mean, std, corr
expected_mean, expected_std, expected_corr = get_moments(expected)
actual_mean, actual_std, actual_corr = get_moments(actual)
assert_close(actual_mean, expected_mean, atol=0.1, rtol=0.02)
assert_close(actual_std, expected_std, atol=0.1, rtol=0.02)
assert_close(actual_corr, expected_corr, atol=0.05)
def __init__(self,
initial_dist,
transition_matrix,
transition_dist,
observation_matrix,
observation_dist,
validate_args=None):
assert isinstance(initial_dist, torch.distributions.MultivariateNormal)
assert isinstance(transition_matrix, torch.Tensor)
assert isinstance(transition_dist,
torch.distributions.MultivariateNormal)
assert isinstance(observation_matrix, torch.Tensor)
assert (isinstance(observation_dist,
torch.distributions.MultivariateNormal) or
(isinstance(observation_dist, torch.distributions.Independent)
and isinstance(observation_dist.base_dist,
torch.distributions.Normal)))
hidden_dim, obs_dim = observation_matrix.shape[-2:]
assert initial_dist.event_shape == (hidden_dim, )
assert transition_matrix.shape[-2:] == (hidden_dim, hidden_dim)
assert transition_dist.event_shape == (hidden_dim, )
assert observation_dist.event_shape == (obs_dim, )
shape = broadcast_shape(initial_dist.batch_shape + (1, ),
transition_matrix.shape[:-2],
transition_dist.batch_shape,
observation_matrix.shape[:-2],
observation_dist.batch_shape)
batch_shape, time_shape = shape[:-1], shape[-1:]
event_shape = time_shape + (obs_dim, )
super(GaussianHMM, self).__init__(batch_shape,
event_shape,
validate_args=validate_args)
self.hidden_dim = hidden_dim
self.obs_dim = obs_dim
self._init = mvn_to_gaussian(initial_dist)
self._trans = matrix_and_mvn_to_gaussian(transition_matrix,
transition_dist)
self._obs = matrix_and_mvn_to_gaussian(observation_matrix,
observation_dist)
def test_gaussian_hmm_distribution(diag, sample_shape, batch_shape, num_steps,
hidden_dim, obs_dim):
init_dist = random_mvn(batch_shape, hidden_dim)
trans_mat = torch.randn(batch_shape + (num_steps, hidden_dim, hidden_dim))
trans_dist = random_mvn(batch_shape + (num_steps, ), hidden_dim)
obs_mat = torch.randn(batch_shape + (num_steps, hidden_dim, obs_dim))
obs_dist = random_mvn(batch_shape + (num_steps, ), obs_dim)
if diag:
scale = obs_dist.scale_tril.diagonal(dim1=-2, dim2=-1)
obs_dist = dist.Normal(obs_dist.loc, scale).to_event(1)
d = dist.GaussianHMM(init_dist,
trans_mat,
trans_dist,
obs_mat,
obs_dist,
duration=num_steps)
if diag:
obs_mvn = dist.MultivariateNormal(
obs_dist.base_dist.loc,
scale_tril=obs_dist.base_dist.scale.diag_embed())
else:
obs_mvn = obs_dist
data = obs_dist.sample(sample_shape)
assert data.shape == sample_shape + d.shape()
actual_log_prob = d.log_prob(data)
# Compare against hand-computed density.
# We will construct enormous unrolled joint gaussians with shapes:
# t | 0 1 2 3 1 2 3 T = 3 in this example
# ------+-----------------------------------------
# init | H
# trans | H H H H H = hidden
# obs | H H H O O O O = observed
# like | O O O
# and then combine these using gaussian_tensordot().
T = num_steps
init = mvn_to_gaussian(init_dist)
trans = matrix_and_mvn_to_gaussian(trans_mat, trans_dist)
obs = matrix_and_mvn_to_gaussian(obs_mat, obs_mvn)
like_dist = dist.Normal(torch.randn(data.shape), 1).to_event(2)
like = mvn_to_gaussian(like_dist)
unrolled_trans = reduce(operator.add, [
trans[..., t].event_pad(left=t * hidden_dim,
right=(T - t - 1) * hidden_dim)
for t in range(T)
])
unrolled_obs = reduce(operator.add, [
obs[..., t].event_pad(left=t * obs.dim(),
right=(T - t - 1) * obs.dim()) for t in range(T)
])
unrolled_like = reduce(operator.add, [
like[..., t].event_pad(left=t * obs_dim, right=(T - t - 1) * obs_dim)
for t in range(T)
])
# Permute obs from HOHOHO to HHHOOO.
perm = torch.cat(
[torch.arange(hidden_dim) + t * obs.dim() for t in range(T)] +
[torch.arange(obs_dim) + hidden_dim + t * obs.dim() for t in range(T)])
unrolled_obs = unrolled_obs.event_permute(perm)
unrolled_data = data.reshape(data.shape[:-2] + (T * obs_dim, ))
assert init.dim() == hidden_dim
assert unrolled_trans.dim() == (1 + T) * hidden_dim
assert unrolled_obs.dim() == T * (hidden_dim + obs_dim)
logp = gaussian_tensordot(init, unrolled_trans, hidden_dim)
logp = gaussian_tensordot(logp, unrolled_obs, T * hidden_dim)
expected_log_prob = logp.log_density(unrolled_data)
assert_close(actual_log_prob, expected_log_prob)
d_posterior, log_normalizer = d.conjugate_update(like_dist)
assert_close(
d.log_prob(data) + like_dist.log_prob(data),
d_posterior.log_prob(data) + log_normalizer)
if batch_shape or sample_shape:
return
# Test mean and covariance.
prior = "prior", d, logp
posterior = "posterior", d_posterior, logp + unrolled_like
for name, d, g in [prior, posterior]:
logging.info("testing {} moments".format(name))
with torch.no_grad():
num_samples = 100000
samples = d.sample([num_samples]).reshape(num_samples, T * obs_dim)
actual_mean = samples.mean(0)
delta = samples - actual_mean
actual_cov = (delta.unsqueeze(-1) * delta.unsqueeze(-2)).mean(0)
actual_std = actual_cov.diagonal(dim1=-2, dim2=-1).sqrt()
actual_corr = actual_cov / (actual_std.unsqueeze(-1) *
actual_std.unsqueeze(-2))
expected_cov = g.precision.cholesky().cholesky_inverse()
expected_mean = expected_cov.matmul(
g.info_vec.unsqueeze(-1)).squeeze(-1)
expected_std = expected_cov.diagonal(dim1=-2, dim2=-1).sqrt()
expected_corr = expected_cov / (expected_std.unsqueeze(-1) *
expected_std.unsqueeze(-2))
assert_close(actual_mean, expected_mean, atol=0.05, rtol=0.02)
assert_close(actual_std, expected_std, atol=0.05, rtol=0.02)
assert_close(actual_corr, expected_corr, atol=0.02)
def _init(self):
# To save computation in _sequential_gaussian_tensordot(), we expand
# only _init, which is applied only after
# _sequential_gaussian_tensordot().
return mvn_to_gaussian(self.initial_dist).expand(self.batch_shape)
