def _default_prior(event_shape, posterior, prior, posterior_kwargs):
if not isinstance(event_shape, (Sequence, MutableSequence, tf.TensorShape)):
raise ValueError("event_shape must be list of integer but given: "
f"{event_shape} type: {type(event_shape)}")
if isinstance(prior, (Distribution, DistributionLambda, Callable)):
return prior
elif not isinstance(prior, (string_types, type(None))):
raise ValueError("prior must be string or instance of "
f"Distribution or DistributionLambda, but given: {prior}")
# no prior given
layer, dist = parse_distribution(posterior)
if isinstance(prior, dict):
kw = dict(prior)
prior = None
else:
kw = {}
event_size = int(np.prod(event_shape))
## helper function
def _kwargs(**args):
for k, v in args.items():
if k not in kw:
kw[k] = v
return kw
## Normal
if layer == obl.GaussianLayer:
prior = obd.Independent(
obd.Normal(**_kwargs(loc=tf.zeros(shape=event_shape),
scale=tf.ones(shape=event_shape))),
reinterpreted_batch_ndims=1,
)
## Multivariate Normal
elif issubclass(layer, obl.MultivariateNormalLayer):
cov = layer._partial_kwargs['covariance']
if cov == 'diag': # diagonal covariance
loc = tf.zeros(shape=event_shape)
if tf.rank(loc) == 0:
loc = tf.expand_dims(loc, axis=-1)
prior = obd.MultivariateNormalDiag(
**_kwargs(loc=loc, scale_identity_multiplier=1.))
else: # low-triangle covariance
bijector = tfp.bijectors.FillScaleTriL(
diag_bijector=tfp.bijectors.Identity(), diag_shift=1e-5)
size = tf.reduce_prod(event_shape)
loc = tf.zeros(shape=[size])
scale_tril = bijector.forward(tf.ones(shape=[size * (size + 1) // 2]))
prior = obd.MultivariateNormalTriL(
**_kwargs(loc=loc, scale_tril=scale_tril))
## Log Normal
elif layer == obl.LogNormalLayer:
prior = obd.Independent(
obd.LogNormal(**_kwargs(loc=tf.zeros(shape=event_shape),
scale=tf.ones(shape=event_shape))),
reinterpreted_batch_ndims=1,
)
## mixture
elif issubclass(layer, obl.MixtureGaussianLayer):
if hasattr(layer, '_partial_kwargs'):
cov = layer._partial_kwargs['covariance']
else:
cov = 'none'
n_components = int(posterior_kwargs.get('n_components', 2))
if cov == 'diag':
scale_shape = [n_components, event_size]
fn = lambda l, s: obd.MultivariateNormalDiag(loc=l,
scale_diag=tf.nn.softplus(s))
elif cov == 'none':
scale_shape = [n_components, event_size]
fn = lambda l, s: obd.Independent(
obd.Normal(loc=l, scale=tf.math.softplus(s)),
reinterpreted_batch_ndims=1,
)
elif cov in ('full', 'tril'):
scale_shape = [n_components, event_size * (event_size + 1) // 2]
fn = lambda l, s: obd.MultivariateNormalTriL(
loc=l,
scale_tril=tfp.bijectors.FillScaleTriL(diag_shift=1e-5)
(tf.math.softplus(s)))
loc = tf.cast(tf.fill([n_components, event_size], 0.), dtype=tf.float32)
log_scale = tf.cast(tf.fill(scale_shape, np.log(np.expm1(1.))),
dtype=tf.float32)
p = 1. / n_components
mixture_logits = tf.cast(tf.fill([n_components], np.log(p / (1 - p))),
dtype=tf.float32)
prior = obd.MixtureSameFamily(
components_distribution=fn(loc, log_scale),
mixture_distribution=obd.Categorical(logits=mixture_logits))
## discrete
elif dist in (obd.OneHotCategorical, obd.Categorical) or \
layer == obl.RelaxedOneHotCategoricalLayer:
p = 1. / event_size
prior = dist(**_kwargs(logits=[np.log(p / (1 - p))] * event_size),
dtype=tf.float32)
elif dist == obd.Dirichlet:
prior = dist(**_kwargs(concentration=[1.] * event_size))
elif dist == obd.Bernoulli:
prior = obd.Independent(
obd.Bernoulli(**_kwargs(logits=np.zeros(event_shape)),
dtype=tf.float32),
reinterpreted_batch_ndims=len(event_shape),
)
## other
return prior
posteriors_info = [
('gaussian', 'mvndiag', 'mvntril'),
(
D.Sample(D.Normal(loc=0., scale=1.),
sample_shape=encoded_size,
name='independent'),
D.MultivariateNormalDiag(loc=tf.zeros(encoded_size),
scale_diag=tf.ones(encoded_size),
name='mvndiag'),
D.MultivariateNormalTriL(loc=tf.zeros(encoded_size),
scale_tril=bj.FillScaleTriL()(tf.ones(
encoded_size * (encoded_size + 1) // 2)),
name='mvntril'),
D.MixtureSameFamily(
components_distribution=D.MultivariateNormalDiag(
loc=tf.zeros([10, encoded_size]),
scale_diag=tf.ones([10, encoded_size])),
mixture_distribution=D.Categorical(logits=tf.fill([10], 1.0 / 10)),
name='gmm10'),
D.MixtureSameFamily(components_distribution=D.MultivariateNormalDiag(
loc=tf.zeros([100, encoded_size]),
scale_diag=tf.ones([100, encoded_size])),
mixture_distribution=D.Categorical(
logits=tf.fill([100], 1.0 / 100)),
name='gmm100'),
),
('identity', 'relu', 'softplus', 'softplus1'),
]
# ===========================================================================
# Main
def _default_prior(event_shape, posterior, prior, posterior_kwargs):
if isinstance(prior, obd.Distribution):
return prior
layer, dist = parse_distribution(posterior)
if isinstance(prior, dict):
kw = dict(prior)
prior = None
else:
kw = {}
event_size = int(np.prod(event_shape))
## helper function
def _kwargs(**args):
for k, v in args.items():
if k not in kw:
kw[k] = v
return kw
## Normal
if layer == obl.GaussianLayer:
prior = obd.Independent(
obd.Normal(**_kwargs(loc=tf.zeros(shape=event_shape),
scale=tf.ones(shape=event_shape))), 1)
## Multivariate Normal
elif issubclass(layer, obl.MultivariateNormalLayer):
cov = layer._partial_kwargs['covariance']
if cov == 'diag': # diagonal covariance
loc = tf.zeros(shape=event_shape)
if tf.rank(loc) == 0:
loc = tf.expand_dims(loc, axis=-1)
prior = obd.MultivariateNormalDiag(
**_kwargs(loc=loc, scale_identity_multiplier=1.))
else: # low-triangle covariance
bijector = tfp.bijectors.FillScaleTriL(
diag_bijector=tfp.bijectors.Identity(), diag_shift=1e-5)
size = tf.reduce_prod(event_shape)
loc = tf.zeros(shape=[size])
scale_tril = bijector.forward(
tf.ones(shape=[size * (size + 1) // 2]))
prior = obd.MultivariateNormalTriL(
**_kwargs(loc=loc, scale_tril=scale_tril))
## Log Normal
elif layer == obl.LogNormalLayer:
prior = obd.Independent(
obd.LogNormal(**_kwargs(loc=tf.zeros(shape=event_shape),
scale=tf.ones(shape=event_shape))), 1)
## mixture
elif issubclass(layer, obl.MixtureGaussianLayer):
if hasattr(layer, '_partial_kwargs'):
cov = layer._partial_kwargs['covariance']
else:
cov = 'none'
n_components = int(posterior_kwargs.get('n_components', 2))
if cov == 'diag':
scale_shape = [n_components, event_size]
fn = lambda l, s: obd.MultivariateNormalDiag(
loc=l, scale_diag=tf.nn.softplus(s))
elif cov == 'none':
scale_shape = [n_components, event_size]
fn = lambda l, s: obd.Independent(
obd.Normal(loc=l, scale=tf.math.softplus(s)), 1)
elif cov in ('full', 'tril'):
scale_shape = [n_components, event_size * (event_size + 1) // 2]
fn = lambda l, s: obd.MultivariateNormalTriL(
loc=l,
scale_tril=tfp.bijectors.FillScaleTriL(diag_shift=1e-5)
(tf.math.softplus(s)))
loc = tf.cast(tf.fill([n_components, event_size], 0.),
dtype=tf.float32)
log_scale = tf.cast(tf.fill(scale_shape, np.log(np.expm1(1.))),
dtype=tf.float32)
mixture_logits = tf.cast(tf.fill([n_components], 1.), dtype=tf.float32)
prior = obd.MixtureSameFamily(
components_distribution=fn(loc, log_scale),
mixture_distribution=obd.Categorical(logits=mixture_logits))
## discrete
elif dist in (obd.OneHotCategorical, obd.Categorical) or \
layer == obl.RelaxedOneHotCategoricalLayer:
prior = dist(**_kwargs(logits=np.log([1. / event_size] * event_size),
dtype=tf.float32))
elif dist == obd.Dirichlet:
prior = dist(**_kwargs(concentration=[1.] * event_size))
elif dist == obd.Bernoulli:
prior = obd.Independent(
obd.Bernoulli(**_kwargs(logits=np.full(event_shape, np.log(0.5)),
dtype=tf.float32)), len(event_shape))
## other
return prior