def __init__(self,
temperature,
probs=None,
logits=None,
validate_args=None):
super(RelaxedBernoulli,
self).__init__(LogitRelaxedBernoulli(temperature, probs, logits),
SigmoidTransform(),
validate_args=validate_args)
def get_transforms(cache_size):
transforms = [
AbsTransform(cache_size=cache_size),
ExpTransform(cache_size=cache_size),
PowerTransform(exponent=2,
cache_size=cache_size),
PowerTransform(exponent=torch.tensor(5.).normal_(),
cache_size=cache_size),
PowerTransform(exponent=torch.tensor(5.).normal_(),
cache_size=cache_size),
SigmoidTransform(cache_size=cache_size),
TanhTransform(cache_size=cache_size),
AffineTransform(0, 1, cache_size=cache_size),
AffineTransform(1, -2, cache_size=cache_size),
AffineTransform(torch.randn(5),
torch.randn(5),
cache_size=cache_size),
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
SoftmaxTransform(cache_size=cache_size),
SoftplusTransform(cache_size=cache_size),
StickBreakingTransform(cache_size=cache_size),
LowerCholeskyTransform(cache_size=cache_size),
CorrCholeskyTransform(cache_size=cache_size),
ComposeTransform([
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
]),
ComposeTransform([
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
ExpTransform(cache_size=cache_size),
]),
ComposeTransform([
AffineTransform(0, 1, cache_size=cache_size),
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
AffineTransform(1, -2, cache_size=cache_size),
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
]),
ReshapeTransform((4, 5), (2, 5, 2)),
IndependentTransform(
AffineTransform(torch.randn(5),
torch.randn(5),
cache_size=cache_size),
1),
CumulativeDistributionTransform(Normal(0, 1)),
]
transforms += [t.inv for t in transforms]
return transforms
def train_moons(model,
optimizer,
n_epochs=10001,
base_distr="normal",
d=2,
device=None,
plot_val=True,
plot_interval=1000,
input_grad=False):
if device is None:
device = "cuda" if torch.cuda.is_available() else "cpu"
if base_distr == "normal":
distr = torch.distributions.multivariate_normal.MultivariateNormal(
torch.zeros(d, device=device), torch.eye(d, device=device))
elif base_distr == "logistic":
distr = TransformedDistribution(
Uniform(torch.zeros(d, device=device), torch.ones(d,
device=device)),
SigmoidTransform().inv)
else:
raise ValueError("wrong base distribution")
train_loss = []
pbar = trange(n_epochs)
for i in pbar: #range(n_epochs):
x, y = datasets.make_moons(128, noise=.1)
x = torch.tensor(x, dtype=torch.float32,
requires_grad=input_grad).to(device)
model.train()
z, log_det = model(x)
l = loss(z[-1], log_det, distr, base_distr)
l.backward()
optimizer.step()
optimizer.zero_grad()
train_loss.append(l.item())
if i % 100 == 0:
pbar.set_postfix_str(f"loss = {train_loss[-1]:.3f}")
if plot_val and i % plot_interval == 0:
print(i, train_loss[-1])
if input_grad:
val_moons_grad(model, distr, i, device, base_distr)
else:
val_moons(model, distr, i, device, base_distr)
return train_loss
def __init__(self,
loc,
scale,
transforms,
sigmoid_last=True,
validate_args=None):
if sigmoid_last:
transforms.append(SigmoidTransform())
super(AutoregressiveFlow, self).__init__(Normal(loc, scale),
transforms,
validate_args=validate_args)
def true_model(design):
w1 = torch.tensor([-1., 1.])
w2 = torch.tensor([-.5, .5, -.5, .5, -.5, 2., -2., 2., -2., 0.])
w = torch.cat([w1, w2], dim=-1)
k = torch.tensor(.1)
response_mean = rmv(design, w)
base_dist = dist.Normal(response_mean, torch.tensor(1.)).to_event(1)
k = k.expand(response_mean.shape)
transforms = [AffineTransform(loc=0., scale=k), SigmoidTransform()]
response_dist = dist.TransformedDistribution(base_dist, transforms)
return pyro.sample("y", response_dist)
def test_overdispersed_asymptote(probs, overdispersion):
total_count = 100000
# Check binomial_dist converges in distribution to LogitNormal.
d1 = binomial_dist(total_count, probs)
d2 = dist.TransformedDistribution(
dist.Normal(math.log(probs / (1 - probs)), overdispersion),
SigmoidTransform())
# CRPS is equivalent to the Cramer-von Mises test.
# https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93von_Mises_criterion
k = torch.arange(0., total_count + 1.)
cdf1 = d1.log_prob(k).exp().cumsum(-1)
cdf2 = d2.cdf(k / total_count)
crps = (cdf1 - cdf2).pow(2).mean()
assert crps < 0.02
def get_transforms(cache_size):
transforms = [
AbsTransform(cache_size=cache_size),
ExpTransform(cache_size=cache_size),
PowerTransform(exponent=2,
cache_size=cache_size),
PowerTransform(exponent=torch.tensor(5.).normal_(),
cache_size=cache_size),
SigmoidTransform(cache_size=cache_size),
TanhTransform(cache_size=cache_size),
AffineTransform(0, 1, cache_size=cache_size),
AffineTransform(1, -2, cache_size=cache_size),
AffineTransform(torch.randn(5),
torch.randn(5),
cache_size=cache_size),
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
SoftmaxTransform(cache_size=cache_size),
StickBreakingTransform(cache_size=cache_size),
LowerCholeskyTransform(cache_size=cache_size),
CorrCholeskyTransform(cache_size=cache_size),
ComposeTransform([
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
]),
ComposeTransform([
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
ExpTransform(cache_size=cache_size),
]),
ComposeTransform([
AffineTransform(0, 1, cache_size=cache_size),
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
AffineTransform(1, -2, cache_size=cache_size),
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
]),
]
transforms += [t.inv for t in transforms]
return transforms
def sigmoid_example(design):
n = design.shape[-2]
random_effect_k = pyro.sample("k", dist.Gamma(2.*torch.ones(n), torch.tensor(2.)))
random_effect_offset = pyro.sample("w2", dist.Normal(torch.tensor(0.), torch.ones(n)))
w1 = pyro.sample("w1", dist.Normal(torch.tensor([1., -1.]),
torch.tensor([10., 10.])).to_event(1))
mean = torch.matmul(design[..., :-2], w1.unsqueeze(-1)).squeeze(-1)
offset_mean = mean + random_effect_offset
base_dist = dist.Normal(offset_mean, torch.tensor(1.)).to_event(1)
transforms = [
AffineTransform(loc=torch.tensor(0.), scale=random_effect_k),
SigmoidTransform()
]
response_dist = dist.TransformedDistribution(base_dist, transforms)
y = pyro.sample("y", response_dist)
return y
def test_logistic():
base_distribution = Uniform(0, 1)
transforms = [SigmoidTransform().inv, AffineTransform(loc=torch.tensor([2.]), scale=torch.tensor([1.]))]
model = TransformedDistribution(base_distribution, transforms)
transform = Logistic(2., 1.)
x = model.sample((4,)).reshape(-1, 1)
assert torch.all(transform.log_prob(x)- model.log_prob(x).view(-1) < 1e-4)
x = transform.sample(4)
assert x.shape == (4, 1)
assert torch.all(transform.log_prob(x)- model.log_prob(x).view(-1) < 1e-4)
x = transform.sample(1)
assert x.shape == (1, 1)
assert torch.all(transform.log_prob(x)- model.log_prob(x).view(-1) < 1e-4)
transform.get_parameters()
def __init__(self,
obs_dim,
act_dim,
act_low,
act_high,
log_std_min=-20,
log_std_max=20,
hidden_size=256):
super(GaussianActorNetwork, self).__init__(obs_dim,
hidden_size=hidden_size)
self._mean_layer = nn.Linear(self._hidden_size, act_dim)
self._std_layer = nn.Linear(self._hidden_size, act_dim)
self._act_dim = act_dim
self._log_std_min = log_std_min
self._log_std_max = log_std_max
act_scale = torch.FloatTensor(act_high - act_low).to(device)
act_low = torch.FloatTensor(act_low).to(device)
self._transforms = [
SigmoidTransform(),
AffineTransform(loc=act_low, scale=act_scale)
]
def __init__(self, prior, coupling, in_out_dim, mid_dim, hidden,
bottleneck, compress, device, n_layers):
"""Initialize a NICE.
Args:
coupling: number of coupling layers.
in_out_dim: input/output dimensions.
mid_dim: number of units in a hidden layer.
hidden: number of hidden layers.
device: run on cpu or gpu
"""
super(NICE, self).__init__()
self.device = device
if prior == 'gaussian':
self.prior = torch.distributions.Normal(
torch.tensor(0.).to(device),
torch.tensor(1.).to(device))
elif prior == 'logistic':
self.prior = TransformedDistribution(
Uniform(
torch.tensor(0.).to(device),
torch.tensor(1.).to(device)),
[SigmoidTransform().inv,
AffineTransform(loc=0., scale=1.)])
else:
raise ValueError('Prior not implemented.')
self.in_out_dim = in_out_dim
self.coupling = coupling
self.n_layers = n_layers
layer = AdditiveCoupling if coupling == 'additive' else AffineCoupling
self.coupling_layers = nn.ModuleList([
layer(in_out_dim, mid_dim, hidden, i % 2)
for i in range(self.n_layers)
]).to(device)
self.scale = Scaling(in_out_dim).to(device)
self.bottleneck_factor = compress
self.bottleneck_loss = nn.MSELoss()
self.bottleneck = bottleneck
def bayesian_linear_model(design,
w_means={},
w_sqrtlambdas={},
re_group_sizes={},
re_alphas={},
re_betas={},
obs_sd=None,
alpha_0=None,
beta_0=None,
response="normal",
response_label="y",
k=None):
"""
A pyro model for Bayesian linear regression.
If :param:`response` is `"normal"` this corresponds to a linear regression
model
:math:`Y = Xw + \\epsilon`
with `\\epsilon`` i.i.d. zero-mean Gaussian. The observation standard deviation
(:param:`obs_sd`) may be known or unknown. If unknown, it is assumed to follow an
inverse Gamma distribution with parameters :param:`alpha_0` and :param:`beta_0`.
If the response type is `"bernoulli"` we instead have :math:`Y \\sim Bernoulli(p)`
with
:math:`logit(p) = Xw`
Given parameter groups in :param:`w_means` and :param:`w_sqrtlambda`, the fixed effects
regression coefficient is taken to be Gaussian with mean `w_mean` and standard deviation
given by
:math:`\\sigma / \\sqrt{\\lambda}`
corresponding to the normal inverse Gamma family.
The random effects coefficient is constructed as follows. For each random effect
group, standard deviations for that group are sampled from a normal inverse Gamma
distribution. For each group, a random effect coefficient is then sampled from a zero
mean Gaussian with those standard deviations.
:param torch.Tensor design: a tensor with last two dimensions `n` and `p`
corresponding to observations and features respectively.
:param OrderedDict w_means: map from variable names to tensors of fixed effect means.
:param OrderedDict w_sqrtlambdas: map from variable names to tensors of square root
:math:`\\lambda` values for fixed effects.
:param OrderedDict re_group_sizes: map from variable names to int representing the
group size
:param OrderedDict re_alphas: map from variable names to `torch.Tensor`, the tensor
consists of Gamma dist :math:`\\alpha` values
:param OrderedDict re_betas: map from variable names to `torch.Tensor`, the tensor
consists of Gamma dist :math:`\\beta` values
:param torch.Tensor obs_sd: the observation standard deviation (if assumed known).
This is still relevant in the case of Bernoulli observations when coefficeints
are sampled using `w_sqrtlambdas`.
:param torch.Tensor alpha_0: Gamma :math:`\\alpha` parameter for unknown observation
covariance.
:param torch.Tensor beta_0: Gamma :math:`\\beta` parameter for unknown observation
covariance.
:param str response: Emission distribution. May be `"normal"` or `"bernoulli"`.
:param str response_label: Variable label for response.
:param torch.Tensor k: Only used for a sigmoid response. The slope of the sigmoid
transformation.
"""
# design is size batch x n x p
# tau is size batch
batch_shape = design.shape[:-2]
with ExitStack() as stack:
for plate in iter_plates_to_shape(batch_shape):
stack.enter_context(plate)
if obs_sd is None:
# First, sample tau (observation precision)
tau_prior = dist.Gamma(alpha_0.unsqueeze(-1),
beta_0.unsqueeze(-1)).to_event(1)
tau = pyro.sample("tau", tau_prior)
obs_sd = 1. / torch.sqrt(tau)
elif alpha_0 is not None or beta_0 is not None:
warnings.warn("Values of `alpha_0` and `beta_0` unused becased"
"`obs_sd` was specified already.")
obs_sd = obs_sd.expand(batch_shape + (1, ))
# Build the regression coefficient
w = []
# Allow different names for different coefficient groups
# Process fixed effects
for name, w_sqrtlambda in w_sqrtlambdas.items():
w_mean = w_means[name]
# Place a normal prior on the regression coefficient
w_prior = dist.Normal(w_mean, obs_sd / w_sqrtlambda).to_event(1)
w.append(pyro.sample(name, w_prior))
# Process random effects
for name, group_size in re_group_sizes.items():
# Sample `G` once for this group
alpha, beta = re_alphas[name], re_betas[name]
G_prior = dist.Gamma(alpha, beta).to_event(1)
G = 1. / torch.sqrt(pyro.sample("G_" + name, G_prior))
# Repeat `G` for each group
repeat_shape = tuple(1 for _ in batch_shape) + (group_size, )
u_prior = dist.Normal(torch.tensor(0.),
G.repeat(repeat_shape)).to_event(1)
w.append(pyro.sample(name, u_prior))
# Regression coefficient `w` is batch x p
w = broadcast_cat(w)
# Run the regressor forward conditioned on inputs
prediction_mean = rmv(design, w)
if response == "normal":
# y is an n-vector: hence use .to_event(1)
return pyro.sample(
response_label,
dist.Normal(prediction_mean, obs_sd).to_event(1))
elif response == "bernoulli":
return pyro.sample(
response_label,
dist.Bernoulli(logits=prediction_mean).to_event(1))
elif response == "sigmoid":
base_dist = dist.Normal(prediction_mean, obs_sd).to_event(1)
# You can add loc via the linear model itself
k = k.expand(prediction_mean.shape)
transforms = [
AffineTransform(loc=torch.tensor(0.), scale=k),
SigmoidTransform()
]
response_dist = dist.TransformedDistribution(base_dist, transforms)
return pyro.sample(response_label, response_dist)
else:
raise ValueError(
"Unknown response distribution: '{}'".format(response))
Args:
x: input tensor.
reverse: True in inference mode, False in sampling mode.
Returns:
transformed tensor and log-determinant of Jacobian.
"""
scale = torch.exp(self.scale) + self.eps
det = torch.sum(self.scale)
return x * (scale if not reverse else scale.reciprocal()), det
"""Standard logistic distribution.
"""
logistic = TransformedDistribution(Uniform(
0, 1), [SigmoidTransform().inv,
AffineTransform(loc=0., scale=1.)])
"""NICE main model.
"""
class NICE(nn.Module):
def __init__(self, prior, coupling, in_out_dim, mid_dim, hidden,
bottleneck, compress, device, n_layers):
"""Initialize a NICE.
Args:
coupling: number of coupling layers.
in_out_dim: input/output dimensions.
mid_dim: number of units in a hidden layer.
hidden: number of hidden layers.
def __init__(self, loc, scale):
super().__init__(
D.Uniform(torch.zeros_like(loc), 1),
[SigmoidTransform().inv,
AffineTransform(loc=loc, scale=scale)])
self.loc = loc
class TransformMixIn:
"""Mixin for providing pre- and post-processing capabilities to encoders.
Class should have a ``transformation`` attribute to indicate how to preprocess data.
"""
# dict of PyTorch functions that transforms and inversely transforms values.
# inverse entry required if "reverse" is not the "inverse" of "forward".
TRANSFORMATIONS = {
"log":
dict(forward=_clipped_log,
reverse=torch.exp,
inverse_torch=ExpTransform()),
"log1p":
dict(forward=torch.log1p,
reverse=torch.exp,
inverse=torch.expm1,
inverse_torch=Expm1Transform()),
"logit":
dict(forward=_clipped_logit,
reverse=_clipped_sigmoid,
inverse_torch=SigmoidTransform()),
"count":
dict(forward=_plus_one,
reverse=F.softplus,
inverse=_minus_one,
inverse_torch=MinusOneTransform()),
"softplus":
dict(forward=softplus_inv,
reverse=F.softplus,
inverse_torch=SoftplusTransform()),
"relu":
dict(forward=_identity,
reverse=F.relu,
inverse=_identity,
inverse_torch=ReLuTransform()),
"sqrt":
dict(forward=torch.sqrt,
reverse=_square,
inverse_torch=PowerTransform(exponent=2.0)),
}
@classmethod
def get_transform(
cls, transformation: Union[str,
Dict[str,
Callable]]) -> Dict[str, Callable]:
"""Return transformation functions.
Args:
transformation (Union[str, Dict[str, Callable]]): name of transformation or
dictionary with transformation information.
Returns:
Dict[str, Callable]: dictionary with transformation functions (forward, reverse, inverse and inverse_torch)
"""
return cls.TRANSFORMATIONS.get(transformation, transformation)
def preprocess(
self, y: Union[pd.Series, pd.DataFrame, np.ndarray, torch.Tensor]
) -> Union[np.ndarray, torch.Tensor]:
"""
Preprocess input data (e.g. take log).
Uses ``transform`` attribute to determine how to apply transform.
Returns:
Union[np.ndarray, torch.Tensor]: return rescaled series with type depending on input type
"""
if self.transformation is None:
return y
if isinstance(y, torch.Tensor):
y = self.get_transform(self.transformation)["forward"](y)
else:
# convert first to tensor, then transform and then convert to numpy array
if isinstance(y, (pd.Series, pd.DataFrame)):
y = y.to_numpy()
y = torch.as_tensor(y)
y = self.get_transform(self.transformation)["forward"](y)
y = np.asarray(y)
return y
def inverse_preprocess(
self, y: Union[pd.Series, np.ndarray, torch.Tensor]
) -> Union[np.ndarray, torch.Tensor]:
"""
Inverse preprocess re-scaled data (e.g. take exp).
Uses ``transform`` attribute to determine how to apply inverse transform.
Returns:
Union[np.ndarray, torch.Tensor]: return rescaled series with type depending on input type
"""
if self.transformation is None:
pass
elif isinstance(y, torch.Tensor):
y = self.get_transform(self.transformation)["reverse"](y)
else:
# convert first to tensor, then transform and then convert to numpy array
y = torch.as_tensor(y)
y = self.get_transform(self.transformation)["reverse"](y)
y = np.asarray(y)
return y
def __init__(self, loc, scale, validate_args=None):
base_dist = Normal(loc, scale)
#super(LogitNormal, self).__init__(base_dist, SigmoidTransform(), validate_args=validate_args) # causes an error if using importlib.reload
super().__init__(base_dist,
SigmoidTransform(),
validate_args=validate_args)
