from typing import Optional, Tuple
import torch
from torch import Tensor
from torch.nn import Module
from torch_geometric.nn.inits import reset
from torch_geometric.utils import negative_sampling
EPS = 1e-15
MAX_LOGSTD = 10
[docs]class InnerProductDecoder(torch.nn.Module):
r"""The inner product decoder from the `"Variational Graph Auto-Encoders"
<https://arxiv.org/abs/1611.07308>`_ paper.
.. math::
\sigma(\mathbf{Z}\mathbf{Z}^{\top})
where :math:`\mathbf{Z} \in \mathbb{R}^{N \times d}` denotes the latent
space produced by the encoder.
"""
[docs] def forward(
self,
z: Tensor,
edge_index: Tensor,
sigmoid: bool = True,
) -> Tensor:
r"""Decodes the latent variables :obj:`z` into edge probabilities for
the given node-pairs :obj:`edge_index`.
Args:
z (torch.Tensor): The latent space :math:`\mathbf{Z}`.
edge_index (torch.Tensor): The edge indices.
sigmoid (bool, optional): If set to :obj:`False`, does not apply
the logistic sigmoid function to the output.
(default: :obj:`True`)
"""
value = (z[edge_index[0]] * z[edge_index[1]]).sum(dim=1)
return torch.sigmoid(value) if sigmoid else value
[docs] def forward_all(self, z: Tensor, sigmoid: bool = True) -> Tensor:
r"""Decodes the latent variables :obj:`z` into a probabilistic dense
adjacency matrix.
Args:
z (torch.Tensor): The latent space :math:`\mathbf{Z}`.
sigmoid (bool, optional): If set to :obj:`False`, does not apply
the logistic sigmoid function to the output.
(default: :obj:`True`)
"""
adj = torch.matmul(z, z.t())
return torch.sigmoid(adj) if sigmoid else adj
[docs]class GAE(torch.nn.Module):
r"""The Graph Auto-Encoder model from the
`"Variational Graph Auto-Encoders" <https://arxiv.org/abs/1611.07308>`_
paper based on user-defined encoder and decoder models.
Args:
encoder (torch.nn.Module): The encoder module.
decoder (torch.nn.Module, optional): The decoder module. If set to
:obj:`None`, will default to the
:class:`torch_geometric.nn.models.InnerProductDecoder`.
(default: :obj:`None`)
"""
def __init__(self, encoder: Module, decoder: Optional[Module] = None):
super().__init__()
self.encoder = encoder
self.decoder = InnerProductDecoder() if decoder is None else decoder
GAE.reset_parameters(self)
[docs] def reset_parameters(self):
r"""Resets all learnable parameters of the module."""
reset(self.encoder)
reset(self.decoder)
[docs] def forward(self, *args, **kwargs) -> Tensor: # pragma: no cover
r"""Alias for :meth:`encode`."""
return self.encoder(*args, **kwargs)
[docs] def encode(self, *args, **kwargs) -> Tensor:
r"""Runs the encoder and computes node-wise latent variables."""
return self.encoder(*args, **kwargs)
[docs] def decode(self, *args, **kwargs) -> Tensor:
r"""Runs the decoder and computes edge probabilities."""
return self.decoder(*args, **kwargs)
[docs] def recon_loss(self, z: Tensor, pos_edge_index: Tensor,
neg_edge_index: Optional[Tensor] = None) -> Tensor:
r"""Given latent variables :obj:`z`, computes the binary cross
entropy loss for positive edges :obj:`pos_edge_index` and negative
sampled edges.
Args:
z (torch.Tensor): The latent space :math:`\mathbf{Z}`.
pos_edge_index (torch.Tensor): The positive edges to train against.
neg_edge_index (torch.Tensor, optional): The negative edges to
train against. If not given, uses negative sampling to
calculate negative edges. (default: :obj:`None`)
"""
pos_loss = -torch.log(
self.decoder(z, pos_edge_index, sigmoid=True) + EPS).mean()
if neg_edge_index is None:
neg_edge_index = negative_sampling(pos_edge_index, z.size(0))
neg_loss = -torch.log(1 -
self.decoder(z, neg_edge_index, sigmoid=True) +
EPS).mean()
return pos_loss + neg_loss
[docs] def test(self, z: Tensor, pos_edge_index: Tensor,
neg_edge_index: Tensor) -> Tuple[Tensor, Tensor]:
r"""Given latent variables :obj:`z`, positive edges
:obj:`pos_edge_index` and negative edges :obj:`neg_edge_index`,
computes area under the ROC curve (AUC) and average precision (AP)
scores.
Args:
z (torch.Tensor): The latent space :math:`\mathbf{Z}`.
pos_edge_index (torch.Tensor): The positive edges to evaluate
against.
neg_edge_index (torch.Tensor): The negative edges to evaluate
against.
"""
from sklearn.metrics import average_precision_score, roc_auc_score
pos_y = z.new_ones(pos_edge_index.size(1))
neg_y = z.new_zeros(neg_edge_index.size(1))
y = torch.cat([pos_y, neg_y], dim=0)
pos_pred = self.decoder(z, pos_edge_index, sigmoid=True)
neg_pred = self.decoder(z, neg_edge_index, sigmoid=True)
pred = torch.cat([pos_pred, neg_pred], dim=0)
y, pred = y.detach().cpu().numpy(), pred.detach().cpu().numpy()
return roc_auc_score(y, pred), average_precision_score(y, pred)
[docs]class VGAE(GAE):
r"""The Variational Graph Auto-Encoder model from the
`"Variational Graph Auto-Encoders" <https://arxiv.org/abs/1611.07308>`_
paper.
Args:
encoder (torch.nn.Module): The encoder module to compute :math:`\mu`
and :math:`\log\sigma^2`.
decoder (torch.nn.Module, optional): The decoder module. If set to
:obj:`None`, will default to the
:class:`torch_geometric.nn.models.InnerProductDecoder`.
(default: :obj:`None`)
"""
def __init__(self, encoder: Module, decoder: Optional[Module] = None):
super().__init__(encoder, decoder)
def reparametrize(self, mu: Tensor, logstd: Tensor) -> Tensor:
if self.training:
return mu + torch.randn_like(logstd) * torch.exp(logstd)
else:
return mu
def encode(self, *args, **kwargs) -> Tensor:
"""""" # noqa: D419
self.__mu__, self.__logstd__ = self.encoder(*args, **kwargs)
self.__logstd__ = self.__logstd__.clamp(max=MAX_LOGSTD)
z = self.reparametrize(self.__mu__, self.__logstd__)
return z
[docs] def kl_loss(self, mu: Optional[Tensor] = None,
logstd: Optional[Tensor] = None) -> Tensor:
r"""Computes the KL loss, either for the passed arguments :obj:`mu`
and :obj:`logstd`, or based on latent variables from last encoding.
Args:
mu (torch.Tensor, optional): The latent space for :math:`\mu`. If
set to :obj:`None`, uses the last computation of :math:`\mu`.
(default: :obj:`None`)
logstd (torch.Tensor, optional): The latent space for
:math:`\log\sigma`. If set to :obj:`None`, uses the last
computation of :math:`\log\sigma^2`. (default: :obj:`None`)
"""
mu = self.__mu__ if mu is None else mu
logstd = self.__logstd__ if logstd is None else logstd.clamp(
max=MAX_LOGSTD)
return -0.5 * torch.mean(
torch.sum(1 + 2 * logstd - mu**2 - logstd.exp()**2, dim=1))
[docs]class ARGA(GAE):
r"""The Adversarially Regularized Graph Auto-Encoder model from the
`"Adversarially Regularized Graph Autoencoder for Graph Embedding"
<https://arxiv.org/abs/1802.04407>`_ paper.
Args:
encoder (torch.nn.Module): The encoder module.
discriminator (torch.nn.Module): The discriminator module.
decoder (torch.nn.Module, optional): The decoder module. If set to
:obj:`None`, will default to the
:class:`torch_geometric.nn.models.InnerProductDecoder`.
(default: :obj:`None`)
"""
def __init__(
self,
encoder: Module,
discriminator: Module,
decoder: Optional[Module] = None,
):
super().__init__(encoder, decoder)
self.discriminator = discriminator
reset(self.discriminator)
[docs] def reset_parameters(self):
super().reset_parameters()
reset(self.discriminator)
[docs] def reg_loss(self, z: Tensor) -> Tensor:
r"""Computes the regularization loss of the encoder.
Args:
z (torch.Tensor): The latent space :math:`\mathbf{Z}`.
"""
real = torch.sigmoid(self.discriminator(z))
real_loss = -torch.log(real + EPS).mean()
return real_loss
[docs] def discriminator_loss(self, z: Tensor) -> Tensor:
r"""Computes the loss of the discriminator.
Args:
z (torch.Tensor): The latent space :math:`\mathbf{Z}`.
"""
real = torch.sigmoid(self.discriminator(torch.randn_like(z)))
fake = torch.sigmoid(self.discriminator(z.detach()))
real_loss = -torch.log(real + EPS).mean()
fake_loss = -torch.log(1 - fake + EPS).mean()
return real_loss + fake_loss
[docs]class ARGVA(ARGA):
r"""The Adversarially Regularized Variational Graph Auto-Encoder model from
the `"Adversarially Regularized Graph Autoencoder for Graph Embedding"
<https://arxiv.org/abs/1802.04407>`_ paper.
Args:
encoder (torch.nn.Module): The encoder module to compute :math:`\mu`
and :math:`\log\sigma^2`.
discriminator (torch.nn.Module): The discriminator module.
decoder (torch.nn.Module, optional): The decoder module. If set to
:obj:`None`, will default to the
:class:`torch_geometric.nn.models.InnerProductDecoder`.
(default: :obj:`None`)
"""
def __init__(
self,
encoder: Module,
discriminator: Module,
decoder: Optional[Module] = None,
):
super().__init__(encoder, discriminator, decoder)
self.VGAE = VGAE(encoder, decoder)
@property
def __mu__(self) -> Tensor:
return self.VGAE.__mu__
@property
def __logstd__(self) -> Tensor:
return self.VGAE.__logstd__
def reparametrize(self, mu: Tensor, logstd: Tensor) -> Tensor:
return self.VGAE.reparametrize(mu, logstd)
def encode(self, *args, **kwargs) -> Tensor:
"""""" # noqa: D419
return self.VGAE.encode(*args, **kwargs)
def kl_loss(
self,
mu: Optional[Tensor] = None,
logstd: Optional[Tensor] = None,
) -> Tensor:
return self.VGAE.kl_loss(mu, logstd)