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infomax.py
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import torch
import math
import torch.nn.functional as F
# from cortex_DIM.functions.gan_losses import get_positive_expectation, get_negative_expectation
def log_sum_exp(x, axis=None):
"""Log sum exp function
Args:
x: Input.
axis: Axis over which to perform sum.
Returns:
torch.Tensor: log sum exp
"""
x_max = torch.max(x, axis)[0]
y = torch.log((torch.exp(x - x_max)).sum(axis)) + x_max
return y
def random_permute(X):
"""Randomly permutes a tensor.
Args:
X: Input tensor.
Returns:
torch.Tensor
"""
X = X.transpose(1, 2)
b = torch.rand((X.size(0), X.size(1))).cuda()
idx = b.sort(0)[1]
adx = torch.range(0, X.size(1) - 1).long()
X = X[idx, adx[None, :]].transpose(1, 2)
return X
def get_positive_expectation(p_samples, measure, average=True):
"""Computes the positive part of a divergence / difference.
Args:
p_samples: Positive samples.
measure: Measure to compute for.
average: Average the result over samples.
Returns:
torch.Tensor
"""
log_2 = math.log(2.)
if measure == 'GAN':
Ep = - F.softplus(-p_samples)
elif measure == 'JSD':
Ep = log_2 - F.softplus(- p_samples)
elif measure == 'X2':
Ep = p_samples ** 2
elif measure == 'KL':
Ep = p_samples + 1.
elif measure == 'RKL':
Ep = -torch.exp(-p_samples)
elif measure == 'DV':
Ep = p_samples
elif measure == 'H2':
Ep = 1. - torch.exp(-p_samples)
elif measure == 'W1':
Ep = p_samples
else:
raise_measure_error(measure)
if average:
# print("get_positive_expectation"+str(Ep.mean()))
return Ep.mean()
else:
# print("get_positive_expectation"+str(Ep))
return Ep
def get_negative_expectation(q_samples, measure, average=True):
"""Computes the negative part of a divergence / difference.
Args:
q_samples: Negative samples.
measure: Measure to compute for.
average: Average the result over samples.
Returns:
torch.Tensor
"""
log_2 = math.log(2.)
if measure == 'GAN':
Eq = F.softplus(-q_samples) + q_samples
elif measure == 'JSD':
Eq = F.softplus(-q_samples) + q_samples - log_2
elif measure == 'X2':
Eq = -0.5 * ((torch.sqrt(q_samples ** 2) + 1.) ** 2)
elif measure == 'KL':
Eq = torch.exp(q_samples)
elif measure == 'RKL':
Eq = q_samples - 1.
elif measure == 'DV':
Eq = log_sum_exp(q_samples, 0) - math.log(q_samples.size(0))
elif measure == 'H2':
Eq = torch.exp(q_samples) - 1.
elif measure == 'W1':
Eq = q_samples
else:
raise_measure_error(measure)
if average:
# print("get_negative_expectation"+str(Eq.mean()))
return Eq.mean()
else:
# print("get_negative_expectation"+str(Eq))
return Eq
def local_global_loss_(l_enc, g_enc, edge_index, batch, measure):
'''
Args:
l: Local feature map.
g: Global features.
measure: Type of f-divergence. For use with mode `fd`
mode: Loss mode. Fenchel-dual `fd`, NCE `nce`, or Donsker-Vadadhan `dv`.
Returns:
torch.Tensor: Loss.
'''
num_graphs = g_enc.shape[0]
num_nodes = l_enc.shape[0]
pos_mask = torch.zeros((num_nodes, num_graphs)).cuda()
neg_mask = torch.ones((num_nodes, num_graphs)).cuda()
for nodeidx, graphidx in enumerate(batch):
pos_mask[nodeidx][graphidx] = 1.
neg_mask[nodeidx][graphidx] = 0.
res = torch.mm(l_enc, g_enc.t())
E_pos = get_positive_expectation(res * pos_mask, measure, average=False)
E_pos = (E_pos * pos_mask).sum() / pos_mask.sum()
E_neg = get_negative_expectation(res * neg_mask, measure, average=False)
E_neg = (E_neg * neg_mask).sum() / neg_mask.sum()
# print("Infomax local_global_loss_ E_neg-> " + str(E_neg))
# print("Infomax local_global_loss_ E_pos-> " + str(E_pos))
# print("Infomax local_global_loss_ subs " + str(E_neg - E_pos))
return E_neg - E_pos
def global_global_loss_(g_enc, g_enc1, edge_index, batch, measure):
'''
Args:
g: Global features
g1: Global features.
measure: Type of f-divergence. For use with mode `fd`
mode: Loss mode. Fenchel-dual `fd`, NCE `nce`, or Donsker-Vadadhan `dv`.
Returns:
torch.Tensor: Loss.
'''
num_graphs = g_enc.shape[0]
pos_mask = torch.eye(num_graphs).cuda()
neg_mask = 1 - pos_mask
res = torch.mm(g_enc, g_enc1.t())
E_pos = get_positive_expectation(res * pos_mask, measure, average=False)
E_pos = (E_pos * pos_mask).sum() / pos_mask.sum()
E_neg = get_negative_expectation(res * neg_mask, measure, average=False)
E_neg = (E_neg * neg_mask).sum() / neg_mask.sum()
return E_neg - E_pos