class ExponentialDistribution(BaseModule):
"""Exponential distribution (a.k.a. constant intensity model).
Same model was used in Upadhyay et al., NeurIPS 2018.
"""
def __init__(self, config, hypernet_hidden_sizes=[]):
super().__init__()
self.use_history(config.use_history)
self.use_embedding(config.use_embedding)
self.hypernet = Hypernet(config, param_sizes=[1])
self.reset_parameters()
def reset_parameters(self):
self.hypernet.reset_parameters()
def get_params(self, h, emb):
if not self.using_history:
h = None
if not self.using_embedding:
emb = None
lam = self.hypernet(h, emb)
return F.softplus(lam)
def log_prob(self, y, h=None, emb=None):
y = y.unsqueeze(-1) + 1e-8
lam = self.get_params(h, emb)
log_p = lam.log() - lam * y
return log_p.squeeze(-1)
def log_cdf(self, y, h=None, emb=None):
y = y.unsqueeze(-1) + 1e-8
lam = self.get_params(h, emb)
cdf = 1 - torch.exp(-lam * y) + 1e-8
# return torch.log1p(-torch.exp(-lam * y)).squeeze(-1)
# More numerically stable
return torch.log(-torch.expm1(-lam * y)).squeeze(-1)
def sample(self, n_samples, h=None, emb=None):
lam = self.get_params(h, emb)
dist = td.exponential.Exponential(lam)
samples = dist.rsample([n_samples])
if (h is not None):
first_dims = h.shape[:-1]
elif (emb is not None):
first_dims = emb.shape[:-1]
else:
first_dims = torch.Size()
shape = first_dims + torch.Size([n_samples])
return samples.reshape(shape)
class GompertzDistribution(BaseModule):
"""Gompertz distribution used in the RMTPP model.
References:
"Recurrent Marked Temporal Point Processes: Embedding
Event History to Vector", Du et al., KDD 2016
"""
def __init__(self, config, hypernet_hidden_sizes=[]):
super().__init__()
self.use_history(config.use_history)
self.use_embedding(config.use_embedding)
# w has to be positive for RMTPP to define a valid density
# we use softplus as done in the reference implementation
self.pre_w = nn.Parameter(torch.empty(1))
self.hypernet = Hypernet(config, param_sizes=[1])
self.reset_parameters()
def reset_parameters(self):
self.pre_w.data.fill_(-5.0)
self.hypernet.reset_parameters()
def get_params(self, h, emb):
if not self.using_history:
h = None
if not self.using_embedding:
emb = None
bias = self.hypernet(h, emb)
w = F.softplus(self.pre_w)
# w = torch.exp(self.pre_w)
return w, bias
def log_prob(self, y, h=None, emb=None):
"""Compute log probability of the sample.
Args:
y: shape (*)
h: shape (*, history_size)
emb: shape (*, embedding_size)
Returns:
log_p: shape (*)
"""
y = y.unsqueeze(-1) + 1e-8
w, bias = self.get_params(h, emb)
wt = y * w
log_p = bias + wt + 1 / w * (bias.exp() - (wt + bias).exp())
return log_p.squeeze(-1)
def log_cdf(self, y, h=None, emb=None):
# TODO: a numerically stable version?
return torch.log(self.cdf(y, h, emb) + 1e-8)
def cdf(self, y, h=None, emb=None):
"""Compute CDF of the sample.
Args:
y: shape (*)
h: shape (*, history_size)
emb: shape (*, embedding_size)
Returns:
cdf: shape (*)
"""
y = y.unsqueeze(-1) + 1e-8
w, bias = self.get_params(h, emb)
wt = y * w
cdf_ = 1 - torch.exp(1 / w * (bias.exp() - (wt + bias).exp()))
return cdf_.squeeze(-1)
def intensity(self, y, h=None, emb=None):
w, bias = self.get_params(h, emb)
wt = y * w
return torch.exp(wt + bias)
def sample(self, n_samples, h=None, emb=None):
"""Can be obtained with inverse CDF transform as
z ~ U(0, 1)
t = (log(exp(bias) - w*log(1 - z)) - b) / w
"""
raise NotImplementedError