def nll_pmf(phi, idx_durations, events, reduction='mean', epsilon=1e-7):
"""Negative log-likelihood for the PMF parametrized model [1].
Arguments:
phi {torch.tensor} -- Estimates in (-inf, inf), where pmf = somefunc(phi).
idx_durations {torch.tensor} -- Event times represented as indices.
events {torch.tensor} -- Indicator of event (1.) or censoring (0.).
Same length as 'idx_durations'.
reduction {string} -- How to reduce the loss.
'none': No reduction.
'mean': Mean of tensor.
'sum: sum.
Returns:
torch.tensor -- The negative log-likelihood.
References:
[1] Håvard Kvamme and Ørnulf Borgan. Continuous and Discrete-Time Survival Prediction
with Neural Networks. arXiv preprint arXiv:1910.06724, 2019.
https://arxiv.org/pdf/1910.06724.pdf
"""
if (idx_durations.max()) >= phi.shape[1]:
raise ValueError("""'t_idx' too large. Probably need to increase output size of net.""")
events = events.view(-1)
idx_durations = idx_durations.view(-1, 1)
phi = utils.pad_col(phi)
gamma = phi.max(1)[0]
cumsum = phi.sub(gamma.view(-1, 1)).exp().cumsum(1)
sum_ = cumsum[:, -1]
part1 = phi.gather(1, idx_durations).view(-1).sub(gamma).mul(events)
part2 = - sum_.relu().add(epsilon).log()
part3 = sum_.sub(cumsum.gather(1, idx_durations).view(-1)).relu().add(epsilon).log().mul(1. - events)
# need relu() in part3 (and possibly part2) because cumsum on gpu has some bugs and we risk getting negative numbers.
loss = - part1.add(part2).add(part3)
return _reduction(loss, reduction)
def _hazard_const_haz(self,
input,
batch_size=8224,
numpy=None,
eval_=True,
to_cpu=False,
num_workers=0):
"""Computes the continuous-time constant hazard interpolation.
Essentially we what the discrete survival estimates to match the continuous time at the knots.
So essentially we want
$$S(tau_j) = prod_{k=1}^j [1 - h_k] = prod_{k=1}{j} exp[-eta_k].$$
where $h_k$ is the discrete hazard estimates and $eta_k$ continuous time hazards multiplied
with the length of the duration interval as they are defined for the PC-Hazard method.
Thus we get
$$eta_k = - log[1 - h_k]$$
which can be divided by the length of the time interval to get the continuous time hazards.
"""
haz_orig = self.model.predict_hazard(input, batch_size, False, eval_,
to_cpu, num_workers)
haz = (1 - haz_orig).add(
self.epsilon).log().mul(-1).relu()[:, 1:].contiguous()
n = haz.shape[0]
haz = haz.view(-1, 1).repeat(1, self.sub).view(n, -1).div(self.sub)
haz = utils.pad_col(haz, where='start')
haz[:, 0] = haz_orig[:, 0]
return tt.utils.array_or_tensor(haz, numpy, input)
def predict_pmf(self,
input,
batch_size=8224,
numpy=None,
eval_=True,
to_cpu=False,
num_workers=0):
"""Predict the probability mass function (PMF) for `input`.
Arguments:
input {tuple, np.ndarray, or torch.tensor} -- Input to net.
Keyword Arguments:
batch_size {int} -- Batch size (default: {8224})
numpy {bool} -- 'False' gives tensor, 'True' gives numpy, and None give same as input
(default: {None})
eval_ {bool} -- If 'True', use 'eval' mode on net. (default: {True})
grads {bool} -- If gradients should be computed (default: {False})
to_cpu {bool} -- For larger data sets we need to move the results to cpu
(default: {False})
num_workers {int} -- Number of workers in created dataloader (default: {0})
Returns:
[np.ndarray or tensor] -- Predictions
"""
preds = self.predict(input, batch_size, False, eval_, False, to_cpu,
num_workers)
pmf = pad_col(preds).softmax(1)[:, :-1]
return array_or_tensor(pmf, numpy, input)
def nll_pmf_cr(phi, idx_durations, events, reduction='mean', epsilon=1e-7):
"""Negative log-likelihood for PMF parameterizations. `phi` is the ''logit''.
Arguments:
phi {torch.tensor} -- Predictions as float tensor with shape [batch, n_risks, n_durations]
all in (-inf, inf).
idx_durations {torch.tensor} -- Int tensor with index of durations.
events {torch.tensor} -- Int tensor with event types.
{0: Censored, 1: first group, ..., n_risks: n'th risk group}.
Keyword Arguments:
reduction {string} -- How to reduce the loss.
'none': No reduction.
'mean': Mean of tensor.
else: sum.
Returns:
torch.tensor -- Negative log-likelihood.
"""
# Should improve numerical stability by, e.g., log-sum-exp trick.
events = events.view(-1) - 1
event_01 = (events != -1).float()
idx_durations = idx_durations.view(-1)
batch_size = phi.size(0)
sm = utils.pad_col(phi.view(batch_size, -1)).softmax(1)[:, :-1].view(phi.shape)
index = torch.arange(batch_size)
part1 = sm[index, events, idx_durations].relu().add(epsilon).log().mul(event_01)
part2 = (1 - sm.cumsum(2)[index, :, idx_durations].sum(1)).relu().add(epsilon).log().mul(1 - event_01)
loss = - part1.add(part2)
return _reduction(loss, reduction)
def predict_hazard(self,
input,
batch_size=8224,
numpy=None,
eval_=True,
to_cpu=False,
num_workers=0):
"""Predict the hazard function for `input`.
Arguments:
input {tuple, np.ndarra, or torch.tensor} -- Input to net.
Keyword Arguments:
batch_size {int} -- Batch size (default: {8224})
numpy {bool} -- 'False' gives tensor, 'True' gives numpy, and None give same as input
(default: {None})
eval_ {bool} -- If 'True', use 'eval' mode on net. (default: {True})
to_cpu {bool} -- For larger data sets we need to move the results to cpu
(default: {False})
num_workers {int} -- Number of workers in created dataloader (default: {0})
Returns:
[np.ndarray or tensor] -- Predicted hazards
"""
preds = self.predict(input, batch_size, False, eval_, False, to_cpu,
num_workers)
n = preds.shape[0]
hazard = F.softplus(preds).view(-1, 1).repeat(1, self.sub).view(
n, -1).div(self.sub)
hazard = pad_col(hazard, where='start')
return tt.utils.array_or_tensor(hazard, numpy, input)
def rank_loss_deephit_cr(phi: Tensor,
idx_durations: Tensor,
events: Tensor,
rank_mat: Tensor,
sigma: float,
reduction: str = 'mean') -> Tensor:
"""Rank loss proposed by DeepHit authors for competing risks [1].
Arguments:
phi {torch.tensor} -- Predictions as float tensor with shape [batch, n_risks, n_durations]
all in (-inf, inf).
idx_durations {torch.tensor} -- Int tensor with index of durations.
events {torch.tensor} -- Int tensor with event types.
{0: Censored, 1: first group, ..., n_risks: n'th risk group}.
rank_mat {torch.tensor} -- See pair_rank_mat function.
sigma {float} -- Sigma from DeepHit paper, chosen by you.
Keyword Arguments:
reduction {string} -- How to reduce the loss.
'none': No reduction.
'mean': Mean of tensor.
else: sum.
Returns:
torch.tensor -- Rank loss.
References:
[1] Changhee Lee, William R Zame, Jinsung Yoon, and Mihaela van der Schaar. Deephit: A deep learning
approach to survival analysis with competing risks. In Thirty-Second AAAI Conference on Artificial
Intelligence, 2018.
http://medianetlab.ee.ucla.edu/papers/AAAI_2018_DeepHit
"""
idx_durations = idx_durations.view(-1)
events = events.view(-1) - 1
event_01 = (events == -1).float()
batch_size, n_risks = phi.shape[:2]
pmf = utils.pad_col(phi.view(batch_size, -1)).softmax(1)
pmf = pmf[:, :-1].view(phi.shape)
y = torch.zeros_like(pmf)
y[torch.arange(batch_size), :, idx_durations] = 1.
loss = []
for i in range(n_risks):
rank_loss_i = _rank_loss_deephit(pmf[:, i, :], y[:, i, :], rank_mat,
sigma, 'none')
loss.append(rank_loss_i.view(-1) * (events == i).float())
if reduction == 'none':
return sum(loss)
elif reduction == 'mean':
return sum([lo.mean() for lo in loss])
elif reduction == 'sum':
return sum([lo.sum() for lo in loss])
return _reduction(loss, reduction)
def predict_pmf(self,
input,
batch_size=8224,
numpy=None,
eval_=True,
to_cpu=False,
num_workers=0):
preds = self.predict(input, batch_size, False, eval_, False, to_cpu,
num_workers)
pmf = pad_col(preds).softmax(1)[:, :-1]
return tt.utils.array_or_tensor(pmf, numpy, input)
def _surv_const_haz(self,
input,
batch_size=8224,
numpy=None,
eval_=True,
to_cpu=False,
num_workers=0):
haz = self._hazard_const_haz(input, batch_size, False, eval_, to_cpu,
num_workers)
surv_0 = 1 - haz[:, :1]
surv = utils.pad_col(haz[:, 1:],
where='start').cumsum(1).mul(-1).exp().mul(surv_0)
return tt.utils.array_or_tensor(surv, numpy, input)
def nll_pc_hazard_loss(phi: Tensor,
idx_durations: Tensor,
events: Tensor,
interval_frac: Tensor,
reduction: str = 'mean') -> Tensor:
"""Negative log-likelihood of the PC-Hazard parametrization model [1].
Arguments:
phi {torch.tensor} -- Estimates in (-inf, inf), where hazard = sigmoid(phi).
idx_durations {torch.tensor} -- Event times represented as indices.
events {torch.tensor} -- Indicator of event (1.) or censoring (0.).
Same length as 'idx_durations'.
interval_frac {torch.tensor} -- Fraction of last interval before event/censoring.
reduction {string} -- How to reduce the loss.
'none': No reduction.
'mean': Mean of tensor.
'sum: sum.
Returns:
torch.tensor -- The negative log-likelihood.
References:
[1] Håvard Kvamme and Ørnulf Borgan. Continuous and Discrete-Time Survival Prediction
with Neural Networks. arXiv preprint arXiv:1910.06724, 2019.
https://arxiv.org/pdf/1910.06724.pdf
"""
if events.dtype is torch.bool:
events = events.float()
idx_durations = idx_durations.view(-1, 1)
events = events.view(-1)
interval_frac = interval_frac.view(-1)
keep = idx_durations.view(-1) >= 0
phi = phi[keep, :]
idx_durations = idx_durations[keep, :]
events = events[keep]
interval_frac = interval_frac[keep]
# log_h_e = F.softplus(phi.gather(1, idx_durations).view(-1)).log().mul(events)
log_h_e = utils.log_softplus(phi.gather(
1, idx_durations).view(-1)).mul(events)
haz = F.softplus(phi)
scaled_h_e = haz.gather(1, idx_durations).view(-1).mul(interval_frac)
haz = utils.pad_col(haz, where='start')
sum_haz = haz.cumsum(1).gather(1, idx_durations).view(-1)
loss = -log_h_e.sub(scaled_h_e).sub(sum_haz)
return _reduction(loss, reduction)
def predict_pmf(self,
input,
batch_size=8224,
numpy=None,
eval_=True,
to_cpu=False,
num_workers=0):
if not self.scheme in ['const_pdf', 'lin_surv']:
raise NotImplementedError
pmf = self.model.predict_pmf(input, batch_size, False, eval_, to_cpu,
num_workers)
n, m = pmf.shape
pmf_cdi = pmf[:, 1:].contiguous().view(-1, 1).repeat(1, self.sub).div(
self.sub).view(n, -1)
pmf_cdi = utils.pad_col(pmf_cdi, where='start')
pmf_cdi[:, 0] = pmf[:, 0]
return tt.utils.array_or_tensor(pmf_cdi, numpy, input)
def nll_pmf(phi: Tensor,
idx_durations: Tensor,
events: Tensor,
reduction: str = 'mean',
epsilon: float = 1e-7) -> Tensor:
"""Negative log-likelihood for the PMF parametrized model [1].
Arguments:
phi {torch.tensor} -- Estimates in (-inf, inf), where pmf = somefunc(phi).
idx_durations {torch.tensor} -- Event times represented as indices.
events {torch.tensor} -- Indicator of event (1.) or censoring (0.).
Same length as 'idx_durations'.
reduction {string} -- How to reduce the loss.
'none': No reduction.
'mean': Mean of tensor.
'sum: sum.
Returns:
torch.tensor -- The negative log-likelihood.
References:
[1] Håvard Kvamme and Ørnulf Borgan. Continuous and Discrete-Time Survival Prediction
with Neural Networks. arXiv preprint arXiv:1910.06724, 2019.
https://arxiv.org/pdf/1910.06724.pdf
"""
if phi.shape[1] <= idx_durations.max():
raise ValueError(
f"Network output `phi` is too small for `idx_durations`." +
f" Need at least `phi.shape[1] = {idx_durations.max().item()+1}`,"
+ f" but got `phi.shape[1] = {phi.shape[1]}`")
if events.dtype is torch.bool:
events = events.float()
events = events.view(-1)
idx_durations = idx_durations.view(-1, 1)
phi = utils.pad_col(phi)
gamma = phi.max(1)[0]
cumsum = phi.sub(gamma.view(-1, 1)).exp().cumsum(1)
sum_ = cumsum[:, -1]
part1 = phi.gather(1, idx_durations).view(-1).sub(gamma).mul(events)
part2 = -sum_.relu().add(epsilon).log()
part3 = sum_.sub(cumsum.gather(
1, idx_durations).view(-1)).relu().add(epsilon).log().mul(1. - events)
# need relu() in part3 (and possibly part2) because cumsum on gpu has some bugs and we risk getting negative numbers.
loss = -part1.add(part2).add(part3)
return _reduction(loss, reduction)
def rank_loss_deephit_single(phi: Tensor,
idx_durations: Tensor,
events: Tensor,
rank_mat: Tensor,
sigma: Tensor,
reduction: str = 'mean') -> Tensor:
"""Rank loss proposed by DeepHit authors [1] for a single risks.
Arguments:
pmf {torch.tensor} -- Matrix with probability mass function pmf_ij = f_i(t_j)
y {torch.tensor} -- Matrix with indicator of duration and censoring time.
rank_mat {torch.tensor} -- See pair_rank_mat function.
sigma {float} -- Sigma from DeepHit paper, chosen by you.
Arguments:
phi {torch.tensor} -- Predictions as float tensor with shape [batch, n_durations]
all in (-inf, inf).
idx_durations {torch.tensor} -- Int tensor with index of durations.
events {torch.tensor} -- Float indicator of event or censoring (1 is event).
rank_mat {torch.tensor} -- See pair_rank_mat function.
sigma {float} -- Sigma from DeepHit paper, chosen by you.
Keyword Arguments:
reduction {string} -- How to reduce the loss.
'none': No reduction.
'mean': Mean of tensor.
'sum': sum.
Returns:
torch.tensor -- Rank loss.
References:
[1] Changhee Lee, William R Zame, Jinsung Yoon, and Mihaela van der Schaar. Deephit: A deep learning
approach to survival analysis with competing risks. In Thirty-Second AAAI Conference on Artificial
Intelligence, 2018.
http://medianetlab.ee.ucla.edu/papers/AAAI_2018_DeepHit
"""
idx_durations = idx_durations.view(-1, 1)
# events = events.float().view(-1)
pmf = utils.pad_col(phi).softmax(1)
y = torch.zeros_like(pmf).scatter(1, idx_durations, 1.) # one-hot
rank_loss = _rank_loss_deephit(pmf, y, rank_mat, sigma, reduction)
return rank_loss
def test_pad_col_start(val):
x = torch.ones((2, 3))
x_pad = pad_col(x, val, where='start')
pad = torch.ones(2, 1) * val
assert (x_pad == torch.cat([pad, x], dim=1)).all()
def test_pad_col_end(val):
x = torch.ones((2, 3))
x_pad = pad_col(x, val)
pad = torch.ones(2, 1) * val
assert (x_pad == torch.cat([x, pad], dim=1)).all()
