survival_distributions

This package extends the functionality of univariate distributions in torch.distributions by implementing several new methods:

• sf: survival function (complementary CDF)
• logsf: logarithm of the survival function (negative cumulative hazard function)
• logcdf: logarithm of the CDF
• log_hazard: logarithm of the hazard function (logarithm of the failure rate)
• isf: inverse of the survival function
• sample_cond: instead of sampling from the full support of the distribution, generate samples between lower_bound and upper_bound

This is especially useful when working with temporal point processes or survival analysis.

Naive implementation based on existing PyTorch functionality (e.g., torch.log(1.0 - dist.cdf(x)) for logsf) will often not be as accurate and numerically stable as the implementation provided by survival_distributions. Hopefully, these methods will be implemented in PyTorch sometime in the future, but this package provides an alternative for the time being.

See DISTRIBUTIONS.md for more details about the implemented functions and supported distributions.

Installation

1. Install the latest version of PyTorch.
2. Install survival_distributions

   pip install survival_distributions
   

Supported distributions

Numerically stable implementation

For these distributions we provide a numerically stable implementation of logsf.

• Exponential
• Logistic
• LogLogistic
• MixtureSameFamily
• TransformedDistribution
• Uniform
• Weibull

Naive implementation

For these distributions we implement logsf(x) as log(1.0 - dist.cdf(x)), which is less numerically stable.

• LogNormal
• Normal

Usage

The package provides a drop-in replacement for torch.distributions, so you can just modify your code as follows.

Old code

import torch

dist = torch.distributions.Exponential(rate=torch.tensor(2.0))
x = torch.tensor(1.5)

log_survival_proba = torch.log(1.0 - dist.cdf(x))

New code

import torch
import survival_distributions as sd

dist = sd.Exponential(rate=torch.tensor(2.0))
x = torch.tensor(1.5)

log_survival_proba = dist.logsf(x)