Stable Truncated Gaussian

A differentiable implementation of the Truncated Gaussian (Normal) distribution using Python and Pytorch, which is numerically stable even when the μ parameter lies outside the interval [a,b] given by the bounds of the distribution. In this situation, a naive evaluation of the mean, variance and log-probability of the distribution could otherwise result in catastrophic cancellation. Our code is inspired by TruncatedNormal.jl and torch_truncnorm. Currently, we provide numerically-stable methods for calculating the mean, variance, log-probability, KL-divergence and sampling from the distribution. Our current implementation of icdf (which is used for sampling from the distribution) still needs some work for those situations where the [a,b] interval is small. For a comparison between our icdf implementation and the one provided by scipy, take a look at the images_cdf_comparison folder.

Installation

Simply install with pip:

pip install stable-trunc-gaussian

Example

Run the following code in Python:

from stable_trunc_gaussian import TruncatedGaussian as TG
from torch import tensor as t

# Create a Truncated Gaussian with mu=0, sigma=1, a=10, b=11
# Notice how mu is outside the interval [a,b]
dist = TG(t(0),t(1),t(10),t(11))

print("Mean:", dist.mean)
print("Variance:", dist.variance)
print("Log-prob(10.5):", dist.log_prob(t(10.5)))

Result:

Mean: tensor(10.0981)
Variance: tensor(0.0094)
Log-prob(10.5): tensor(-2.8126)

Parallel vs Sequential Implementation

The class obtained by doing from stable_trunc_gaussian import TruncatedGaussian corresponds to a parallel implementation of the truncated gaussian, which makes possible to obtain several values (mean, variance and log-probs) in parallel. In case you are only interested in computing values sequentially, i.e., one at a time, we also provide a sequential implementation which results more efficient only for this case. In order to use this sequential implementation, simply do from stable_trunc_gaussian import SeqTruncatedGaussian. Here is an example:

from stable_trunc_gaussian import TruncatedGaussian, SeqTruncatedGaussian
from torch import tensor as t

# Parallel computation
means = TruncatedGaussian(t([0,0.5]),t(1,1),t(-1,2),t(1,5)).mean

# Sequential computation
# Note: the 'TruncatedGaussian' class can also be used for this sequential case
mean_0 = SeqTruncatedGaussian(t([0]),t(1),t(-1),t(1)).mean
mean_1 = SeqTruncatedGaussian(t([0.5]),t(1),t(2),t(5)).mean

Acknowledgements

We want to thank users KFrank and ptrblck for their help in solving the bug when computing the gradients for the parallel version (bug solved in version 1.1.1).