Installation | Quickstart | Methods | Friends | Contributing | Citation | Documentation | Paper

What is posteriors?

General purpose python library for uncertainty quantification with PyTorch.

• Composable: Use with transformers, lightning, torchopt, torch.distributions, pyro and more!
• Extensible: Add new methods! Add new models!
• Functional: Easier to test, closer to mathematics!
• Scalable: Big model? Big data? No problem!
• Swappable: Swap between algorithms with ease!

Installation

posteriors is available on PyPI and can be installed via pip:

pip install posteriors

Quickstart

posteriors is functional first and aims to be easy to use and extend. Let's try it out by training a simple model with variational inference:

from torchvision.datasets import MNIST
from torchvision.transforms import ToTensor
from torch import nn, utils, func
import torchopt
import posteriors

dataset = MNIST(root="./data", transform=ToTensor())
train_loader = utils.data.DataLoader(dataset, batch_size=32, shuffle=True)
num_data = len(dataset)

classifier = nn.Sequential(nn.Linear(28 * 28, 64), nn.ReLU(), nn.Linear(64, 10))
params = dict(classifier.named_parameters())


def log_posterior(params, batch):
    images, labels = batch
    images = images.view(images.size(0), -1)
    output = func.functional_call(classifier, params, images)
    log_post_val = (
        -nn.functional.cross_entropy(output, labels)
        + posteriors.diag_normal_log_prob(params) / num_data
    )
    return log_post_val, output


transform = posteriors.vi.diag.build(
    log_posterior, torchopt.adam(), temperature=1 / num_data
)  # Can swap out for any posteriors algorithm

state = transform.init(params)

for batch in train_loader:
    state, aux = transform.update(state, batch)

Observe that posteriors recommends specifying log_posterior and temperature such that log_posterior remains on the same scale for different batch sizes. posteriors algorithms are designed to be stable as temperature goes to zero.

Further, the output of log_posterior is a tuple containing the evaluation (single-element Tensor) and an additional argument (TensorTree) containing any auxiliary information we'd like to retain from the model call, here the model predictions. If you have no auxiliary information, you can simply return torch.tensor([]) as the second element. For more info see torch.func.grad (with has_aux=True) or the documentation.

Check out the tutorials for more detailed usage!

Methods

posteriors supports a variety of methods for uncertainty quantification, including:

• Extended Kalman filter
• Laplace approximation
• Stochastic gradient MCMC
• Variational inference

With full details available in the API documentation.

posteriors is designed to be easily extensible, if you're favorite method is not listed above, raise an issue and we'll see what we can do!

Friends

Interfaces seamlessly with:

• torch and in particular torch.func.
• torch.distributions for distributions and sampling, (note that it's typically required to set validate_args=False to conform with the control flows in torch.func).
• Functional and flexible torch optimizers from torchopt.
• transformers for pre-trained models.
• lightning for convenient training and logging, see examples/lightning_autoencoder.py.

The functional transform interface is strongly inspired by frameworks such as optax and blackjax.

As well as other UQ libraries fortuna, laplace, numpyro, pymc and uncertainty-baselines.

Contributing

You can report a bug or request a feature by creating a new issue on GitHub.

If you want to contribute code, please check the contributing guide.

Citation

If you use posteriors in your research, please cite the library using the following BibTeX entry:

@inproceedings{duffield2025scalable,
    title={Scalable Bayesian Learning with posteriors},
    author={Samuel Duffield and Kaelan Donatella and Johnathan Chiu and Phoebe Klett and Daniel Simpson},
    booktitle={The Thirteenth International Conference on Learning Representations},
    year={2025},
    url={https://openreview.net/forum?id=fifXzmzeGy}
}