laplace-torch 0.1a2

laplace - Laplace approximations for deep learning

The laplace package facilitates the application of Laplace approximations for entire neural networks, subnetworks of neural networks, or just their last layer. The package enables posterior approximations, marginal-likelihood estimation, and various posterior predictive computations. The library documentation is available at https://aleximmer.github.io/Laplace.

There is also a corresponding paper, Laplace Redux — Effortless Bayesian Deep Learning, which introduces the library, provides an introduction to the Laplace approximation, reviews its use in deep learning, and empirically demonstrates its versatility and competitiveness. Please consider referring to the paper when using our library:

@inproceedings{laplace2021,
  title={Laplace Redux--Effortless {B}ayesian Deep Learning},
  author={Erik Daxberger and Agustinus Kristiadi and Alexander Immer 
          and Runa Eschenhagen and Matthias Bauer and Philipp Hennig},
  booktitle={{N}eur{IPS}},
  year={2021}
}

Setup

We assume python3.8 since the package was developed with that version. To install laplace with pip, run the following:

pip install laplace-torch

For development purposes, clone the repository and then install:

# or after cloning the repository for development
pip install -e .
# run tests
pip install -e .[tests]
pytest tests/

Structure

The laplace package consists of two main components:

1. The subclasses of laplace.BaseLaplace that implement different sparsity structures: different subsets of weights ('all', 'subnetwork' and 'last_layer') and different structures of the Hessian approximation ('full', 'kron', 'lowrank' and 'diag'). This results in eight currently available options: laplace.FullLaplace, laplace.KronLaplace, laplace.DiagLaplace, the corresponding last-layer variations laplace.FullLLLaplace, laplace.KronLLLaplace, and laplace.DiagLLLaplace (which are all subclasses of laplace.LLLaplace), laplace.SubnetLaplace (which only supports a 'full' Hessian approximation) and laplace.LowRankLaplace (which only supports inference over 'all' weights). All of these can be conveniently accessed via the laplace.Laplace function.
2. The backends in laplace.curvature which provide access to Hessian approximations of the corresponding sparsity structures, for example, the diagonal GGN.

Additionally, the package provides utilities for decomposing a neural network into feature extractor and last layer for LLLaplace subclasses (laplace.utils.feature_extractor) and effectively dealing with Kronecker factors (laplace.utils.matrix).

Finally, the package implements several options to select/specify a subnetwork for SubnetLaplace (as subclasses of laplace.utils.subnetmask.SubnetMask). Automatic subnetwork selection strategies include: uniformly at random (laplace.utils.subnetmask.RandomSubnetMask), by largest parameter magnitudes (LargestMagnitudeSubnetMask), and by largest marginal parameter variances (LargestVarianceDiagLaplaceSubnetMask and LargestVarianceSWAGSubnetMask). In addition to that, subnetworks can also be specified manually, by listing the names of either the model parameters (ParamNameSubnetMask) or modules (ModuleNameSubnetMask) to perform Laplace inference over.

Extendability

To extend the laplace package, new BaseLaplace subclasses can be designed, for example, Laplace with a block-diagonal Hessian structure. One can also implement custom subnetwork selection strategies as new subclasses of SubnetMask.

Alternatively, extending or integrating backends (subclasses of curvature.curvature) allows to provide different Hessian approximations to the Laplace approximations. For example, currently the curvature.BackPackInterface based on BackPACK and curvature.AsdlInterface based on ASDL are available. The curvature.AsdlInterface provides a Kronecker factored empirical Fisher while the curvature.BackPackInterface does not, and only the curvature.BackPackInterface provides access to Hessian approximations for a regression (MSELoss) loss function.

Example usage

Post-hoc prior precision tuning of diagonal LA

In the following example, a pre-trained model is loaded, then the Laplace approximation is fit to the training data (using a diagonal Hessian approximation over all parameters), and the prior precision is optimized with cross-validation 'CV'. After that, the resulting LA is used for prediction with the 'probit' predictive for classification.

from laplace import Laplace

# Pre-trained model
model = load_map_model()  

# User-specified LA flavor
la = Laplace(model, 'classification',
             subset_of_weights='all',
             hessian_structure='diag')
la.fit(train_loader)
la.optimize_prior_precision(method='CV', val_loader=val_loader)

# User-specified predictive approx.
pred = la(x, link_approx='probit')

Differentiating the log marginal likelihood w.r.t. hyperparameters

The marginal likelihood can be used for model selection [10] and is differentiable for continuous hyperparameters like the prior precision or observation noise. Here, we fit the library default, KFAC last-layer LA and differentiate the log marginal likelihood.

from laplace import Laplace

# Un- or pre-trained model
model = load_model()  

# Default to recommended last-layer KFAC LA:
la = Laplace(model, likelihood='regression')
la.fit(train_loader)

# ML w.r.t. prior precision and observation noise
ml = la.log_marginal_likelihood(prior_prec, obs_noise)
ml.backward()

Applying the LA over only a subset of the model parameters

This example shows how to fit the Laplace approximation over only a subnetwork within a neural network (while keeping all other parameters fixed at their MAP estimates), as proposed in [11]. It also exemplifies different ways to specify the subnetwork to perform inference over.

from laplace import Laplace

# Pre-trained model
model = load_model()

# Examples of different ways to specify the subnetwork
# via indices of the vectorized model parameters
#
# Example 1: select the 128 parameters with the largest magnitude
from laplace.utils import LargestMagnitudeSubnetMask
subnetwork_mask = LargestMagnitudeSubnetMask(model, n_params_subnet=128)
subnetwork_indices = subnetwork_mask.select()

# Example 2: specify the layers that define the subnetwork
from laplace.utils import ModuleNameSubnetMask
subnetwork_mask = ModuleNameSubnetMask(model, module_names=['layer.1', 'layer.3'])
subnetwork_mask.select()
subnetwork_indices = subnetwork_mask.indices

# Example 3: manually define the subnetwork via custom subnetwork indices
import torch
subnetwork_indices = torch.tensor([0, 4, 11, 42, 123, 2021])

# Define and fit subnetwork LA using the specified subnetwork indices
la = Laplace(model, 'classification',
             subset_of_weights='subnetwork',
             hessian_structure='full',
             subnetwork_indices=subnetwork_indices)
la.fit(train_loader)

Documentation

The documentation is available here or can be generated and/or viewed locally:

# assuming the repository was cloned
pip install -e .[docs]
# create docs and write to html
bash update_docs.sh
# .. or serve the docs directly
pdoc --http 0.0.0.0:8080 laplace --template-dir template

References

This package relies on various improvements to the Laplace approximation for neural networks, which was originally due to MacKay [1]. Please consider citing the respective papers if you use any of their proposed methods via our laplace library.

• [1] MacKay, DJC. A Practical Bayesian Framework for Backpropagation Networks. Neural Computation 1992.
• [2] Gibbs, M. N. Bayesian Gaussian Processes for Regression and Classification. PhD Thesis 1997.
• [3] Snoek, J., Rippel, O., Swersky, K., Kiros, R., Satish, N., Sundaram, N., Patwary, M., Prabhat, M., Adams, R. Scalable Bayesian Optimization Using Deep Neural Networks. ICML 2015.
• [4] Ritter, H., Botev, A., Barber, D. A Scalable Laplace Approximation for Neural Networks. ICLR 2018.
• [5] Foong, A. Y., Li, Y., Hernández-Lobato, J. M., Turner, R. E. 'In-Between' Uncertainty in Bayesian Neural Networks. ICML UDL Workshop 2019.
• [6] Khan, M. E., Immer, A., Abedi, E., Korzepa, M. Approximate Inference Turns Deep Networks into Gaussian Processes. NeurIPS 2019.
• [7] Kristiadi, A., Hein, M., Hennig, P. Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks. ICML 2020.
• [8] Immer, A., Korzepa, M., Bauer, M. Improving predictions of Bayesian neural nets via local linearization. AISTATS 2021.
• [9] Sharma, A., Azizan, N., Pavone, M. Sketching Curvature for Efficient Out-of-Distribution Detection for Deep Neural Networks. UAI 2021.
• [10] Immer, A., Bauer, M., Fortuin, V., Rätsch, G., Khan, EM. Scalable Marginal Likelihood Estimation for Model Selection in Deep Learning. ICML 2021.
• [11] Daxberger, E., Nalisnick, E., Allingham, JU., Antorán, J., Hernández-Lobato, JM. Bayesian Deep Learning via Subnetwork Inference. ICML 2021.