Epistemic Neural Networks

A library for uncertainty representation and training in neural networks.

Introduction

Many applications in deep learning requires or benefit from going beyond a point estimte and representing uncertainty about the model. The coherent use of Bayes’ rule and probability theory are the gold standard for updating beliefs and estimating uncertainty. But exact computation quickly becomes infeasible for even simple problems. Modern machine learning has developed an effective toolkit for learning in high-dimensional using a simple and coherent convention. Epistemic neural network (ENN) is a library that provides a similarly simple and coherent convention for defining and training neural networks that represent uncertainty over a hypothesis class of models.

Technical overview

In a supervised setting, For input x_i ∈ X and outputs y_i ∈ Y a point estimate f_θ(x) is trained by fitting the observed data D = {(xi, yi) for i = 1, ..., N} by minimizing a loss function l(θ, D) ∈ R. In epistemic neural networks we introduce the concept of an epistemic index z ∈ I ⊆ R^{n_z} distributed according to some reference distribution p_z(·). An augmented epistemic function approximator then takes the form f_θ(x, z); where the function class fθ(·, z) is a neural network. The index z allows unambiguous identification of a corresponding function value and sampling z corresponds to sampling from the hypothesis class of functions.

On some level, ENNs are purely a notational convenience and most existing approaches to dealing with uncertainty in deep learning can be rephrased in this way. For example, an ensemble of point estimates {f_θ1, ..., f_θK } can be viewed as an ENN with θ = (θ1, .., θK), z ∈ {1, .., K}, and f_θ(x, z) := f_θz(x). However, this simplicity hides a deeper insight: that the process of epistemic update itself can be tackled through the tools of machine learning typically reserved for point estimates, through the addition of this epistemic index. Further, since these machine learning tools were explicitly designed to scale to large and complex problems, they might provide tractable approximations to large scale Bayesian inference even where the exact computations are intractable.

For a more comprehensive overview, see the accompanying paper.

Reproducing NeurIPS experiments

To reproduce the experiments from our paper please see experiments/neurips_2021.

Getting started

You can get started in our colab tutorial without installing anything on your machine.

Installation

We have tested ENN on Python 3.7. To install the dependencies:

1. Optional: We recommend using a Python virtual environment to manage your dependencies, so as not to clobber your system installation:

   python3 -m venv enn
   source enn/bin/activate
   pip install --upgrade pip setuptools

2. Install ENN directly from github:

   pip install git+https://github.com/deepmind/enn

3. Test that you can load ENN by training a simple ensemble ENN.

   from acme.utils.loggers.terminal import TerminalLogger
   
   from enn import losses
   from enn import networks
   from enn import supervised
   from enn.supervised import regression_data
   import optax
   
   # A small dummy dataset
   dataset = regression_data.make_dataset()
   
   # Logger
   logger = TerminalLogger('supervised_regression')
   
   # ENN
   enn = networks.MLPEnsembleMatchedPrior(
       output_sizes=[50, 50, 1],
       num_ensemble=10,
   )
   
   # Loss
   loss_fn = losses.average_single_index_loss(
       single_loss=losses.L2LossWithBootstrap(),
       num_index_samples=10
   )
   
   # Optimizer
   optimizer = optax.adam(1e-3)
   
   # Train the experiment
   experiment = supervised.Experiment(
       enn, loss_fn, optimizer, dataset, seed=0, logger=logger)
   experiment.train(FLAGS.num_batch)

More examples can be found in the colab tutorial.

4. Optional: run the tests by executing ./test.sh from ENN root directory.

Citing

If you use ENN in your work, please cite the accompanying paper:

@inproceedings{,
    title={Epistemic Neural Networks},
    author={Ian Osband, Zheng Wen, Mohammad Asghari, Morteza Ibrahimi, Xiyuan Lu, Benjamin Van Roy},
    booktitle={arxiv},
    year={2021},
    url={https://arxiv.org/abs/2107.08924}
}