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Spatially referenced time series (i.e., spatiotemporal) datasets are ubiquitous in scientific, engineering, and business-intelligence applications. This repository contains an implementation of the Bayesian Neural Field (BayesNF), a spatiotemporal modeling method that integrates hierarchical Bayesian inference for accurate uncertainty estimation with deep neural networks for high-capacity function approximation.

BayesNF infer joint probability distributions over field values at arbitrary points in time and space, which makes the model suitable for many data-analysis tasks including spatial interpolation, temporal forecasting, and variography. Posterior inference is conducted using variationally learned surrogates trained via mini-batch stochastic gradient descent for handling large-scale data. The system is build on the JAX machine learning platform.

The probabilistic model and inference algorithm are described in the following paper:

Scalable spatiotemporal prediction with Bayesian neural fields. Feras Saad, Jacob Burnim, Colin Carroll, Brian Patton, Urs Köster, Rif A. Saurous, Matthew Hoffman. Nature Communications 15, 7942 (2024). https://doi.org/10.1038/s41467-024-51477-5

@article{
title     = {Scalable Spatiotemporal Prediction with {Bayesian} Neural Fields},
authors   = {Saad, Feras and Burnim, Jacob and Carroll, Colin and Patton, Brian and Köster, Urs  and Saurous, Rif A. and Hoffman, Matthew}
journal   = {Nature Communications},
volume    = {15},
issue     = {7942},
year      = {2024},
doi       = {10.1038/s41467-024-51477-5},
publisher = {Springer Nature},
}

bayesnf can be installed from the Python Package Index (PyPI) using:

$ python -m pip install bayesnf

The typical install time is 1 minute. This software is tested on Python 3.10 with a standard Debian GNU/Linux setup. The large-scale experiments in scripts/ were run using TPU v3-8 accelerators. To run BayesNF locally on medium to large-scale data, a GPU is required at minimum.

Installation into a virtual environment is highly recommended, using the following steps:

$ python -m venv pyenv
$ source pyenv/bin/activate
$ python -m pip install -U bayesnf

The versions of dependencies will depend on the Python version. Github Actions tests the software using Python 3.10. If encountering any version issues, please refer to the following file for the versions of libraries used in the test suite: requirements.Python3.10.14.txt. These specific versions can be installed into the virtual environment using the following command:

$ python -m pip install -r requirements.Python3.10.14.txt

Please visit https://google.github.io/bayesnf

# Load a dataframe with "long" format spatiotemporal data.
df_train = pd.read_csv('chickenpox.5.train.csv',
  index_col=0, parse_dates=['datetime'])

# Build a BayesianNeuralFieldEstimator
model = BayesianNeuralFieldMAP(
  width=256,
  depth=2,
  freq='W',
  seasonality_periods=['M', 'Y'],
  num_seasonal_harmonics=[2, 10],
  feature_cols=['datetime', 'latitude', 'longitude'],
  target_col='chickenpox',
  observation_model='NORMAL',
  timetype='index',
  standardize=['latitude', 'longitude'],
  interactions=[(0, 1), (0, 2), (1, 2)])

# Fit the model.
model = model.fit(
  df_train,
  seed=jax.random.PRNGKey(0),
  ensemble_size=ensemble_size,
  num_epochs=num_epochs)

# Make predictions of means and quantiles on test data.
df_test = pd.read_csv('chickenpox.5.test.csv',
  index_col=0, parse_dates=['datetime'])

yhat, yhat_quantiles = model.predict(df_test, quantiles=(0.025, 0.5, 0.975))