NeuralBayesianNetworks (NBN)

PyTorch-native Bayesian networks with neural conditional distributions and GPU-batched inference.

NBN represents a Bayesian network over a known DAG as an nn.Module. Each node holds a learnable conditional distribution P(X | parents(X)), called a mechanism: a probability table, a linear-Gaussian model, a mixture density network or a normalising flow. You fit the network from data, then answer conditional and interventional queries. Thousands of queries run as one batched tensor operation on CUDA, on Apple-Silicon GPUs (mps) or on the CPU.

• One API for discrete, continuous and hybrid networks. Mixed discrete/continuous networks with non-Gaussian continuous nodes are a first-class case.
• Swappable mechanisms. Every mechanism is an nn.Module behind the same interface, from closed-form tables to neural density estimators.
• Batched inference. query_batch answers B queries with different evidence in one call: exact variable elimination for discrete networks, likelihood weighting elsewhere, picked automatically.
• Causal queries. do= interventions work in every engine and can vary per batch row.
• Autograd-friendly. Likelihoods and samples are differentiable, so NBN composes with your own PyTorch models.
• Reproducible benchmarks. A suite (nbn-bench) compares NBN with pgmpy, pomegranate and Pyro on networks with known ground truth.

Contents

• Installation: Linux · macOS · from source
• Quick start
• Core concepts
• Hardware acceleration
• Benchmark highlights
• Running the benchmarks
• Development
• Citing NBN · License

Installation

NBN needs Python ≥ 3.10 and PyTorch ≥ 2.2. The PyPI package is nbn, and so is the import name.

pip install nbn                  # core library
pip install "nbn[neural]"        # + normalising flows (zuko)
pip install "nbn[all]"           # + benchmark suite and every baseline library

Using a virtual environment is recommended.

Linux

python3 -m venv .venv && source .venv/bin/activate
pip install -U pip
pip install "nbn[neural]"

For an NVIDIA GPU, install a CUDA build of PyTorch first by following the selector at pytorch.org. After that, pip install nbn keeps the build you have. Check it with:

python -c "import torch; print(torch.cuda.is_available())"   # True

macOS (Apple Silicon and Intel)

On Apple-Silicon Macs (M1 and later), NBN uses the GPU through PyTorch's Metal backend (mps). The standard PyPI PyTorch wheel includes it, so there is nothing extra to install and nothing to configure.

1. Get Python ≥ 3.10. macOS does not ship a usable one. Check with python3 --version, and if it is missing or older, install it with either:

brew install python@3.12        # Homebrew (https://brew.sh)

or the official installer from python.org. On macOS the command is python3 (Homebrew also provides python3.12), and there is no plain python until you activate a virtual environment.

2. Create a virtual environment and install NBN.

python3 -m venv .venv
source .venv/bin/activate
pip install -U pip
pip install "nbn[neural]"        # or "nbn[all]" for the benchmark suite

3. Check that the GPU is visible.

python -c "import torch; print(torch.backends.mps.is_available())"   # True

With the bench extra, nbn-bench check-env checks the whole environment. It ends with a line like platform darwin; accelerator mps (Apple Metal; float64 unavailable, accumulations run in float32).

Intel Macs run NBN on the CPU. PyTorch stopped publishing Intel-macOS wheels after 2.2, so pip installs torch 2.2.x there. If you then see a NumPy ABI error, run pip install "numpy<2".

From source

git clone https://github.com/Giovannibriglia/NeuralBayesianNetworks.git
cd NeuralBayesianNetworks
python3 -m venv .venv && source .venv/bin/activate
pip install -U pip
pip install -e ".[dev,all]"
pytest -m "not slow"             # fast test suite

Quick start

import torch
from nbn import NeuralBayesianNetwork

# Rain → WetGrass ← Sprinkler, and WetGrass → SoilMoisture (continuous)
model = NeuralBayesianNetwork(
    [("Rain", "WetGrass"), ("Sprinkler", "WetGrass"), ("WetGrass", "SoilMoisture")],
    variables={
        "Rain": ("discrete", 2),
        "Sprinkler": ("discrete", 2),
        "WetGrass": ("discrete", 2),
        "SoilMoisture": ("continuous", 1),
    },
    device="auto",  # cuda > mps (Apple Silicon) > cpu
)

# Toy data from a known process
n = 10_000
rain = torch.bernoulli(torch.full((n,), 0.3)).long()
sprinkler = torch.bernoulli(torch.full((n,), 0.4)).long()
wet = ((rain | sprinkler).bool() & (torch.rand(n) < 0.9)).long()
soil = (2.0 * wet + 0.5 * torch.randn(n)).unsqueeze(-1)
data = {"Rain": rain, "Sprinkler": sprinkler, "WetGrass": wet, "SoilMoisture": soil}

model.auto_mechanisms()  # tables for discrete nodes, mixture density networks for continuous
model.fit(data)

# P(Rain | WetGrass = 1)                     ≈ [0.48, 0.52]
print(model.query(["Rain"], evidence={"WetGrass": 1}))

# 1,024 conditional queries in one batched call → shape [1024, 2]
evidence = {"WetGrass": torch.randint(0, 2, (1024,))}
print(model.query_batch(["Rain"], evidence).shape)

# Intervention: P(WetGrass | do(Sprinkler = 1)) ≈ [0.10, 0.90]
print(model.query(["WetGrass"], do={"Sprinkler": 1}))

# Ancestral samples and the (differentiable) log-likelihood of data
samples = model.sample(5)
print(model.log_prob(data).mean())

To choose a mechanism per node instead of auto_mechanisms(), call model.set_mechanism("SoilMoisture", LinearGaussianMechanism()) (all mechanisms import from nbn) before fit. More end-to-end examples (continuous, hybrid, neural, interventional) are in tests/integration/.

Core concepts

Network. NeuralBayesianNetwork(edges, variables, device=...) holds the DAG, the variable types (("discrete", cardinality) or ("continuous", dim)) and one mechanism per node. The main methods are fit (all mechanisms, node by node), update (fold in new data without retraining), query / query_batch, sample, log_prob and intervene.

Mechanisms (nbn.mechanisms) are the conditional distributions:

Inference engines (nbn.inference):

Pass engine= to query / query_batch to override the default.

Gradients. log_prob and sample (including sample(n, do=...)) are differentiable with respect to the parameters, and parent values or do= values computed by your own nn.Module carry gradients back into it. query / query_batch are not differentiable (VE detaches at factor build; likelihood weighting runs under inference_mode). intervene() returns a deep copy for querying. To get gradients through an intervention, use sample(n, do=...).

Snapshotting. To revert an optimisation step, copy the state dict: snap = copy.deepcopy(mech.state_dict()). A plain state_dict() shares storage with the live parameters, so an optimiser step silently changes the snapshot too.

Hardware acceleration

device="auto" (the default for models, nbn-bench --device and YAML configs) picks CUDA, then MPS (Apple Silicon), then CPU. The results are the same on every backend, up to floating-point precision and Monte-Carlo noise.

On MPS, NBN works around the Metal backend's gaps for you:

• No float64 on Metal. Sufficient statistics (counts, normal equations, weighted moments) accumulate in float32 on mps and in float64 elsewhere.
• No linalg.lstsq kernel. The small closed-form Gaussian solves run on the CPU. They are [D_pa+1, D_pa+1] matrices, so this costs nothing.
• Other missing kernels. import nbn sets PYTORCH_ENABLE_MPS_FALLBACK=1 on macOS unless you have set it. Any op a dependency needs that Metal lacks then runs on the CPU with a one-time warning instead of failing. Set it to 0 before importing to opt out.

When the GPU helps. GPUs pay off on large batches: many queries per query_batch call, large training sets, wide networks. A toy network like the quick start is often faster on device="cpu", because kernel-launch overhead dominates. CI runs the full test suite on Linux and on an Apple-Silicon macOS runner, where the device-parametrised tests use a real mps device.

Benchmark highlights

These numbers come from the paper-data run at tag v0.6c-d (RTX 4070 Laptop GPU, 5 seeds, networks of 10–1000 nodes). The full tables and the list of cells that did not finish are in docs/v0.6c-d/run_summary.md.

Pyro's importance sampler was added as a hybrid baseline after that run. Numbers vary within Monte-Carlo noise across hardware.

Running the benchmarks

pip install -U "nbn[all]" && nbn-bench check-env          # must print "environment OK"
nbn-bench inference --config nbn/bench/configs/synthetic/smoke_tests/inference_smoke.yaml
nbn-bench plot results/benchmark_synthetic_smoke_<timestamp> --output-dir results/figures

The configs, metrics, the paper-scale runs (scripts/run_all_benchmarks.sh), the figures and how to reproduce the published numbers are documented in docs/BENCHMARKS.md. Colab notebooks for each paper-scale benchmark are in notebooks/.

Development

pip install -e ".[dev,all]"
pytest -m "not slow"                  # fast suite
pytest                                # everything (slow tests download bnlearn networks)
ruff check nbn/ tests/ scripts/ && mypy nbn/core nbn/mechanisms

Repository layout:

nbn/                 the library: core/, mechanisms/, inference/, learning/, sampling/, update/
nbn/bench/           benchmark suite: runner, baseline adapters, configs, bnlearn data
tests/               unit and integration tests
notebooks/           Colab notebooks for the paper-scale benchmarks
scripts/             run_all_benchmarks.sh and other helpers
docs/                benchmark guide, design notes and audits

Releases are cut by pushing a v* tag; .github/workflows/publish.yml builds and uploads to PyPI. Known limitations and the roadmap are tracked in the issues.

Citing NBN

If you use NBN in your research, please cite the software:

@software{briglia_nbn,
  author  = {Briglia, Giovanni},
  title   = {{NeuralBayesianNetworks}: PyTorch-native Bayesian networks with neural mechanisms and GPU-batched inference},
  url     = {https://github.com/Giovannibriglia/NeuralBayesianNetworks},
  license = {Apache-2.0}
}

License

Apache License 2.0. See LICENSE.