VBPCApy

Variational Bayesian PCA (Ilin & Raiko, 2010) with support for missing data, sparse masks, optional bias terms, and an orthogonal post-rotation to a PCA basis. The implementation follows the original MATLAB reference while adding Python-native APIs, fast C++ extensions, and runtime autotuning.

Documentation · API Reference · Tutorials

Statement of need

Missing values are common in scientific and industrial tabular datasets, but many analysis pipelines either impute first (masking uncertainty) or drop incomplete samples. VBPCApy models missingness directly and exposes posterior uncertainty outputs alongside reconstructions, enabling uncertainty-aware latent-factor analysis in a single reproducible Python API.

Installation

From PyPI (pre-built wheels for Python 3.11–3.14, Linux/macOS/Windows):

pip install vbpca-py

With plotting support:

pip install vbpca-py[plot]

See the installation guide for building from source and Eigen setup.

Quick start

import numpy as np
from vbpca_py import VBPCA

# 50 features, 200 samples
x = np.random.randn(50, 200)
mask = np.ones_like(x)  # 1 = observed, 0 = missing

model = VBPCA(n_components=5, maxiters=100)
scores = model.fit_transform(x, mask=mask)
recon = model.reconstruction_
var = model.variance_

More examples: quickstart, dense PCA tutorial, missing data & model selection, sparse data.

Features

• Dense or sparse data with explicit missing-entry masks
• Optional bias estimation and rotation to PCA-aligned solution
• Posterior covariances for scores and loadings; held-out probe RMS
• C++ extensions with runtime autotune for threading and memory
• Missing-aware preprocessing: one-hot, standard/minmax scaling, log, power, winsorize, auto-routing (AutoEncoder)
• Preflight data diagnostics via check_data() / DataReport
• scikit-learn-compatible estimator (fit/transform/inverse_transform, get_params/set_params, cloning) — scikit-learn is an optional dependency
• Model selection via select_n_components and cross_validate_components
• Configurable convergence: subspace angle, RMS/cost plateau, ELBO, curvature, composite rules, patience, with per-criterion enable/disable and custom ordering
• Convergence diagnostics (n_iter_, converged_, convergence_reason_, learning_curve_, best-probe state metadata) and calibrated predictive_variance_ (includes observation noise)
• recommend_config(n, p, priority) — regime-aware default hyperparameters from a surrogate trade study

See the concept guides and API reference for full details.

Development

git clone https://github.com/yoavram-lab/VBPCApy.git
cd VBPCApy
uv sync --extra dev --extra plot
just ci          # lint + typecheck + test
just docs-serve  # local docs preview

See CONTRIBUTING.md for guidelines.

Citation

If you use this package in your research, please cite:

@software{vbpca_py2026,
  author = {Macdonald, Joshua and Naim, Shany and Ram, Yoav},
  title = {{VBPCApy}: Variational Bayesian PCA with Missing Data Support},
  year = {2026},
  url = {https://github.com/yoavram-lab/VBPCApy},
  version = {0.4.2},
}

@article{ilin2010practical,
  title={Practical Approaches to Principal Component Analysis in the Presence of Missing Values},
  author={Ilin, Alexander and Raiko, Tapani},
  journal={Journal of Machine Learning Research},
  volume={11},
  pages={1957--2000},
  year={2010}
}

See CITATION.cff for machine-readable metadata.

License

MIT — see LICENSE.