fastrvm

A fast and clean implementation of the Relevance Vector Machine (RVM).

fastrvm implements the accelerated RVM training algorithm described in [3] in a high-performance C++ core and exposes scikit-learn-compatible Python wrappers for:

• RVR — relevance vector regression
• RVC — relevance vector classification

Key benefits

• Fast training and prediction due to the greedy learning algorithm and a tuned C++ linear-algebra core (Armadillo + Einsmallen for optimization).
• Sparse models that automatically select a small set of relevance vectors.
• scikit-learn-compatible Python wrappers: plug into pipelines, grid search, and common tooling.

Quick Start

Install the latest release from PyPI (wheels are provided for Ubuntu and macOS, Windows requires building from source):

pip install fastrvm

Regression example (RVR):

from fastrvm import RVR
from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from sklearn.metrics import r2_score

X, y = make_regression(n_samples=500, n_features=50, noise=0.1, random_state=0)
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)

model = RVR(kernel='linear', fit_intercept=True, max_iter=2000)
model.fit(X_train, y_train)
print('R2:', r2_score(y_test, model.predict(X_test)))

Classification example (RVC)

from fastrvm import RVC
from sklearn.datasets import make_classification
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import StandardScaler
from sklearn.model_selection import cross_val_score

X, y = make_classification(n_samples=300, n_features=50, n_informative=10, random_state=0)
clf = make_pipeline(StandardScaler(), RVC(kernel='rbf', gamma='scale', n_jobs=-1))
scores = cross_val_score(clf, X, y, cv=5, scoring='accuracy')
print('5-fold accuracy:', scores.mean())

Notes on the Python API

• Classes: RVR and RVC available from fastrvm.
• Estimator API: implements scikit-learn conventions (fit, predict, etc.).
• Kernel options: rbf, linear, poly, precomputed (scikit-learn-style names). Various kernel hyperparameters such as gamma, degree, and coef0 are supported.
• Multiclass classification: For efficiency reasons RVC uses a one-vs-rest classifier for multiclass classification.

See docs/fastrvm.md for a short reference doc.

Limitations of the RVM

While powerful and often very sparse, the RVM can be viewed as a finite, data-dependent Gaussian process (GP): the kernel is a weighted sum of basis functions centred on the training inputs (see Rasmussen and Williams, 2006, chapter 6.6). Because the prior then depends on the observed inputs and the kernel is degenerate (finite rank), this departs from a strict Bayesian GP interpretation. With localized bases (e.g., RBFs), predictions far from any relevance vector can become spuriously overconfident: both the mean and the predictive variance may collapse toward zero (or the estimated noise level) even in clear extrapolation regions. This behavior is a modeling artifact of the degenerate kernel—computationally attractive, but it can harm uncertainty quantification in out-of-support areas.

Installation from Source

For development install from source:

git clone https://github.com/brdav/fastrvm.git
cd fastrvm
python -m pip install -e '.[dev]'

Minimum build dependencies

• CMake >= 3.18
• Python >= 3.10 (development headers)
• C++17-capable compiler (clang, gcc, or MSVC)
• BLAS/LAPACK implementation (OpenBLAS, MKL, or Accelerate)

Note: Builds on Windows are untested in CI. You can attempt a Windows build but expect manual steps.

The C++ core (sparse Bayesian learning algorithm) can also be built independently:

cmake -S src/cpp -B build/cpp -DCMAKE_BUILD_TYPE=Release
cmake --build build/cpp --target sparsebayes -j

Citation

Key references:

1. Tipping, M. E. (2001). Sparse Bayesian Learning and the Relevance Vector Machine. Journal of Machine Learning Research, 1, 211–244.

2. Faul, A. C., & Tipping, M. E. (2002). Analysis of Sparse Bayesian Learning. In Advances in Neural Information Processing Systems 14 (NeurIPS 2002).

3. Tipping, M. E., & Faul, A. C. (2003). Fast Marginal Likelihood Maximisation for Sparse Bayesian Models. In Proceedings of the 4th International Workshop on Artificial Intelligence and Statistics (AISTATS). PMLR, 276–283.

This implementation follows the ideas and practical choices from the SparseBayes (v2.0) MATLAB package by Michael Tipping — see the SparseBayes v2.0 download page. Please cite [1] for the core algorithm and [3] for the marginal-likelihood acceleration where applicable.

License

MIT — see LICENSE for details.

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Questions, feature requests, or issues? Open an issue on GitHub.