Bayesian Quadrature

bayesian_quadrature is a Python library for Bayesian quadrature methods.

• Documentation
• GitHub Repository

API Documentation

• Bayesian Quadrature (BQ) object
• Utilities
• Cython module: bq_c
• Cython module: gauss_c
• Cython module: linalg_c
• Cython module: util_c

Tests

• Visual and analytic solution comparison
  • int_K
  • int_K1_K2
  • int_int_K1_K2_K1
  • int_int_K1_K2
  • int_int_K
  • Mean of Z
  • Variance of Z
• Unit tests
  • Tests for bq.py
  • Tests for bq_c.pyx
  • Tests for util.py
  • Testing utilities

Examples

• Gaussian Kernel Example
• Periodic Kernel Example
• Active Sampling Example

Derivations

• Bayesian Quadrature: Mean Derivation
• Bayesian Quadrature: Variance Derivation
  • First integral
  • Second integral
• Bayesian Quadrature: Expected Variance

Bibliography

[OD12]

Osborne, M. A., Duvenaud, D., Garnett, R., Rasmussen, C. E., Roberts, S. J., & Ghahramani, Z. (2012). Active Learning of Model Evidence Using Bayesian Quadrature. Advances in Neural Information Processing Systems, 25.

[O13]

Osborne, M. A. (2013). Gaussian Identities.