Adaptive Sampling

The project is created to distribute code written as part of my master thesis entitled: Adaptive Markov Chain Monte Carlo for Bayesian Inference.

Adaptive Markov Chain Monte Carlo (MCMC) and stochastic optimization methods are techniques for evaluating intractable integrals. Code for sampling and optimization algorithms, as found in their original papers, has been written in Python and tested against established benchmarks. In addition, an improvement has been made by incorporating adaptation into stochastic optimization methods, thereby transforming them into samplers. Namely, Gaussian Adaptation (GaA) and Covariance Matrix Adaptation Evolution strategy(CMA-ES) optimizers have been transformed into the Metropolis-GaA, and (1 + 1) CMA, respectively. Performance is quantified using existing convergence and performance measuring tools. Results show adaptive MCMCs with better convergence, mixing, and acceptance ratios.

Getting Started

You will need Jupyter notebook with Python 3 and the modules listed below. For detailed information and examples of experiment runs, see Adaptive_MCMC_for_Bayesian_Inference.pdf, Chapter 6: Experiments.

Python modules:

Five sampler modules

• Adaptive Metropolis: AM_Sampling.py
• Covariance Matrix Adaptation: CMA_Sampling.py
• Gaussian Adaptation: GaA_Sampling.py
• Metropolis Hastings: MH_Sampling.py
• Adaptive MH using Cholesky decomposition of the covariance: L_MH_Sampling.py

Test suite module

• Test suites found in Haario et al. (1999): TestSuite.py

Supporting modules

• FileHandling.py
• Visualization.py

Comparing samplers via autocorrelation

Running the tests

The module Experiments.ipynb offers an easy way to run any of the five samplers and plot their results.

Open the Experiments module in a Jupyter notebook. You will also need the supporting and test modules imported, along with the required libraries as specified in Experiments.ipynb.

Example

To run the Adaptive Metropolis sampler, type AM instead of the current sampler CMA. Sampler names are found in Experiments.ipynb under The Samplers.

In this case, the code:

SPEC = specify_run(dim=2, N=10000, name_target='Pi_4', name_sampler='CMA', run_idx=0)
DATA = execute_run(SPEC)

becomes:

SPEC = specify_run(dim=2, N=10000, name_target='Pi_4', name_sampler='AM', run_idx=0)
DATA = execute_run(SPEC)

Also, you might want to change the target distribution. To do so, you need to change name_target For reference, see Adaptive_MCMC_for_Bayesian_Inference.pdf Chapter 6.

Biased coin example

Built With

• Jupyter - Jupyter Notebooks
• PyMC3 - Bayesian statistical modeling and Probabilistic Machine Learning focusing on advanced MCMC

Authors

• Prof. Dr. Bernard Manderik - Initial work

Acknowledgments

• Hat tip to Nixon Kipkorir Ronoh and Edna Chelangat Milgo