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README.md

VBLinLogit example scripts

The files starting vb_linear provide examples for the use of variational Bayesian linear regression. The files starting in vb_logit provide examples for variational Bayesian logistic regression. Calling vb_examples results in running all example scripts in this folder.

The scripts vb_linear_example_highdim, vb_linear_example_modelsel, vb_linear_example_sparse, vb_logit_example_coeff, vb_logit_example_highdim and vb_logit_example_modelsel reproduce the figures in Variational Bayesian inference for linear and logistic regression, arxiv:1310.5438 [stat.ML].

Linear regression examples

  • vb_linear_example: demonstrates that variational Bayesian linear regression without and with ARD provides more robust fit than least-squares for datasets with uninformative dimensions.

  • vb_linear_example_highdim: shows how the Bayesian regularization inherit to variational Bayesian linear regression perform beneficial for high-dimensional datasets and few training examples per dimension.

  • vb_linear_example_sparse: more elaborate version of vb_linear_example which demonstrates that ARD is able to detect and ignore uninformative input dimensions, leading to overall better test-set predictions.

  • vb_linear_example_modelsel: demonstrates how to use the variational bound to comare a set of linear models of varying complexity, and choose the most adequate model for a given dataset.

Logistic regression examples

  • vb_logit_example: demonstrates that variational Bayesian logistic regression without and with ARD provides a more robust fit than linear discriminant analysis for datasets with uninformative dimensions.

  • vb_logit_example_coeff: similar to vb_logit_example, demonstrates the use variational Bayesian logistic regression to recover the correlations coefficients, and to compare the fits to linear discriminant analysis.

  • vb_logit_example_highdim: demonstrates that ARD is able to detect and ignore uninformative input dimensions, leading to overall better test-set predictions.

  • vb_logit_example_modelsel: demonstrates how to use the variational bound to comare a set of logistic models of varying complexity, and choose the most adequate model for a given dataset.