BSS (Bayesian Structured Sparsity) documentation

Companion code for the paper

Bayesian Structured Sparsity from Gaussian Fields

Barbara E. Engelhardt, Ryan P. Adams

Substantial research on structured sparsity has contributed to analysis of many different applications. However, there have been few Bayesian procedures among this work. Here, we develop a Bayesian model for structured sparsity that uses a Gaussian process (GP) to share parameters of the sparsity-inducing prior in proportion to feature similarity as defined by an arbitrary positive definite kernel. For linear regression, this sparsity-inducing prior on regression coefficients is a relaxation of the canonical spike-and-slab prior that flattens the mixture model into a scale mixture of normals. This prior retains the explicit posterior probability on inclusion parameters — now with GP probit prior distributions — but enables tractable computation via elliptical slice sampling for the latent Gaussian field. We motivate development of this prior using the genomic application of association mapping, or identifying genetic variants associated with a continuous trait.

Our Bayesian structured sparsity model produced sparse results with substantially improved sensitivity and precision relative to comparable methods. Through simulations, we show that three properties are key to this improvement:

1. modeling structure in the covariates,
2. significance testing using the posterior probabilities of inclusion, and
3. model averaging.

We present results from applying this model to a large genomic dataset to demonstrate computational tractability.

Modules:

• bss
  • bss package

Indices and tables

• Index
• Module Index
• Search Page

References

[EA14]

Barbara E Engelhardt and Ryan P Adams. Bayesian structured sparsity from gaussian fields. arXiv preprint arXiv:1407.2235, 1:1–23, July 2014. arXiv:1407.2235.

[MA10]

Iain Murray and Ryan Prescott Adams. Slice sampling covariance hyperparameters of latent gaussian models. Advances in Neural Information Processing Systems, 2010. arXiv:1006.0868.

[MAM10]

Iain Murray, Ryan Prescott Adams, and David J.C. MacKay. Elliptical slice sampling. Proceedings of the 13th International Conference on Artificial Intelligence and Statistics, pages 541–548, 2010. arXiv:1001.0175.

[Nea03]

Radford M. Neal. Slice sampling. The Annals of Statistics, 31(3):705–767, 2003. URL: https://projecteuclid.org/euclid.aos/1056562461.