|
Abstract:
|
Variable selection for structured covariates lying on an underlying known graph is a problem motivated by practical applications, and has been a topic of increasing interest, with the primary focus being on spike and slab type approaches. However, most of the existing methods are not scalable to high dimensional settings, for example, in genomic studies involving tens of thousands of genes lying on known pathways. We propose a Bayesian shrinkage approach which incorporates prior information by smoothing the shrinkage parameters, with the coefficients for two connected variables in the graph being encouraged to have a similar degree of shrinkage. We fit our model via a computationally efficient expectation maximization algorithm which is scalable to high dimensional settings (p =100000). Theoretical properties for fixed as well as increasing dimensions are established, even when the number of variables increases faster than the sample size. We demonstrate the advantages of our approach in terms of accuracy, computational speed, and scalability, via a simulation study, and apply the method to a real data example.
|
