  We propose a general algorithmic framework for Bayesian model selection. A
spike-and-slab Laplacian prior is introduced to model the underlying structural
assumption. Using the notion of effective resistance, we derive an EM-type
algorithm with closed-form iterations to efficiently explore possible
candidates for Bayesian model selection. The deterministic nature of the
proposed algorithm makes it more scalable to large-scale and high-dimensional
data sets compared with existing stochastic search algorithms. When applied to
sparse linear regression, our framework recovers the EMVS algorithm [Rockova
and George, 2014] as a special case. We also discuss extensions of our
framework using tools from graph algebra to incorporate complex Bayesian models
such as biclustering and submatrix localization. Extensive simulation studies
and real data applications are conducted to demonstrate the superior
performance of our methods over its frequentist competitors such as $\ell_0$ or
$\ell_1$ penalization.
