  A common strategy for sparse linear regression is to introduce
regularization, which eliminates irrelevant features by letting the
corresponding weights be zeros. However, regularization often shrinks the
estimator for relevant features, which leads to incorrect feature selection.
Motivated by the above-mentioned issue, we propose Bayesian masking (BM), a
sparse estimation method which imposes no regularization on the weights. The
key concept of BM is to introduce binary latent variables that randomly mask
features. Estimating the masking rates determines the relevance of the features
automatically. We derive a variational Bayesian inference algorithm that
maximizes the lower bound of the factorized information criterion (FIC), which
is a recently developed asymptotic criterion for evaluating the marginal
log-likelihood. In addition, we propose reparametrization to accelerate the
convergence of the derived algorithm. Finally, we show that BM outperforms
Lasso and automatic relevance determination (ARD) in terms of the
sparsity-shrinkage trade-off.
