  We develop a flexible framework for low-rank matrix estimation that allows us
to transform noise models into regularization schemes via a simple bootstrap
algorithm. Effectively, our procedure seeks an autoencoding basis for the
observed matrix that is stable with respect to the specified noise model; we
call the resulting procedure a stable autoencoder. In the simplest case, with
an isotropic noise model, our method is equivalent to a classical singular
value shrinkage estimator. For non-isotropic noise models, e.g., Poisson noise,
the method does not reduce to singular value shrinkage, and instead yields new
estimators that perform well in experiments. Moreover, by iterating our stable
autoencoding scheme, we can automatically generate low-rank estimates without
specifying the target rank as a tuning parameter.
