  Spatial Transformer Networks (STNs) estimate image transformations that can
improve downstream tasks by `zooming in' on relevant regions in an image.
However, STNs are hard to train and sensitive to mis-predictions of
transformations. To circumvent these limitations, we propose a probabilistic
extension that estimates a stochastic transformation rather than a
deterministic one. Marginalizing transformations allows us to consider each
image at multiple poses, which makes the localization task easier and the
training more robust. As an additional benefit, the stochastic transformations
act as a localized, learned data augmentation that improves the downstream
tasks. We show across standard imaging benchmarks and on a challenging
real-world dataset that these two properties lead to improved classification
performance, robustness and model calibration. We further demonstrate that the
approach generalizes to non-visual domains by improving model performance on
time-series data.
