How Well Can a CNN Marginalize Simple Nuisances It is Designed for?

We conduct an empirical study to test the ability of convolutional neural networks (CNNs) to reduce the effects of nuisance transformations of the input data, such as location, scale and aspect ratio. We isolate factors by adopting a common convolutional architecture either deployed globally on the image to compute class posterior distributions, or restricted locally to compute class conditional distributions given location, scale and aspect ratios of bounding boxes determined by proposal heuristics. As explained in the paper, averaging the latter should in principle yield performance inferior to proper marginalization. Empirical tests yield the converse, however, leading us to conclude that - at the current level of complexity of convolutional architectures and scale of the data sets used to train them - CNNs are not very effective at marginalizing nuisance variability. We also quantify the effects of context on the overall classification task and its impact on the performance of CNNs, and propose improved sampling techniques for heuristic proposal schemes that improve end-to-end performance to state-of-the-art levels. We test our hypothesis on classification task using the ImageNet Challenge benchmark, on detection and on wide-baseline matching using the Oxford and Fischer matching datasets.