  Out-of-distribution (OOD) detection and lossless compression constitute two
problems that can be solved by the training of probabilistic models on a first
dataset with subsequent likelihood evaluation on a second dataset, where data
distributions differ. By defining the generalization of probabilistic models in
terms of likelihood we show that, in the case of image models, the OOD
generalization ability is dominated by local features. This motivates our
proposal of a Local Autoregressive model that exclusively models local image
features towards improving OOD performance. We apply the proposed model to OOD
detection tasks and achieve state-of-the-art unsupervised OOD detection
performance without the introduction of additional data. Additionally, we
employ our model to build a new lossless image compressor: NeLLoC (Neural Local
Lossless Compressor) and report state-of-the-art compression rates and model
size.
