Autoregressive models are among the most successful neural network methods for estimating a distribution from a set of samples. However, these models, such as other neural methods, need large data sets to provide good estimations. We believe that knowing structural information about the data can improve their performance on small data sets. Masked autoencoder for distribution estimation (MADE) is a well-structured density estimator, which alters a simple autoencoder by setting a set of masks on its connections to satisfy the autoregressive condition. Nevertheless, this model does not benefit from extra information that we might know about the structure of the data. This information can especially be advantageous in case of training on small data sets. In this article, we propose two autoencoders for estimating the density of a small set of observations, where the data have a known Markov random field (MRF) structure. These methods modify the masking process of MADE, according to conditional dependencies inferred from the MRF structure, to reduce either the model complexity or the problem complexity. We compare the proposed methods with some related binary, discrete, and continuous density estimators on MNIST, binarized MNIST, OCR-letters, and two synthetic data sets.

This paper presents a robust tracking approach to handle challenges such as occlusion and appearance change. Here, the target is partitioned into a number of patches. Then, the appearance of each patch is modeled using a dictionary composed of corresponding target patches in previous frames. In each frame, the target is found among a set of candidates generated by a particle filter, via a likelihood measure that is shown to be proportional to the sum of patch-reconstruction errors of each candidate. Since the target's appearance often changes slowly in a video sequence, it is assumed that the target in the current frame and the best candidates of a small number of previous frames, belong to a common subspace. This is imposed using joint sparse representation to enforce the target and previous best candidates to have a common sparsity pattern. Moreover, an occlusion detection scheme is proposed that uses patch-reconstruction errors and a prior probability of occlusion, extracted from an adaptive Markov chain, to calculate the probability of occlusion per patch. In each frame, occluded patches are excluded when updating the dictionary. Extensive experimental results on several challenging sequences shows that the proposed method outperforms state-of-the-art trackers.