  We present a coupled Variational Auto-Encoder (VAE) method that improves the
accuracy and robustness of the probabilistic inferences on represented data.
The new method models the dependency between input feature vectors (images) and
weighs the outliers with a higher penalty by generalizing the original loss
function to the coupled entropy function, using the principles of nonlinear
statistical coupling. We evaluate the performance of the coupled VAE model
using the MNIST dataset. Compared with the traditional VAE algorithm, the
output images generated by the coupled VAE method are clearer and less blurry.
The visualization of the input images embedded in 2D latent variable space
provides a deeper insight into the structure of new model with coupled loss
function: the latent variable has a smaller deviation and a more compact latent
space generates the output values. We analyze the histogram of the likelihoods
of the input images using the generalized mean, which measures the model's
accuracy as a function of the relative risk. The neutral accuracy, which is the
geometric mean and is consistent with a measure of the Shannon cross-entropy,
is improved. The robust accuracy, measured by the -2/3 generalized mean, is
also improved.
