There is an award-winning compressor that uses many statistical models (and a 3-layered dense neural network) to compress the data losslessly: http://www.byronknoll.com/cmix.html

Also there is a free book that contains descriptions of various common and exotic compression formats http://www.mattmahoney.net/dc/dce.html

Overall I think we are yet to see the full potential of deep learning unleashed on data compression. For example the neural network in cmix compressor is quite primitive compared to modern architectures. Someone will certainly find a way to do better than that!