Auto-associative MLP networks have been used for learning similar mappings as we have done. Both the generative model and its inversion are learned simultaneously, but separately without utilising the fact that the models are connected. This means that the learning is much slower than in this case where the inversion is defined as a gradient descent process.
Much of the work with auto-associative MLPs uses point estimates for weights and sources. As argued in the beginning of the chapter, it is then impossible to reliably choose the structure of the model and problems with over- or underlearning may be severe. Hochreiter and Schmidhuber have used and MDL based method which does estimate the distribution of the weights but has no model for the sources [3]. It is then impossible to measure the description length of the sources.