can you say that a autoencoder is parametric or non-parametric (in terms of pattern recognition) in general? I think both is possible because you can assume an underlying error distribution but you can also estimate the error with a different method, right?
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Unless you are using non-standard definition of parametric or an autoencoder - autoencoder is 100% parametric.
It has nothing to do with assuming error distribution - in the end the modeled distribution is represented by a finite set of parameters (weights of your neural network), thus the model is parametric. Every neural network-based model is parametric (unless one considers unbounded NN architectures, but as long as it is a single, fixed architecture, every "classical" NN is parametric in nature).
Of course one can define "freaky" autoencoders that are non-parametric, use GPs or other non-parametric methods to do so, but then it just becomes the question of naming convention - what is, and what is not - an autoencoder. If by autoencoder we mean the "traditional" neural network - it is parametric. If we mean any model f(x|theta) which is trained to minimise E[L(f(x|theta), x)] then there is no way to answer, as this family consists of both parametric and non-parametric models.
lejlot
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