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[D] Quality of VAE embeddings, depending on likelihood function?

tl;dr: Which log-likelihood function should I use for training VQ-VAE, when I only care about the embeddings?

Hi.

Since no one responded on r/MLQuestions, this might be better suited here:

I have a question concerning the use of VAEs for encoding, as opposed to using them for data generation. In particular, I want to use a vector-quantising variational autoencoder to find a discrete representation of continuous data for some downstream task. I wonder if the choice of the decoder likelihood function would have a noticeable impact on the quality of the discrete representation.

The objective for a batch size of 1 has the following form (omitting some VQ-VAE specific terms):

max log p_dec(x|z_enc) – KL( q(z) || p(z) )

where x is a training sample, z_enc is a latent random value generated by the encoder, p_dec is the likelihood function for the decoder, q is the posterior estimate of the decoder over latent variable z and p(z) is the actual prior.

When I assume p_dec(X | z_enc) to be a multivariate normal distribution where the mean is given by some neural network and the covariance is an identity matrix, I can replace the log-likelihood term with the negative mean squared error, as in normal regression. This is what I’ve seen being used in some implementations.

But I could also let the decoder output an arbitrary covariance matrix. This would of course change the log-likelihood function.

Do you think it makes sense to use a more involved log-likelihood function (i.e. arbitrary pos. semi-definite covariance matrix), so that the encoder is forced to find a representation that is better for explaining data coming from a complex distribution? Do you know of any non-domain-specific papers investigating the use of VQ-VAEs for encoding?

submitted by /u/tanukibellydrum
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Toronto AI is a social and collaborative hub to unite AI innovators of Toronto and surrounding areas. We explore AI technologies in digital art and music, healthcare, marketing, fintech, vr, robotics and more. Toronto AI was founded by Dave MacDonald and Patrick O'Mara.