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badabummbadabing t1_j76tfqt wrote

Reply to comment by jimmymvp in [D] Normalizing Flows in 2023? by wellfriedbeans

Fully agree from a technical perspective with you.

The difference is that at best, you only get the likelihood under your model of choice. If that happens to be a bad model of reality (which I'd argue is the case more often than not with NFs), you might be better off just using some approximate likelihood (or ELBO) of a more powerful model.

But I am not an expert in MCMC models, so I might be talking out of my depth here. I was mainly using these models for MAP estimation.

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jimmymvp t1_j7aend6 wrote

Indeed, if your model is bad at modeling the data there's not much use in computing the likelihoods. If you want to just sample images that look cool, you don't care that much about likelihoods. However, there are certain use-cases where we care about exact likelihoods, estimating normalizing constants and providing guarantees for MCMC. Granted, you can always run MCMC with something close to a proposal distribution. However, obtaining nice guarantees on convergence and mixing times (correctness??) is difficult then, I don't know how are you supposed to do this when using a proposal for which you can't evaluate the likelihood. Similarly when you talk about importance sampling, you can only obtain correct weights if you have the correct likelihoods, otherwise it's approximate, not just in the model but also in the estimator.

This is the way I see it at least, but I'll be sure to read the aforementioned paper. I'm also not sure how much having the lower bound hurts you in estimation.

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