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Lately, I've been getting into energy-based models (EBMs) through some of Yann LeCun's recent talks, where he advocates the use of non-normalized models because it allows for more flexibility in the choice of the loss function and convenient inference over high-dimensional spaces.

However, after reading some papers on the recent approaches to training EBMs (e.g Kingma's How to Train Your Energy-Based Models), most approaches still use likelihood to optimize the EBMs parameters.

I'm lost in the necessity of using a normalized likelihood for training, while the whole idea of EBMs is that they are not normalized. Why are methods that shape the energy-function directly not popular?

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