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The WakeโSleep algorithm trains a pair of models: a generative model that explains how data are produced and a recognition model that guesses hidden causes from observed data.
The reparameterization trick rewrites a random variable as a deterministic function of noise that does not depend on the parameters, such as z = ฮผ + ฯ ยท ฮต with ฮต ~ N(0, 1).