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Generative models like latent variable models (e.g. VAE) use directed graphical models and these sort of factorizations as a foundation for learning. In VAEs, Neural nets are used to estimate posteriors/priors to generate samples. This sort of explicit factorization is helpful in other generative models as well like autoregressive models which are basically ...


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As far as I know, it doesn't make sense to say that a probability distribution is i.i.d., as you're saying. The property i.i.d. is a property of a sequence of random variables. In your case, the random variables are $z_i = (x_i, y_i)$, so it's not just the input $y_i$ or the label $y_i$, but both. The rest of the explanation can be taken from the other ...


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A sequence of $n$ random variables $z_{1:n} = z_1, z_2, \dots, z_n$ is i.i.d. if they are identically distributed, i.e. each random variable $z_i$ has the same distribution the joint distribution of all of them is just the product of the marginal distributions of each r.v. So, let's imagine a thought experiment in which we throw a coin $n$ times, so you ...


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