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{{Main|Evidence lower bound}}
For variational autoencoders, the idea is to jointly optimize the generative model parameters <math>\theta</math> to reduce the reconstruction error between the input and the output, and <math>\phi</math> to make <math>q_\phi({z| x})</math> as close as possible to <math>p_\theta(z|x)</math>. As reconstruction loss, [[mean squared error]] and [[cross entropy]] are often used.
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