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Ans 1. The motive of Variational Inference(on which VAE is based), is to decrease $KL(q(z|x)||p(z))$, where p(z) is our chosen distribution of the hidden variable z. After doing some math, we can write this expression as- $KL(q||x) = log(p(x)) - \Sigma_z q(z)log(\frac{p(x,z)}{q(z)})$ For a given x, the first term of RHS is constant. So we maximise the ...