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Why do we use the reparameterization trick in VAE?
This is because we backpropagate the gradients of the loss function ultimately and the“reparameterization” trick actually helps in the backpropagation process when happening in a VAE. Recall from the above section that a VAE is trying to learn a distribution for the latent space.
Which is the problem of the reparameterization trick?
Reparameterization trick Recall that our object of interest is the gradient of the expected value of the function. Also recall that the problem in evaluating this quantity is the fact that the expectation is taken wrt a distribution with parameters and we can’t compute the derivative of that stochastic quantity.
Why does the reparameterization trick work with variational autoencoders?
A common explanation for the reparameterization trick with variational autoencoders is that we cannot backpropagate through a stochastic node. I provide a more formal justification. Published
Which is the best way to counter reparameterization?
To counter this, a common solution is to use something called control variates. The basic idea is to replace the function under the expectation with another function which has the same expected value but lesser variance. This can be done by subtracting from the original function, a term which has its expectation as zero.
When did we first learn the reparameterization trick?
We first encountered the reparameterization trick when learning about variational autoencoders and how they approximate posterior distributions using KL divergence and the Evidence Lower Bound (ELBO).
How does the reparameterization trick work in statistics?
Reparameterization trick is a way to rewrite the expectation so that the distribution with respect to which we take the gradient is independent of parameter θ. To achieve this, we need to make the stochastic element in q independent of θ. Hence, we write x as x = θ + ϵ, ϵ ∼ N (0, 1)
How are the parameters of a VAE trained?
The parameters of a VAE are trained via two loss functions: a reconstruction loss that forces the decoded samples to match the initial inputs, and a regularization loss that helps learn well-formed latent spaces and reduce overfitting to the training data. The regularization loss is handled with the Kullback-Liebler Divergence.