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How is gradient descent used in the Elbo?
Gradient descent is a standard approach for optimizing complicated objectives like the ELBO. The idea is to calculate its gradient and update the current set of parameters proportional to the gradient. ∇ λ E L B O ( λ) = E q ( z; λ) [ ∇ λ log q ( z; λ) ( log p ( x, z) − log q ( z; λ))].
What does maximizing the Elbo do to the data?
ELBO(λ). As per its name, the ELBO is a lower bound on the evidence, and optimizing it tries to maximize the probability of observing the data. What does maximizing the ELBO do? Splitting the ELBO reveals a trade-off
Which is the lower bound of the Elbo?
The optimization problem we seek to solve becomes λ ∗ = arg max λ E L B O ( λ). ELBO(λ). As per its name, the ELBO is a lower bound on the evidence, and optimizing it tries to maximize the probability of observing the data.
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How to stop worrying and write Elbo ( and its )?
We already know that reparametrisation trick ( path derivative) has the benefit of lower variance for gradient estimation compared to score function. The kicker here is — the gradient of ELBO actually contains a score function term, causing the estimator to have large variance!
Is the KL divergence a symmetric or non-symmetric measure?
The KL divergence is a non-symmetric, information theoretic measure of similarity between two probability distributions (Hinton & Camp, 1993; Jordan, Ghahramani, Jaakkola, & Saul, 1999; Waterhouse, MacKay, & Robinson, 1996). The Evidence Lower Bound The above optimization problem is intractable because it directly depends on the posterior
How is variational inference done in autoencoders?
Variational inference is done by maximizing the ELBO ( E vidence L ower BO und). Which is often written in a more intuitive form: Where we have a likelihood term (in Variational Autoencoders often called reconstruction loss) and the KL-divergence between the prior and the variational distribution.
When to use reconstruction loss in variational inference?
Where we have a likelihood term (in Variational Autoencoders often called reconstruction loss) and the KL-divergence between the prior and the variational distribution. We are going to rewrite this ELBO definition so that it is more clear how we can use it to optimize the model, we’ve just defined.