How does expectation maximization and variational inference work?
Since the KL-divergence is non-negative, The ELBO provides a lower bound for the marginal likelihood. Instead of maximizing the marginal likelihood directly, the Expectation Maximization (EM) and variational inference maximize the variational lower bound.
How is the evidence lower bound used in statistical inference?
Postdoctoral Fellow at the Morgridge Institute for Research. The evidence lower bound is an important quantity at the core of a number of important algorithms used in statistical inference including expectation-maximization and variational inference. In this post, I describe its context, definition, and derivation.
Which is an example of the variational lower bound?
In others words, the lower bound L hits the log probability iff the approximation distribution is perfectly closed to the true posterior distribution. Now, we can use our understanding of the variational lower bound to deduce the learning rules in practical problems. We use the paper [2] as an example.
Which is the best tutorial for variational inference?
There are many great tutorials for variational inference, but I found the tutorial by Tzikas et al. 1 to be the most helpful. It follows the steps of Bishop et al. 2 and Neal et al. 3 and starts the introduction by formulating the inference as the Expectation Maximization.
How is variational inference used in Gaussian mixture model?
The variational EM gives us a way to bypass computing the partition function and allows us to infer the parameters of a complex model using a deterministic optimization step. In the next post, I will give a concrete example with a simple Gaussian Mixture Model.
What do you need to know about statistical inference?
Statistical inference involves finding the right model and parameters that represent the distribution of observations well. Let x be the observations and θ be the unknown parameters of a ML model.