Notes

Probabilistic Generative Models "When one understands the causes, all vanished images can easily be found again in the brain through the impression of the cause. This is the true art of memory..."- Rene Descartes

We know that our data has some causes v, but it is hard to specify. We do not know the underlying distribution. We can see the real world as a generative model that produced our (observable) data u. Now, we want to mimic this process. We model the causes as prior p(v,G) and our generative model specifies the artificial data distribution p(u|v,G). We have a recognition model that maps the samples gathered in the "real" world somehow to our generative model (not clear from the slides how). Goal: Learn a good generative model that mimics the statistics of the data generation process. Approach: Given data, solve two problems:

1. Estimate the causes by computing the posterior.
2. Learn all parameters G of the model and the latent space statistics.

A very basic example is a mixture of Gaussians:

I assume these parameters are means, variances and mixture scaling factors. There are several ways how one could use a neural network for these challenges. Also known as "Maximum Likelihood Learning":

• Learn the recognition model
• Learn the generative model
• Learn/update the prior p(z).

In the figure we have the difference between a traditional embedding algorithm on the left where we have huge gaps in embedding space and a generative embedding method on the right that densely covers the space. This allows us to sample. Indeed, interpolation between the classes is possible with a generative model.