Autoencoders and singular value decomposition

Autoencoders are interesting mathematical objects that have many applications. These consist of two mappings, an encoder \(E\) which maps data to a vector, often named embedding, code or latent variables, and a decoder \(D\) which maps the embedding back to the data. The optimization problem that we need to solve to obtain these mappings is the following:

Notes On Forward Backward Algorithm

These are some notes on the Forward-Backward algorithm for Hidden Markov Models (HMMs). The focus of this post is on the derivations and on the variations of these algorithms. When possible I try to give an interpretation of the probabilities involved.