The algorithm, PageRank, receives a Markov Chain transition matrix (page links from one to another.) Either by random walk, or more efficiently, eigenvectors, the stationary distribution of the Markov Chain can be found, which conveniently ranks pages based on the likelihood of a visitor being on a given page.
I'm interested in two reverse problems.
- Say, you have the stationary distribution, can you decompose it into its transition matrix?
- Say, you have an arbitrarily long array of state-to-state jumps. In other words, you have the random walk of a latent markov transition matrix. Can you infer what the transition matrix was algorithmically?