I'm a new Computer Science student in a masters program, switching from Applied Math. I'm really new and lacking some background, but I am interested on what literature is out there on graph algorithms, just so I can get an idea of what is possible, what is impossible, what work has been done before, etc. I'm trying to fill some gaps and get up to speed on so I can start reading papers on the topic.
I'm interested in the ways we can represent datasets as graphs and in what scenarios we can learn those graphs. For example, if we have a time series data set, we can model this as a Hidden Markov Model with potentially continuous hidden states. It's possible to write this down as a graph where each hidden state is a node with an edge towards the realized response. Or, if we have a data set, we can write down a Belief Network that represents some kind of causal model for how each random variable affects each other.
In particular, I'm curious about the following questions:
1) Since it is difficult to learn a graph/BN from data under no assumptions, when can we learn a graph/BN? When can it be done quickly?
2) Do we generally use belief networks when talking about graphs and data together, or are there other graphical models for common data problems?
Bonus question: What is the best way to get up to speed on the techniques used in algorithms literature? I'm comfortable with mathematics and proofs but am lacking some experience in how theoretical computer scientists think and solve problems.