Well, I am delving deeper and deeper into the realm of machine learning and inference/learning algorithms, and even a bit of information and graph theory. One book I’ve found to be really helpful so far is Information Theory, Inference, and Learning Algorithms by David MacKay. Basically, besides being a really cool textbook (how many authors actually include a dependency chart in their table of contents?!) it is available for free online!
I also stumbled upon a useful introduction to the world of unsupervised learning in the form of a tutorial by Zoubin Ghahramani. The coolest part of this overview of the different methods for unsupervised learning was the section on exact inference in graphs. A technique new to me for graph-based inference is a method known as “cutset conditioning.” I don’t think I fully understand why it works, the idea is based on “reasoning by assumptions.” Basically you find a smallest set of nodes in the graph that when known form a singly connected graph. Based upon this, as well as a small typo in the paper, I have created my own inference technique for graphs, “cutest conditioning.”
The principle behind this is even simpler than cutset conditioning. Here, we are searching for the minimal set of nodes that when removed form the cutest graph possible. I’m not sure what sort of implications this could have for the field of graph theory and mathematical punnery in general. I have included a diagram of this:
Based solely on the included graph, I can infer that I should find more productive things to pursue in my free time.
