Markov Chains are a gateway drug to more advanced probabilistic graphic models which are worth exploring. I still remember working throughout Koller&Friedman cover to cover as one of the best learning experiences I’ve ever had.

PGMs are a great topic to explore (and Koller+Friedman is a great book), but, as a word of caution to anyone interested: implementation of any of these more advanced models remains a major challenge. For anyone building production facing models, even if your problem is a pretty good match for the more interesting PGMs, the engineering requirements alone are a good reason not to go too far down that path.

The PGM book is also structured very clearly for researchers in PGMs. The book is laid out in 3 major section: the models, inference techniques (the bulk of the book), and learning. Which means, if you follow the logic of the book, you basically have to work through 1000+ pages of content before you can actually start running even toy versions of these models. If you do need to get into the nitty-gritty of particular inference algorithms, I don't believe there is another textbook with nearly the level of scope and detail.

Bishop's section on PGMs from Pattern Recognition and Machine Learning is probably a better place to start learning about these more advanced models, and if you become very interested then Koller+Friedman will be an invaluable text.

It's worth noting that the PGM course taught by Koller was one of the initial, and still very excellent, Coursera courses. I'm not sure if it's still free, but it was a nice way to get a deep dive into the topic in a reasonably short time frame (I do remember those homeworks as brutal though!)[0].

0. https://www.coursera.org/specializations/probabilistic-graph...

Just bought it last week. This book just makes me happy.

It feels like bishops pattern recognition but with a clearer tone (and a different field of course)