Books:
- Ian Hacking - Introduction to probability and Inductive Logic
- John Kruschke - Doing Bayesian Data Analysis
- Gareth Williams - Linear Algebra with Applications, Alternate Edition
- Matthew Scarpino - OpenCL in Action
- Michael Nielsen - Neural Networks and Deep Learning
- Goodfellow, Bengio, and Courville - Deep Learning
1) Have a strong knowledge of undergraduate mathematics, probability, statistics, numerics
2) read a book about machine learning
The jump from classical machine learning to deep learning is not far if you have a good understanding of first principles.
It was helpful to me to have both, as details skipped over in one proof were often highlighted or better explained in its corresponding description. For someone whose training was not theoretical computer science, SSS left me with a better understanding most of the time.
(1) Bayesian data analysis isn't actually necessary for most AI/ML work. Bayes theorem is fundamental of course, but Bayesian data analysis (BDA) seems to rarely come up in practice. ML algorithms like Naive Bayes don't really require knowledge of BDA, plus PGMs aren't really that common (and not within BDA's scope anyway).
The computational methods behind BDA (mostly MCMC-based) are also fairly heavy and I don't know too many ML shops that actually use MCMC-based Bayesian ML.
To me, BDA's primary value is to "upgrade" the type of NHST-based data analysis done in science and social science, and ground it on what I think is more solid epistemology. I don't know if BDA is really that practical for machine learning, where the goal is not analysis but prediction.
(2) Kruschke might not be the best book for learning BDA. I own a copy of Krushke (puppies on cover and all), and found the first few chapters interesting, but it then quickly got tedious. It seemed to me that Kruschke, in an effort to make things accessible to social scientists, belabors the subject a little in later chapters without adding pedagogical value (I realize this is controversial statement to Kruschke fans, and I am prepared to change my mind).
Gelman's BDA on the other hand (I also own a copy) is less accessible to beginners, but ultimately rewards the reader in a more consistent manner.