To briefly explain why I'm asking this, and why the answers may be of value to others in this community:
I'm trying to break into AI, to understand a large amount of the theory you effectively have to be well versed in statistics. I come from an engineering background where it's really more understanding abstract concepts at speed and applying them correctly with frameworks. While I understand a lot can be achieved by going through projects in TensorFlow and doing some Googling, I feel like I don't understand the internals. Thanks for taking the time to read this.
This is one of the clearest and most respected statistics books ever written.
I personally owe the start of my machine learning career to this book!
You will find so many people around the world (online and IRL) who consider this the bible for statistical learning.
It is so readable, and yet filled with gems and insights from one of the world's most preeminent statisticians.
Free PDF: http://ow.ly/v5Uw50obzpO
Datasets & code: http://ow.ly/a8UZ50obzpN
R Code: http://ow.ly/EEdf50kXUBS
Videos: also available at various sources.
https://www.youtube.com/playlist?list=PL5102DFDC6790F3D0
For Probability Theory:
https://www.youtube.com/playlist?list=PLUl4u3cNGP60hI9ATjSFg...
https://www.youtube.com/playlist?list=PL2SOU6wwxB0uwwH80KTQ6...
Since no one has really said much about Bayes yet, I think it worth mentioning just how useful it is in DS and ML. A Bayesian approach makes a very good baseline and often one that is hard to beat.
If you're not particular fluent with Probability and Statistics now, let me suggest you add in Khan Academy (make sure to pick the CLEP version) and JBstatistics. Khan has the advantage of quizzes (so you're not just kidding yourself that you know the material). JBstatistics has the advantage of really good explanations. You'll probably want to watch Khan at x1.5 speed.
Math is wide for AI and moves into multiple disciplines such as calculus, linear algebra.
Once you have done the above courses you can dive accordingly http://sgsa.berkeley.edu/current_students/books/
EDIT: Also very basic. Should have added that.