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I often hear people asking how to start learning Machine Learning, or which books to read. So I've compiled a list of some of what I consider are the best books out there to Self-Learn Machine Learning.
As usual, this is far from an exhaustive list, but if you read most of this books, I'm pretty sure you can understand any paper you find in NIPS or ICML.

Casella, G. and Berger, R.L. (2001). "Statistical Inference" Duxbury Press.
Ferguson, T. (1996). "A Course in Large Sample Theory" Chapman & Hall/CRC.

 Lehmann, E. (2004). "Elements of Large-Sample Theory" Springer.

Gelman, A. et al. (2003). "Bayesian Data Analysis" Chapman & Hall/CRC.
Robert, C. and Casella, G. (2005). "Monte Carlo Statistical Methods" Springer.

Murphy (2012), Machine Learning: A probabilistic Perspective, MIT Press

Izenman (2008), Modern Multivariate Statistical Techniques, Springer
Grimmett, G. and Stirzaker, D. (2001). "Probability and Random Processes" Oxford.

 Pollard, D. (2001). "A User's Guide to Measure Theoretic Probability" Cambridge.
Durrett, R. (2005). "Probability: Theory and Examples" Duxbury.

Bertsimas, D. and Tsitsiklis, J. (1997). "Introduction to Linear Optimization" 

 Boyd, S. and Vandenberghe, L. (2004). "Convex Optimization"
Hastie et Al (2009), The Elements of Statistical Learning, Springer
Johnson and Wichen (2007), Applied Multivariate Statistical Analysis, Pearson
 Golub, G., and Van Loan, C. (1996). "Matrix Computations" Johns Hopkins.
Cover, T. and Thomas, J. "Elements of Information Theory" Wiley.
Kreyszig, E. (1989). "Introductory Functional Analysis with Applications" Wiley.
Bishop, C (2007), Pattern Recognition and Machine Learning, Springer
Koller and Friedman(2009), "Probabilistic Graphical Models", MIT Press
Rasmussen and Williams (2005), Gaussian Processes for Machine Learning, MIT Press

Disclaimer: The images are pulled from their respective editors, authors or sellers websites, I do not own them and their use is only for illustrative purposes. Because of this, I do not link to any seller's website, since I do not intend on monetizing on this list.