Quantitative finance is a fascinating area for anyone who has the mathematical background to understand quant theory and has funds to invest. I decided to share some interesting papers, books and web sites here. These references cover a wide range of areas including machine learning, trading, portfolio optimization and market microstructure. Most references are freely available on the web if you do a search.

It needs to be emphasized this is a personal survey from the point of someone who has a good understanding of probability theory, statistics, signal processing etc. The emphasis is on estimating future returns of financial instruments based on past price information, relative value strategies and other signals that are combined via state of the art machine learning methods. 

[1] The Elements of Statistical Learning, T. Hastie, R. Tibshirani, J. H. Friedman, July 2003. 

This book can be considered as the bible of quantitative finance for anyone who's looking for predictable patterns in financial markets. Key notions of overlearning, overfitting and generalization ability of learners are discussed. Lots (and, I mean lots) of practical algorithms are presented. Very valuable reference and a good starting point.

What's the catch? The area of machine learning & pattern recognition is huge. This book is just a starting point. You need to read the original papers to understand what's going on at a deeper level.

[2]  ECE 901: Statistical Learning Theory, lecture notes by Rob Nowak. 

I would recommend this if you want to understand the theory of statistical learning. Theory and practice tend to differ a lot  when it comes to machine learning (as is true for many disciplines). Theory gives a lot of insight when it comes to design of algorithms, yet performance of most algorithms are demonstrated via simulations. In heart, I tend to agree with Vladimir N. Vapnik, who said "there's nothing more practical than a good theory." ;)

[3] News and trading rules, J.D. Thomas, PhD Thesis, Carnegie Mellon Univ., Pittsburgh, 2003.

I believe that financial markets are by and large efficient, and any single signal has little predictive power. What's the consequence? Statistical learners tend to operate in the low SNR regime. In other words, your signals will be weakly correlated with future returns and misclassification errors will be large.

This thesis gave me the valuable perspective that the goal of learning algorithm design should be robustness to noise. You particularly appreciate this point of view when working with daily or weekly data sets (small sample size). Noisiness of data suggests a different way of looking at the problem: The goal is not to find the best single (and, potentially complex) predictor, but to find lots of simple predictors each marginally powerful, yet when combined, provide significant predictive power & robustness. My experience has been that an optimized neural network (i.e. a complex learner) can have much worse generalization ability than an ensemble of equal-weight combined linear predictors (searched randomly and filtered based on performance in training set).

The thesis also teaches a good lesson on how to do quant research: You should have a null hypothesis (H0) and compute p-value and z-scores based on H0 to test predictive power. I tend to use heteroschedastic random walk as H0 in my tests. If you have a large enough data set, you may not use H0 and rely solely on cross-validation. 

[4] L. Breiman, "Stacked regressions," Machine Learning, Springer, 1996.

Ensemble methods are the name of the game in statistical learning. You should definitely check out papers on bagging, boosting & variants. This paper proposes combining multiple predictors linearly with non-negative weights. The weights are chosen via leave-one-out cross validation. The method is very intuitive and relatively easy to implement.

[5]  A. W. Lo and C. MacKinlay, "Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test," Review of Financial Studies, vol. 1, pp. 41-66, 1988