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Sep 17

Combined Regression and Ranking

Posted by abiao at 13:20 | Code » C++ | Comments(0) | Reads(6766)
Quantivity introduced an interesting article a few days ago Combined Regression and Ranking that may be interesting to some of you.

The basic idea of Combined Regression and Ranking is to optimize regression and ranking objectives simultaneously. Generally we are trying to keep the predicted values as close as possible to the true target value for regression based method, such as minimizing the mean square error (MSE), however, besides accurately producing values, in some circumstances we are more interested in a model able to predict the ranking as well. A good example in the paper is: considering nearly all observations have target value y=0 and only a small fraction have value y=1, therefore a model predicting 0 for all cases is good enough using regression, however, it failes to return a useful & meaningful ranking.

The objective funtion for combined regression and ranking is given by
objective function
where the first part is for regression loss, the second part is for pairwise ranking loss, and the parameter alpha intuitively trades off between optimizing regression loss and optimizing pairwise loss.

Some possible financial applications of combined regression and ranking I am aware:
1, long-tailed distribution fitting. since a large fraction is composed of very low frequency event, hence we want to come up with a model that fits not only the extreme values but also the ranking of them;

2, multiple-factor analysis, where we need to pick the stocks by their past return performance as well as their relative ranking among peers;

3, traders performance analysis, same reason as in 2.

4, company credit ratings, where we may be interested in not only how to predict future ratings, AA or A using infor such as historical default probability, but the relative positions of different companies in investment assets pool.


Download the paper at http://www.eecs.tufts.edu/~dsculley/papers/combined-ranking-and-regression.pdf and free C++ at http://code.google.com/p/sofia-ml.

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