1. A method to perform preference learning on a set of documents, the method comprising: receiving raw input features from the set of documents stored on a data storage device; generating polynomial combinations from the raw input features; generating one or more parameters W; applying W to one or more classifiers to generate outputs; determining a loss function and parameter gradients and updating W; determining one or more sparse regularizing terms and updating W; expressing that one document is preferred over another in a search query and retrieving one or more documents responsive to the search query; and summing over all tuples (q,d + ,d − ) in R: W * = argmin W ⁢ 1  R  ⁢ ∑ ( q , d + , d - ) ∈ R ⁢ L W ⁡ ( q , d + , d - ) , where R is a set of tuples, q is a query, d + is a preferred document, d − is an unprefereed document, and L w is a loss for W.
1. A method to perform preference learning on a set of documents, the method comprising: receiving raw input features from the set of documents stored on a data storage device; generating polynomial combinations from the raw input features; generating one or more parameters W; applying W to one or more classifiers to generate outputs; determining a loss function and parameter gradients and updating W; determining one or more sparse regularizing terms and updating W; expressing that one document is preferred over another in a search query and retrieving one or more documents responsive to the search query; and summing over all tuples (q,d + ,d − ) in R: W * = argmin W ⁢ 1  R  ⁢ ∑ ( q , d + , d - ) ∈ R ⁢ L W ⁡ ( q , d + , d - ) , where R is a set of tuples, q is a query, d + is a preferred document, d − is an unprefereed document, and L w is a loss for W. 14. The method of claim 1 , comprising: initializing with W 0 εR D×D , T, learning rate sequence {η t }; randomly draw a tuple (q,d + ,d − )εR; determining a subgradient of L W t−1 (q,d + ,d − ) with respect to W:∇L W t−1 (q,d + ,d − ); updating W t =W t−1 −η t ∇L W t−1 (q,d + ,d − ); and if (t mod T=0) determining W T = arg ⁢ ⁢ min W ⁢ 1 2 ⁢  W - W 0  F 2 + λ ⁢ ∑ t = 1 T ⁢ ⁢ η t ⁢  W  1 , where ∥W∥ 1 =Σ i,j=1 D |W ij | is an entry-wise l 1 norm of W and λ is a regularization parameter which controls a sparsity level (number of nonzero entries) of W, ∥ ∥ F is a matrix Frobenius norm, R is a set of tuples, q is a query, d + is a preferred document, d − is an unprefereed document, L w is a loss for W, and D is a directory size, t is an iteration count, T is the number of iteration cycles, and η t is a learning rate for a t th iteration.