4. The method of claim 1 , wherein said defining the query error as a difference between an optimal DCG function and an approximated version of a DCG comprises: defining the query error as max π ⁢ ∑ i ∈ U q ⁢ D ⁡ ( π ⁡ ( i ) ) ⁢ G ⁡ ( y i ) - ∑ j = 1 ND q ⁢ D ⁡ ( j ) ⁢ ∑ i ∈ U q ⁢ G ⁡ ( y i ) ⁢ h ij ∑ i ∈ U q ⁢ h ij where D(j)=a discount function, NDq=a number of documents in the set of documents for the query, Uq=the set of documents for the query, π=a permutation from Uq to 1-NDq, y i =a training relevance for document i, G(y i )=a mapping function for y i , and h ij =a continuous version of an indicator function where document i is ranked in a position j by the relevance function.
4. The method of claim 1 , wherein said defining the query error as a difference between an optimal DCG function and an approximated version of a DCG comprises: defining the query error as max π ⁢ ∑ i ∈ U q ⁢ D ⁡ ( π ⁡ ( i ) ) ⁢ G ⁡ ( y i ) - ∑ j = 1 ND q ⁢ D ⁡ ( j ) ⁢ ∑ i ∈ U q ⁢ G ⁡ ( y i ) ⁢ h ij ∑ i ∈ U q ⁢ h ij where D(j)=a discount function, NDq=a number of documents in the set of documents for the query, Uq=the set of documents for the query, π=a permutation from Uq to 1-NDq, y i =a training relevance for document i, G(y i )=a mapping function for y i , and h ij =a continuous version of an indicator function where document i is ranked in a position j by the relevance function. 5. The method of claim 4 , wherein said defining comprises: defining h ij as h ij = exp ⁢ ( -  f ⁡ ( x i , w ) - f ⁡ ( r ⁡ ( j ) , w )  2 2 ⁢ σ 2 ) , where x i =a feature vector containing evaluated feature information for document i of the set of documents, r(j)=the j-th document in the ranking induced by the relevance function, w=a coefficient vector, f(x i , w)=the relevance function evaluated on document i, and σ=a smoothing length-scale parameter.