1. A server device comprising a computer hosting a search engine that uses an adaption model to rank documents in a search domain corresponding to a search domain of a query received by the computer server, the adaptation model being stored on the server device or another server device communicating with the server device, the adaptation model having been derived by a model adaptation process comprising: receiving a trained background model that was trained before performance of the model adaptation process with labeled training data, the background model having been used to rank documents searched and found to match queries; when starting a process for iteratively refining a base model, using the background model as the initial base model; and iteratively refining the base model by repeatedly computing a residual error of the base model as applied to labeled training data, repeatedly computing a basis function that minimizes a difference between the residual error and the basis function as applied to the labeled training data, and repeatedly updating the base model according to the computed basis function, wherein a tree-based boosting algorithm is used as a tree feature generator, and wherein the basis function is combined with the base model in a way that reduces a magnitude of the basis function that is combined with the base model.