Recent approaches to collaborative filtering have concentrated on estimating an algebraic or statistical model, and using the model for predicting missing ratings. In this paper we observe that different models have relative advantages in different regions of the input space. This motivates our approach of using stagewise linear combinations of collaborative filtering algorithms, with non-constant combination coefficients based on kernel smoothing. The resulting stagewise model is computationally scalable and outperforms a wide selection of state-of-the-art collaborative filtering algorithms.