Constrained Multivariate Extrapolation Models With Application to Computer Cache Rates

In this article we propose an approach to building multivariate regression models for prediction beyond the range of the data. The extrapolation model attempts to accurately estimate the high-level trend of the data, which can be extended in a natural way. The constraints of monotonicity and convexity/concavity play an important role in restricting the choice of the high level-trend, which otherwise would remain rather arbitrary. Our extrapolation model incorporates these constraints in multiple dimensions. We describe the trend as a nonnegative linear combination of twice-integrated multivariate B-splines and their variations. The specific basis functions in our approach are chosen so that any such combination is a plausible a priori model. As a result, basis function coefficients can be optimized to best fit the data without losing control over the high-level trend of the extrapolation model. Our approach also allows the use of standard model selection techniques. We illustrate this by applying cross-validation to roughness penalty parameter selection. We demonstrate the validity of our approach by successfully applying it to modeling computer cache miss rates-a key problem in computer system performance analysis.