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Smooth Isotonic Additive Interaction Models With Application to Computer System Architecture Design

The regression relationship between a predictor vector and a response is assumed to be smooth, additive with low-order interactions, and monotone in some of the predictors. We consider two modeling approaches. The first approach is to fit an unconstrained additive model first and subsequently impose the isotonic constraint to cause the least perturbation of the fit. The second approach optimizes the fitting criterion that includes a roughness penalty over isotonic smoothing splines. The advantage of the first approach is its modularity and ease of implementation. One can incorporate a variety of smoothing methods as building blocks of the unconstrained model. In the article we develop the theory for this approach. In particular, we show that one can use a combination of off-the-shelf smoothing, fitting, and isotonic routines. However, it is empirically shown that fitting an isotonic smoothing spline model produces superior results over a broad range of target functions. The methodology is applied to modeling computer cache miss rates, a key problem in computer system performance analysis.