Spline Regression Models for Complex Multi-Model Regulatory Networks

Abstract

In the previous chapter, we gave some details on theory and methods of regression and classification, (C)MARS, and their robust counterpart, R(C)MARS. and we represented and applied our methods to real-world data from different sectors. In this chapter, we apply the data mining tool of regression and classification, (C)MARS, on a dynamics. By this, the amount of condition grows, since each time point (a discrete time, in our case) can be regarded as an extra ‘condition’; in this way, there would be unknown parameters needed in order to balance the number of constraints, i.e., to close the gap of ‘degree of freedom’. In this respect, the number of unknown parameters would need to be relatively high, necessarily. However, in our research, we try to gain from the dataset topologically and geometrically best, to ‘get into’ the dynamics smartly, benefiting from structural features of the dataset. In this respect, the algorithm of MARS and CMARS seems to be an excellent choice as, e.g., in each dimension of the input variables, we get a piecewise linear ‘zig-zag’ function, where the linear parts present and approximate the data over whole intervals. This process is done adaptively, which also means: smartly.