Piecemeal Reduction of Models of Large Networks

Many systems can be modeled as an intricate network of interacting components. Often the level of detail in the model exceeds the richness of the available data, makes the model difficult to learn, or makes it difficult to interpret. Such models can be improved by reducing their complexity. If a model of a network is very large, it may be desirable to split it into pieces and reduce them separately, recombining them after reduction. Such a distributed procedure would also have other advantages in terms of speed and data privacy. We discuss piecemeal reduction of a model in the context of the Manifold Boundary Approximation Method (MBAM), including its advantages over other reduction methods. MBAM changes the model reduction problem into one of selecting an appropriate element from a partially ordered set (poset) of reduced models. We argue that the prime factorization of this poset provides a natural decomposition of the network for piecemeal model reduction via MBAM. We demonstrate on an example network and show that MBAM finds a reduced model that introduces less bias than similar models with randomly selected reductions.