Consensus-based modeling using distributed feature construction with ILP

A particularly successful role for Inductive Logic Programming (ILP) is as a tool for discovering useful relational features for subsequent use in a predictive model. Conceptually, the case for using ILP to construct relational features rests on treating these features as functions, the automated discovery of which necessarily requires some form of first-order learning. Practically, there are now several reports in the literature that suggest that augmenting any existing feature with ILP-discovered relational features can substantially improve the predictive power of a model. While the approach is straightforward enough, much still needs to be done to scale it up to explore more fully the space of possible features that can be constructed by an ILP system. This is in principle, infinite and in practice, extremely large. Applications have been confined to heuristic or random selections from this space. In this paper, we address this computational difficulty by allowing features and models to be constructed in a distributed manner. That is, there is a network of computational units, each of which employs an ILP engine to construct some small number of features and then builds a (local) model. We then employ an asynchronous consensus-based algorithm, in which neighboring nodes share information and update local models. This gossip-based information exchange results in the formation of non-stationary Markov chains. For a category of models (those with convex loss functions), it can be shown (using the Supermartingale Convergence Theorem) that the algorithm will result in all nodes converging to a consensus model. In practice, it may be slow to achieve this convergence. Nevertheless, our results on synthetic and real datasets suggest that in relatively short time the “best” node in the network reaches a model whose predictive accuracy is comparable to that obtained using more computational effort in a non-distributed setting (the best node is identified as the one whose weights converge first).