Fast Approximate Score Computation on Large-Scale Distributed Data for Learning Multinomial Bayesian Networks

Abstract

In this paper, we focus on the problem of learning a Bayesian network over distributed data stored in a commodity cluster. Specically, we address the challenge of computing the scoring function over distributed data in an ecient and scalable manner, which is a fundamental task during learning. While exact score computation can be done using the MapReduce-style computation, our goal is to compute approximate scores much faster with probabilistic error bounds and in a scalable manner. We propose a novel approach which is designed to achieve: (a) decentralized score computation using the principle of gossiping; (b) lower resource consumption via a probabilistic approach for maintaining scores using the properties of a Markov chain; and (c) eective distribution of tasks during score computation (on large datasets) by synergistically combining well-known hashing techniques. We conduct theoretical analysis of our approach in terms of convergence speed of the statistics required for score computation, and memory and network bandwidth consumption. We also discuss how our approach is capable of eciently recomputing scores when new data are available. We conducted a comprehensive evaluation of our approach and compared with the MapReduce-style computation using datasets of dierent characteristics on a 16-node cluster. When the MapReduce-style computation provided exact statistics for score computation, it was nearly 10 times slower than our approach. Although it ran faster on randomly sampled datasets than on the entire datasets, it performed worse than our approach in terms of accuracy. Our approach achieved high accuracy (below 6% average relative error) in estimating the statistics for approximate score computation on all the tested datasets. In conclusion, it provides a feasible tradeo between computation time and accuracy for fast approximate score computation on large-scale distributed data.