Building efficient fuzzy regression trees for large scale and high dimensional problems

Regression trees (RTs) are simple, but powerful models, which have been widely used in the last decades in different scopes. Fuzzy RTs (FRTs) add fuzziness to RTs with the aim of dealing with uncertain environments. Most of the FRT learning approaches proposed in the literature aim to improve the accuracy, measured in terms of mean squared error, and often neglect to consider the computation time and/or the memory requirements. In today's application domains, which require the management of huge amounts of data, this carelessness can strongly limit their use. In this paper, we propose a distributed FRT (DFRT) learning scheme for generating binary RTs from big datasets, that is based on the MapReduce paradigm. We have designed and implemented the scheme on the Apache Spark framework. We have used eight real-world and four synthetic datasets for evaluating its performance, in terms of mean squared error, computation time and scalability. As a baseline, we have compared the results with the distributed RT (DRT) and the Distributed Random Forest (DRF) available in the Spark MLlib library. Results show that our DFRT scales similarly to DRT and better than DRF. Regarding the performance, DFRT generalizes much better than DRT and similarly to DRF.