Distributed multivariate regression based on influential observations

Hang Yu, Ee-Chien Chang

Abstract: Large-scale data sets are sometimes logically and physically distributed in separate databases. The issues of mining these data sets are not just their sizes, but also the distributed nature. The complication is that communicating all the data to a central database would be too slow. To reduce communication costs, one could compress the data during transmission. Another method is random sampling. We propose an approach for distributed multivariate regression based on sampling and discuss its relationship with the compression method. The central idea is motivated by the observation that, although communication is limited, each individual site can still scan and process all the data it holds. Thus it is possible for the site to communicate only influential samples without seeing data in other sites. We exploit this observation and derive a method that provides tradeoff between communication cost and accuracy. Experimental results show that it is better than the compression method and random sampling.