A Scalable Local Algorithm for Distributed Multivariate Regression

Abstract

This paper offers a local distributed algorithm for multivariate regression in large peer-to-peer environments. The algorithm can be used for distributed inferencing, data compaction, data modeling and classification tasks in many emerging peer-to-peer applications for bioinformatics, astronomy, social networking, sensor networks and web mining. Computing a global regression model from data available at the different peer-nodes using a traditional centralized algorithm for regression can be very costly and impractical because of the large number of data sources, the asynchronous nature of the peer-to-peer networks, and dynamic nature of the data/network. This paper proposes a two-step approach to deal with this problem. First, it offers an efficient local distributed algorithm that monitors the "quality" of the current regression model. If the model is outdated, it uses this algorithm as a feedback mechanism for rebuilding the model. The local nature of the monitoring algorithm guarantees low monitoring cost.Experimental results presented in this paper strongly support the theoretical claims.

Scalable Distributed Change Detection from Astronomy Data Streams using Local, Asynchronous Eigen Monitoring Algorithms

“…This can happen, for example, when the each node has a vector in a different convex region and the global average is in another different region. However, as shown in this paper and also by several authors [27] [6] there are several problem instances for which the resource consumption becomes independent of the size of the network. Interested readers are referred to [5] for a detailed discussion on communication complexity and locality of such algorithms.…”

“…The distributed PCA implementation makes use of the Distributed Data Mining Toolkit (DDMT) 6 -a distributed data mining development environment from DIADIC research lab at UMBC. DDMT uses topological information which can be generate by BRITE 7 , a universal topology generator from Boston University.…”

“…Researches have proposed definitions of locality [6] [27]. Note that for an exact algorithm as the eigen monitoring algorithm, the worst case communication complexity is O(sizeof network).…”

Scalable Statistical Monitoring of Fleet Data

“…Though there is much work on distributed computing, there seems to be little prior work on a scalable solution of mixed regression problems with longitudinal data. Distributed regression algorithms are considered in Guestrin et al [2004], Bhaduri and Kargupta [2008], and Bazerque et al [2010]. These algorithms are motivated by sensor networks and the need to distribute the estimation computations over the network, rather than scalability needs.…”

Distributed Monitoring of the R 2 Statistic for Linear Regression

“…Recently, Bhaduri et al [1] have proposed an algorithm for doing regression in large P2P networks which checks the squared error between the predicted and the target variables based on a generic monitoring algorithm proposed by Wolff et al in [16]. If the error exceeds a predefined threshold (ǫ), the nodes raise an alert and the regression model is rebuilt.…”