Distributed regression

Abstract

We present distributed regression, an efficient and general framework for in-network modeling of sensor data. In this framework, the nodes of the sensor network collaborate to optimally fit a global function to each of their local measurements. The algorithm is based upon kernel linear regression, where the model takes the form of a weighted sum of local basis functions; this provides an expressive yet tractable class of models for sensor network data. Rather than transmitting data to one another or outside the network, nodes communicate constraints on the model parameters, drastically reducing the communication required. After the algorithm is run, each node can answer queries for its local region, or the nodes can efficiently transmit the parameters of the model to a user outside the network. We present an evaluation of the algorithm based upon data from a 48-node sensor network deployment at the Intel Research -Berkeley Lab, demonstrating that our distributed algorithm converges to the optimal solution at a fast rate and is very robust to packet losses.

A Decentralized Approach for Nonlinear Prediction of Time Series Data in Sensor Networks

“…Updating cycles can be repeated to refine the model or to track time-varying systems. (Though beyond the scope of this paper, one may assume a time-evolution kernel-based model in the spirit of [4] where the authors fit a cubic polynomial to the temporal measurements of each sensor. )…”

“…Model-based techniques that exploit the temporal and spatial redundancy of data in order to compress communications have also been considered. For instance, in [4], data captured by each sensor over a time interval are fitted by (cubic) polynomial curves whose coefficients are communicated between sensors. Since there is a significant amount of redundancy between measurements performed by two nearby sensors, spatial correlations are also modeled by defining the basis functions over both spatial parameters and time.…”

Optimal Observation for Cyber-physical Systems

“…• Detection and estimation: it is desirable to have distributed detection or estimation algorithms, in order to enhance the scalability and fault tolerance of WSNs. For example, distributed regression [73], distributed least squares (LS) fitting [74], and other distributed algorithms [29,75] are discussed.…”

Distributed Decision‐Tree Induction in Peer‐to‐Peer Systems

“…The local MR models are then transported to the central site and combined to form the global MR model. Several other techniques have been proposed for doing distributed MR using distributed kernel regression such as by Guestrin et al 26 and Predd et al 27.…”