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.

Abstract — Many inference problems that arise in sensor networks require the computation of a global conclusion that is consistent with local information known to each node. A large class of these problems— including probabilistic inference, regression, and control problems—can be solved by message passing on a data structure called a junction tree. In this paper, we present a distributed architecture for solving these problems that is robust to unreliable communication and node failures. In this architecture, the nodes of the sensor network assemble themselves into a junction tree and exchange messages between neighbors to solve the inference problem efficiently and exactly. A key part of the architecture is an efficient distributed algorithm for optimizing the choice of junction tree to minimize the communication and computation required by inference. We present experimental results from a prototype implementation on a 97-node Mica2 mote network, as well as simulation results for three applications: distributed sensor calibration, optimal control, and sensor field modeling. These experiments demonstrate that our distributed architecture can solve many important inference problems exactly, efficiently, and robustly. I.