Learning From Multiple Imperfect Instructors in Sensor Networks

This paper presents a sequential learning framework for sensors in a network, where a few sensors assume the role of an instructor to train other sensors in the network. The instructors provide estimated labels for measurements of new sensors. These labels are possibly noisy, because a classifier of the instructor may not be perfect. A recursive density estimator is proposed to obtain the true measurement model (i.e., the observation density conditioned on the label) in spite of the training with noisy labels. Specifically, this paper answers the question "Can a sensor train other sensors?", provides necessary conditions for sensors to act as instructors, presents a sequential learning framework using recursive nonparametric kernel density estimation, and provides a convergence rate for the expected error in an observation density. The underlying concepts are illustrated and validated with simulation results.