Wireless technologies have become ubiquitous in our everyday life. The continuing advances in microelectronics lead to ever cheaper, smaller and smarter mobile devices at reduced energy consumption, a trend that seems not to stop in the foreseeable future. The lack of cabling, which is essential for the desired flexibility, typically makes these devices dependent on some limited energy resource and thus substantiates the necessity for power aware design at both, the hardware and software development stage.

The type of mobile devices that are considered in this work are wireless sensor nodes, together forming a wireless sensor network (WSN). WSNs should not only be seen as sensing networks like the name suggests, but furthermore as distributed processing and sensing networks. The main advantage of distributed data processing as opposed to centralized data collection, is that the energy consumption for communication and computation better scales with the network size for many applications, i.e. the number of nodes. Assume for instants a network which senses temperature. If the aim is e.g. to determine the maximum temperature measured in the network, it is more efficient to only let each sensor forward the maximum temperature of its surrounding nodes and itself in a multi-hop fashion to some point in the network instead of relaying all the available measured data to this point and determine the maximum temperature there.

The task that we consider here in this work is distributed probabilistic regression of a field function that is spatially sampled by a WSN as schematically depicted in the Figure. We investigate a powerful learning technique named “Sparse Bayesian Learning” (SBL), which is exemplified by the “Relevance Vector Machine” (RVM), for distributed variants. The reason we investigate on SBL is that it is a very powerful regression technique that is elegantly specified only by a probabilistic Bayesian model. It automatically leads to sparse solutions by applying Bayesian inference techniques. And it implicitly handles the problem of over-fitting with an automatic regularization term implicit in the framework.