Sparse Gaussian processes and various extensions thereof are enabled through inducing points, that simultaneously bottleneck the predictive capacity and act as the main contributor towards model complexity. However, the number of inducing points is generally not associated with uncertainty which prevents us from applying the apparatus of Bayesian reasoning in identifying an appropriate trade-off. In this work we place a point process prior on the inducing points and approximate the associated posterior through stochastic variational inference. By letting the prior encourage a moderate number of inducing points, we enable the model to learn which and how many points to utilise. We experimentally show that fewer inducing points are preferred by the model as the points become less informative, and further demonstrate how the method can be applied in deep Gaussian processes and latent variable modelling.

In this paper, we examine the effects of probabilistic response on a task allocation problem for a decentralized multi-agent system (MAS) and how such a mechanism may be used to tune the level of redundancy in an MAS. Redundancy refers to a back up pool of agents, beyond the necessary number required to act on a task, that have experience on that task. We present a formal analysis of a response threshold based system in which agents act probabilistically and show that we can estimate the response probability value needed to ensure that a given number of agents will act and that we can estimate the response probability value needed to achieve a given level of redundancy in the system. We perform an empirical study using an agent-based simulation to verify expectations from the formal analysis.

Agent programming is mostly a symbolic discipline and, as such, draws little benefits from probabilistic areas as machine learning and graphical models. However, the greatest objective of agent research is the achievement of autonomy in dynamical and complex environments --- a goal that implies embracing uncertainty and therefore the entailed representations, algorithms and techniques. This paper proposes an innovative and conflict free two layer approach to agent programming that uses already established methods and tools from both symbolic and probabilistic artificial intelligence. Moreover, this framework is illustrated by means of a widely used agent programming example, GoldMiners.