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We propose an unsupervised stream processing framework that learns a Bayesian representation of observed spatio-temporal activities and their causal relations. The dynamics of the activities are modeled using sparse Gaussian processes and their causal relations using a causal Bayesian graph. This allows the model to be efficient through compactness and(More)
Trajectories are used in many target tracking and other fusion-related applications. In this paper we consider the problem of modeling trajectories as Gaussian processes and learning such models from sets of observed trajectories. We demonstrate that the traditional approach to Gaussian process regression is not suitable when modeling a set of trajectories.(More)
Learning to recognize common activities such as traffic activities and robot behavior is an important and challenging problem related both to AI and robotics. We propose an unsupervised approach that takes streams of observations of objects as input and learns a probabilistic representation of the observed spatio-temporal activities and their causal(More)
—Integrating logical and probabilistic reasoning and integrating reasoning over observations and predictions are two important challenges in AI. In this paper we propose P-MTL as an extension to Metric Temporal Logic supporting temporal logical reasoning over probabilistic and predicted states. The contributions are (1) reasoning over uncertain states at(More)
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