Bayesian Nonparametric Poisson-Process Allocation for Time-Sequence Modeling
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Analyzing the underlying structure of multiple time-sequences provides insight into the understanding of social networks and human activities. In this work, we present the Bayesian nonparametric Poisson process allocation (BaNPPA), a generative model to automatically infer the number of latent functions in temporal data. We model the intensity of each sequence as an infinite mixture of latent functions, each of which is the square of a function drawn from a Gaussian process. A technical challenge for the inference of such mixture models is the identifiability issue between coefficients and the scale of latent functions. We propose to cope with the identifiability issue by regulating the volume of each latent function and derive a variational inference algorithm that can scale well to large-scale data sets. Our algorithm is computationally efficient and scalable to large-scale datasets. Finally, we demonstrate the usefulness of the proposed Bayesian nonparametric model through experiments on both synthetic and real-world data sets.
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