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Abstract:
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Discrete multivariate time series models arise in many settings including finance, neuroscience, social networks and many other settings. For example, we may consider the number of 'likes' a Facebook post receives in a given time interval a such an example. Typically when the number of series M is large, a very long series with data at many time points is required. However in practice the length of the observed time series is typically limited. In this talk, I present an approach to solve this problem with corresponding theoretical guarantees and a fast algorithm in the setting where the number of time points T may be smaller than the number of series M, provided we assume a small number of series interact with each other. The approach I present introduces the Poisson log-linear auto-regressive model and then marries the literature on high-dimensional sparse GLM models with concentration bounds for infinite discrete-space Martingales.
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