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Abstract:
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In a variety of scientific problems ranging from crime dynamics and cell biology to generative models for networks, supercritical and critical branching processes in random and varying environments are used to model the evolution of stochastic system under consideration. In these applications, the population mean of the process can typically be related to a high-dimensional feature set via a regression model. In this presentation, we first provide a rigorous description of the regression models for the branching process data and describe a novel approach to estimating the regression parameters of the proposed model; furthermore, we use the estimates for forecasting multiple generations of branching process. Our approach involves utilizing the regularization idea that explicitly takes into account the underlying branching structure. We provide sharp non-asymptotic bounds concerning the complexity of the proposed procedure and finite sample properties of the estimators. For this reason, we also describe several useful concentration inequalities for branching processes.
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