An interarrival embedding makes signature methods work on TPPs, yielding SIGTPP trained on whole trajectories plus three pathwise distributional evaluation metrics.
Distance covariance in metric spaces.The Annals of Probability, 41(5):3284–3305
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Under Ahlfors regularity of exponent β, the minimal energy distance between a measure and its N-point empirical version decays exactly as N to the power -½(1 + q/β) for power kernels with exponent q in (0,2).
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From Jumps to Signatures: a Generative Method for Temporal Point Processes
An interarrival embedding makes signature methods work on TPPs, yielding SIGTPP trained on whole trajectories plus three pathwise distributional evaluation metrics.
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Sharp Rates of MMD Empirical Estimation with Power Kernels
Under Ahlfors regularity of exponent β, the minimal energy distance between a measure and its N-point empirical version decays exactly as N to the power -½(1 + q/β) for power kernels with exponent q in (0,2).