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- W2042549684 abstract "We consider two related problems of estimating properties of a collection of point processes: estimating the multiset of parameters of continuous-time Poisson processes based on their activities over a period of time t, and estimating the multiset of activity probabilities of discrete-time Bernoulli processes based on their activities over n time instants. For both problems, it is sufficient to consider the observations' profile - the multiset of activity counts, regardless of their process identities. We consider the profile maximum likelihood (PML) estimator that finds the parameter multiset maximizing the profile's likelihood, and establish some of its competitive performance guarantees. For Poisson processes, if any estimator approximates the parameter multiset to within distance ε with error probability δ, then PML approximates the multiset to within distance 2ε with error probability at most δ · e <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>4√t·S</sup> , where S is the sum of the Poisson parameters, and the same result holds for Bernoulli processes. In particular, for the L <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> distance metric, we relate the problems to the long-studied distribution-estimation problem and apply recent results to show that the PML estimator has error probability e <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>-(t·S)0.9</sup> for Poisson processes whenever the number of processes is k = O(tS log(tS)), and show a similar result for Bernoulli processes. We also show experimental results where the EM algorithm is used to compute the PML." @default.
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- W2042549684 date "2012-07-01" @default.
- W2042549684 modified "2023-09-27" @default.
- W2042549684 title "Estimating multiple concurrent processes" @default.
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- W2042549684 doi "https://doi.org/10.1109/isit.2012.6283551" @default.
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