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arXiv:1712.03499math.NA

Linear regression over the max-plus semiring: algorithms and applications

James Hook

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Abstract

In this paper we present theory, algorithms and applications for regression over the max- plus semiring. We show how max-plus 2-norm regression can be used to obtain maximum likelihood estimates for three different inverse problems. Namely inferring a max-plus linear dynamical systems model from a noisy time series recording, inferring the edge lengths of a network from shortest path information and fitting a max-plus polynomial function to data.

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math.NANumerical Analysis

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  1. A ‘Useless’ Perspective That Transformed Mathematics 1 comment

    • There's also lots of clever tricks to make things more linear. There's things like linear approximations. Or, my favourite, picking a clever semi-ring in which your problem is linear. See eg the analysis of Google's BBR TCP variant. Eg…

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