Optimal approximation of signal priors

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    Sammanfattning

    In signal restoration by Bayesian inference, one typically uses a parametric model of the prior distribution of the signal. Here, we consider how the parameters of a prior model should be estimated from observations of uncorrupted signals. A lot of recent work has implicitly assumed that maximum likelihood estimation is the optimal estimation method. Our results imply that this is not the case. We first obtain an objective function that approximates the error occurred in signal restoration due to an imperfect prior model. Next, we show that in an important special case (small gaussian noise), the error is the same as the score-matching objective function, which was previously proposed as an alternative for likelihood based on purely computational considerations. Our analysis thus shows that score matching combines computational simplicity with statistical optimality in signal restoration, providing a viable alternative to maximum likelihood methods. We also show how the method leads to a new intuitive and geometric interpretation of structure inherent in probability distributions.
    Originalspråkengelska
    TidskriftNeural Computation
    Volym20
    Utgåva12
    Sidor (från-till)3087-3110
    Antal sidor24
    ISSN0899-7667
    StatusPublicerad - 2008
    MoE-publikationstypA1 Tidskriftsartikel-refererad

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