Inconsistent parameter estimation in Markov random fields: Benefits in the computation-limited setting

Details Inconsistent parameter estimation in Markov random fields: Benefits in the computation-limited setting Inconsistent parameter estimation in Markov random fields: Benefits in the computation-limited setting

2006-02-27

arxiv.org/abs/cs/0602092v1

Computer Science

Learning

UC Berkeley, Department of Statistics; Technical Report 690

Scientific paper

Consider the problem of joint parameter estimation and prediction in a Markov random field: i.e., the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g., smoothing, denoising, interpolation) on a new noisy observation. Working under the restriction of limited computation, we analyze a joint method in which the \emph{same convex variational relaxation} is used to construct an M-estimator for fitting parameters, and to perform approximate marginalization for the prediction step. The key result of this paper is that in the computation-limited setting, using an inconsistent parameter estimator (i.e., an estimator that returns the ``wrong'' model even in the infinite data limit) can be provably beneficial, since the resulting errors can partially compensate for errors made by using an approximate prediction technique. En route to this result, we analyze the asymptotic properties of M-estimators based on convex variational relaxations, and establish a Lipschitz stability property that holds for a broad class of variational methods. We show that joint estimation/prediction based on the reweighted sum-product algorithm substantially outperforms a commonly used heuristic based on ordinary sum-product.

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