{"paper":{"title":"Inconsistent parameter estimation in Markov random fields: Benefits in the computation-limited setting","arxiv_id":"cs/0602092","primary_cat":"cs.LG","submitted_at":"2006-02-27T05:22:15+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13-20260917 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"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.","hedge":{"p":0.62,"label":"asserted"},"own_p":0.08,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":0.9,"id":"s1","own":true,"role":"method","text":"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.","hedge":{"p":0.72,"label":"asserted"},"own_p":0.84,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.9,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.1,"interpretation":0.0}},{"i":2,"p":0.98,"id":"s2","own":true,"role":"result","text":"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.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.98,"quantitative":false,"quantitative_p":0.17,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.98,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.01}},{"i":3,"p":0.87,"id":"s3","own":true,"role":"contribution","text":"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.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.09,"role_probabilities":{"gap":0.0,"method":0.03,"result":0.1,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.87,"interpretation":0.0}},{"i":4,"p":0.99,"id":"s4","own":true,"role":"result","text":"We show that joint estimation/prediction based on the reweighted sum-product algorithm substantially 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