منابع مشابه
Weak Convergence of Probability Measures
This text contains my lecture notes for the graduate course “Weak Convergence” given in September-October 2013 and then in March-May 2015. The course is based on the book Convergence of Probability Measures by Patrick Billingsley, partially covering Chapters 1-3, 5-9, 12-14, 16, as well as appendices. In this text the formula label (∗) operates locally. The visible theorem labels often show the...
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The first part of the paper deals with general features of weak star convergence from a topological point of view. We present basic facts about weak and weak star topologies, dual spaces and representations of linear functionals as Radon measures. A special attention is payed to finitely additive measures and some results regarding the Baire sets. We prove that in a wide class of topological sp...
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We consider probability measures µ n , µ on a metric space X such that µ n weakly converges to µ. The following convergence lim n→∞ X f n (x)µ n (dx) = X f (x)µ(dx) is proved under some restrictions on real valued functions f n and f which are measurable, not necessarily continuous nor bounded.
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Many classification algorithms produce confidence measures in the form of conditional probability of labels given the features of the target instance. It is desirable to be make these confidence measures calibrated or consistent, in the sense that they correctly capture the belief of the algorithm in the label output. For instance, if the algorithm outputs a label with confidence measure p for ...
متن کاملWeak Convergence and Uniform Normalization in Infinitary Rewriting
We study infinitary term rewriting systems containing finitely many rules. For these, we show that if a weakly convergent reduction is not strongly convergent, it contains a term that reduces to itself in one step (but the step itself need not be part of the reduction). Using this result, we prove the starkly surprising result that for any orthogonal system with finitely many rules, the system ...
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ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 1979
ISSN: 0047-259X
DOI: 10.1016/0047-259x(79)90071-x