Stanford Statistics 311/electrical Engineering 377
نویسنده
چکیده
where f : R+ → R is a convex function satisfying f(1) = 0. If f is not linear, then Df (P ||Q) > 0 unless P = Q. b. Focusing on binary classification case, let us consider some example risks and see what connections they have to f -divergences. (Recall we have X ∈ X and Y ∈ {−1, 1} we would like to classify.) 1. We require a few definitions to understand the performance of different classification strategies. In particular, we consider the difference between the risk possible when we see a point to classify and when we do not. 2. The prior risk is the risk attainable without seeing x, we have for a fixed sign α ∈ R the definition Rprior(α) := P (Y = 1)1 {α ≤ 0}+ P (Y = −1)1 {α ≥ 0} , (11.1.1)
منابع مشابه
Correction to 'Minimum Complexity Density Estimation'
Manuscript submitted July 1991. A. R. Barron is with the Department of Statistics and the Department of Electrical and Computer Engineering, University of Illinois, 101 Illini Hall, 725 S. Wright Street, Champaign, IL. 91820. T. M. Cover is with the Departments of Electrical Engineering and Statistics, Durand, Room 121, Stanford University, Stanford, CA 94305. IEEE Log Number 9103053. ‘A. R. Ba...
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Manuscript received November 28, 1978; revised February 28, 1980. This work was supported in part by the National Science Foundation under Grant ENG 76-23334, in part by the Stanford Research Institute under International Contract D/&C-15-C-0187, and in part by the Joint Scientific Enaineerina Program under Contracts NO001475-C-0601 and F44620-76-C&01. This paper was presented at the 1979 IEEE ...
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