Distribution-free inequalities for the deleted and holdout error estimates | IEEE Journals & Magazine | IEEE Xplore
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Distribution-free inequalities for the deleted and holdout error estimates


Abstract:

In the discrimination problem the random variable\theta, known to take values in{1 ,\ldots ,M}, is estimated from the random vectorXtaking values in{\bfR}^{d}. Ali that i...Show More

Abstract:

In the discrimination problem the random variable\theta, known to take values in{1 ,\ldots ,M}, is estimated from the random vectorXtaking values in{\bfR}^{d}. Ali that is known about the joint distribution of(X,O)is that which can be inferred from a sample(X_{1} , \theta_{1}, \ldots , (X_{n}, \theta_{n})of sizendrawn from that distribution. A discrimination rule is any procedure which determines a decision\hat{\theta}for\thetafromXand(X_{1},\theta_{1}) , \ldots , (X_{n}, \theta_{n}). The rule is calledk-local if the decision\hat{\theta}depends only onXand the pairs(X_{i}, \theta_{i}),for whichX_{i}is one of thekclosest toXfromX_{1} , \ldots ,X_{n}. IfL_{n}denotes the probability of error for ak-local rule given the sample, then estimates\hat{L}_{n}ofL_{n}, are determined for whichP {| \hat{L}_{n} - L_{n} \geq \epsilon} \exp (- Bn), whereAandBare positive constants depending only ond,M, and\epsilon.
Published in: IEEE Transactions on Information Theory ( Volume: 25, Issue: 2, March 1979)
Page(s): 202 - 207
Date of Publication: 31 March 1979

ISSN Information:


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