Error Analysis Of LUMs Classification Algorithms With Non-i.i.d. Sampling

The error analysis of learning algorithms is one of the main research topics of statistical learning theory.The purpose of this paper is to extend the error analysis of Large-margin unified machines(LUMs)classification algorithms to a more general sampling setting.We remove the assumptions on the independence and identical distribution of sample sequence and study the error analysis of LUMs classification algorithms with non-i.i.d.sampling.Firstly,we provide the error decomposition of the LUMs classification algorithms with non-i.i.d.sampling.The total error is decomposed as drift error,sample error and regularization error.Compared with the error decomposition under i.i.d.sampling,the former has one more drift error caused by different marginal distributions.Then,the drift error is estimated under the condition that the marginal distribution satisfies exponential convergence and the kernel function satisfies certain regularity.We use the independent block technique to deal with the ?-mixing sequence,and introduce a new projection operator to overcome the analysis difficulty caused by the unbounded target function.Based on the above,combining the probability inequality and the covering number techniques,we bound the sample error.Finally,we establish the error analysis for the LUMs classification algorithms,and improve the learning rates by iteration technique.