基于函数集信息量的模型选择研究

盛守照; 王道波; 王志胜; 黄向华

基于函数集信息量的模型选择研究

计量
- 文章访问数: 2333
- HTML全文浏览量: 83
- PDF下载量: 665
- 被引次数: 0
出版历程
- 收稿日期: 2003-12-09
- 修回日期: 2004-03-26
- 刊出日期: 2005-04-19

Research on Model Selection Based on Function Set Information Quantity

摘要

摘要: 提出了子空间信息量(SIQ)和函数集信息量(FSIQ)概念，详细讨论了基于函数集信息量的模型选择问题，给出了有限含噪声样本下模型选择的近似解决方法，很好地克服了模型选择过程中普遍存在的欠学习和过学习问题，大大提高了预测模型的泛化性能，在此基础上提出了一种可行的次优模型选择算法。最后通过具体实例验证了上述方法的可行性和优越性。
- 子空间信息量;函数集信息量;模型选择;统计学习理论
Abstract: The concepts of the Subspace Information Quantity(SIQ) and Function Set Information Quantity(FSIQ) are presented; Then the problem of model selection based on FSIQ are discussed explicitly, and the approximate method of model selection based on limited samples with white noise is proposed, which resolves the problem of underletting and overfitting of model selection and improves the generalization of predict model well. A new suboptimal algorithm for model selection is given, and its reliability and advantage are illustrated through concrete test.

HTML全文

参考文献(1)

张学工.关于统计学习理论与支持向量机.自动化学报,2000,26(1):32-42.[2]Sugiyama M, Ogawa H. Subspace information criterion for model selection[J].Neural Computation.2001, 13(8):1863-[3]Stolke A. Bayesian learning of probabilistic language models.[Ph.D. Dissertation], University of California, Berkeley, 1994.[4]Hemant Ishwaran, Lancelot F, Jiayang Sun. Bayesian model selection in finite mixtures by marginal density decompositions[J].Journal of the American Statistical Association.2001, 96(456):1316-[5]Cherkassky V, Shao X, Mulier F M, Vapnik V N. Model complexity control for regression using VC generalization bounds[J].IEEE Trans. on Neural Networks.1999, 10(5):1075-[6]Barron A R, Cover T M. Minimum complexity density estimation[J].IEEE Trans. onInformation Theory.1991, 37(4):1034-[7]Yamanishi K. A decision-theoretic extension of stochastic complexity and its application to learning[J].IEEE Trans. on Information Theory.1998, 44(4):1424-[8]Wood S N. Modelling and smoothing parameter estimation with multiple quadratic penalties[J].J. Royel Statist. Soc. B.2000, 62(1):413-[9]Chapelle O, Vapnik V N, Bengio Y. Model selection for small-sample regression[J].Machine Learning Journal.2002, 48(1):9-[10]Hurvich C M, Tsai C L. Regression and time series model selection in small samples[J].Biometrika.1989, 76(13):297-[11]Bousquet O, Elisseeff A. Stability and generalization. Journal of Machine Learning Research 2, 2002:499 - 526.[12]Konishi S, Kitagawa G. Generalized information criterion in model selection[J].Biometrika.1996, 83(4):875-[13]Akaike H. A new look at the statistical model identification. IEEE Trans. on Automatic Control, 1974, AC-19(6): 716 - 723.[14]Hurvich C M, Tsai C L. Bias of the corrected AIC criterion for under-fitted regression and time series models. Biometrika, 1991,78(2): 499 - 509.[15]Murata N, Yoshizawa S, Amari S. Network information criterion-determining the number of hidden units for an artificial neural network model[J].IEEE Trans. on Neural Networks.1994,5(6):865-[16]Shibata R. Bootstrap estimate of Kullback-Leibler information for model selection. Statistica Sinica, 1997, 7(2): 375 - 394.

施引文献

资源附件(0)

访问统计