摘要翻译:
贝叶斯变量选择在解释变量的数目(x_1,...,x_K)$可能远大于样本量$n$时,在许多应用中取得了很大的经验成功。对于广义线性模型,如果大多数x_j$对响应y$的影响很小,我们证明了用贝叶斯变量选择来减少维数诅咒k\gg n$引起的过拟合是可能的。在这种方法中,一个合适的先验可以用来从许多$X_J$中选择几个来建模$Y$,这样后验就会提出概率密度$P$,在某种意义上,这些概率密度通常接近于真正的密度$P^*$。这种紧密度可以用$P$和$P^*$之间的海林格距离来描述,该距离的幂次非常接近$N^{-1/2}$,这是对应于低维情况的“有限维速率”。这些发现扩展了蒋(西北大学统计学系,技术报告05-02(2005))关于二元分类中贝叶斯变量选择一致性的一些最新工作。
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英文标题:
《Bayesian variable selection for high dimensional generalized linear
models: convergence rates of the fitted densities》
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作者:
Wenxin Jiang
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最新提交年份:
2007
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分类信息:
一级分类:Mathematics 数学
二级分类:Statistics Theory 统计理论
分类描述:Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计:例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类:Statistics 统计学
二级分类:Statistics Theory 统计理论
分类描述:stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近,贝叶斯推论,决策理论,估计,基础,推论,检验。
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英文摘要:
Bayesian variable selection has gained much empirical success recently in a variety of applications when the number $K$ of explanatory variables $(x_1,...,x_K)$ is possibly much larger than the sample size $n$. For generalized linear models, if most of the $x_j$'s have very small effects on the response $y$, we show that it is possible to use Bayesian variable selection to reduce overfitting caused by the curse of dimensionality $K\gg n$. In this approach a suitable prior can be used to choose a few out of the many $x_j$'s to model $y$, so that the posterior will propose probability densities $p$ that are ``often close'' to the true density $p^*$ in some sense. The closeness can be described by a Hellinger distance between $p$ and $p^*$ that scales at a power very close to $n^{-1/2}$, which is the ``finite-dimensional rate'' corresponding to a low-dimensional situation. These findings extend some recent work of Jiang [Technical Report 05-02 (2005) Dept. Statistics, Northwestern Univ.] on consistency of Bayesian variable selection for binary classification.
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PDF链接:
https://arxiv.org/pdf/710.3458