Some theory for Fisher's linear discriminant function, 'naive Bayes', and some alternatives when there are many more variables than observations
Some theory for Fisher's linear discriminant function, 'naive Bayes', and some alternatives when there are many more variables than observations
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DOI：
10.3150/bj/1106314847
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发表时间：
2004-12-01
期刊：
影响因子：
1.5
通讯作者：
Levina, E
中科院分区：
文献类型：
--
作者：
Bickel, PJ;Levina, E
在区分两个正态总体的经典问题中，我们证明了假设独立协变量较大的朴素贝叶斯分类器在较宽的条件下，当变量个数增长快于观测个数时，执行Fisher线性判别规则。我们还引入了一类介于独立和任意依赖之间的规则。这些规则被证明实现了高斯“有色噪声”模型的贝叶斯一致性，并适应了收敛速度的频谱，我们猜测这是极小极大。
We show that the 'naive Bayes' classifier which assumes independent covariates greaty ourperforms the Fisher linear discriminant rule under broad conditions when the number of variable grows,; faster than the number of observations, in the classical problem of discriminating between two normal populations. We also introduce a class of rules spanning the range between independence and arbitrary dependence. These rules are shown to achieve Bayes consistency for the Gaussian 'coloured noise' model and to adapt to a spectrum of convergence rates, which we Conjecture to be minimax.