The Na\"ive Bayes has proven to be a tractable and efficient method for
classification in multivariate analysis. However, features are usually
correlated, a fact that violates the Na\"ive Bayes' assumption of conditional
independence, and may deteriorate the method's performance. Moreover, datasets
are often characterized by a large number of features, which may complicate the
interpretation of the results as well as slow down the method's execution.
In this paper we propose a sparse version of the Na\"ive Bayes classifier
that is characterized by three properties. First, the sparsity is achieved
taking into account the correlation structure of the covariates. Second,
different performance measures can be used to guide the selection of features.
Third, performance constraints on groups of higher interest can be included.
Our proposal leads to a smart search, which yields competitive running times,
whereas the flexibility in terms of performance measure for classification is
integrated. Our findings show that, when compared against well-referenced
feature selection approaches, the proposed sparse Na\"ive Bayes obtains
competitive results regarding accuracy, sparsity and running times for balanced
datasets. In the case of datasets with unbalanced (or with different
importance) classes, a better compromise between classification rates for the
different classes is achieved.

我们提出了一种稀疏版本的朴素贝叶斯分类器，考虑到协变量的相关性，可以使用不同的性能度量来选择特征，并且可以包括对高度相关的组的性能约束。研究结果表明，与其他特征选择方法相比，所提出的稀疏朴素贝叶斯分类器在准确性、稀疏性和运行时间方面都具有竞争力。在不平衡数据集或具有不同重要性的类别的情况下，可以实现更好的分类率平衡。

朴素贝叶斯分类的变量选择

Variable selection for Naïve Bayes classification

We consider processing an n x d matrix A in a stream with row-wise updates
according to a recent algorithm called Frequent Directions (Liberty, KDD 2013).
This algorithm maintains an l x d matrix Q deterministically, processing each
row in O(d l^2) time; the processing time can be decreased to O(d l) with a
slight modification in the algorithm and a constant increase in space. We show
that if one sets l = k+ k/eps and returns Q_k, a k x d matrix that is the best
rank k approximation to Q, then we achieve the following properties: ||A -
A_k||_F^2 <= ||A||_F^2 - ||Q_k||_F^2 <= (1+eps) ||A - A_k||_F^2 and where
pi_{Q_k}(A) is the projection of A onto the rowspace of Q_k then ||A -
pi_{Q_k}(A)||_F^2 <= (1+eps) ||A - A_k||_F^2.
We also show that Frequent Directions cannot be adapted to a sparse version
in an obvious way that retains the l original rows of the matrix, as opposed to
a linear combination or sketch of the rows.

使用 Frequent Directions 算法处理 n x d 矩阵，通过确定性地维护一个 l x d 矩阵 Q 来处理每一行，从而获得一个时间复杂度为 O (d l^2) 的方法，其中 l=k+k/eps 返回最佳秩 k 逼近，同时证明了无法将该算法明显地适应于保留矩阵的原始行的稀疏版本。