Beyond Trees：稀疏成对相似度分类
Beyond Trees: Classification with Sparse Pairwise Dependencies
摘要：
几种分类方法假设底层分布遵循树形结构的图形模型。事实上，树捕获变量对之间的统计依赖性，这对于实现低分类错误可能至关重要。所得分类器在对应于树边缘的对数变换的单变量和双变量密度中是线性的。然而，在实践中，观察到的数据可能无法很好地用树来近似。然而，出于精确分类的成对依赖关系的重要性，在这里，我们建议通过单变量和双变量对数变换密度的稀疏线性组合来近似最优决策边界。我们所提出的方法是半参数的性质：我们非参数估计的单变量和双变量密度，删除几乎独立使用希尔伯特-施密特独立性标准的变量对，并最终构建一个线性SVM上保留的对数转换密度。我们证明使用合成和真实的数据，我们得到的分类，表示SLB（稀疏对数双变量密度），是有竞争力的流行的分类方法。
英文摘要：
Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attain low classification errors. The resulting classifier is linear in the log-transformed univariate and bivariate densities that correspond to the tree edges. In practice, however, observed data may not be well approximated by trees. Yet, motivated by the importance of pairwise dependencies for accurate classification, here we propose to approximate the optimal decision boundary by a sparse linear combination of the univariate and bivariate log-transformed densities. Our proposed approach is semi-parametric in nature: we non-parametrically estimate the univariate and bivariate densities, remove pairs of variables that are nearly independent using the Hilbert-Schmidt independence criteria, and finally construct a linear SVM on the retained log-transformed densities. We demonstrate using both synthetic and real data that our resulting classifier, denoted SLB (Sparse Log-Bivariate density), is competitive with popular classification methods.
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