论文标题
学习与精细控制内核的高阶功能互动
Learning High Order Feature Interactions with Fine Control Kernels
论文作者
论文摘要
我们提供了一种学习稀疏统计模型的方法，该模型用作基础原子集合集合的所有可能的乘法相互作用。尽管所得的优化问题是指数尺寸的，但我们的方法论导致算法通常可以准确地解决这些问题或基于组合高度相关的特征提供近似解决方案。我们还引入了一种算法范式，即精细的控制核框架，之所以命名是因为它基于Fenchel二元性，并让人联想到内核方法。它的理论是针对大型稀疏学习问题量身定制的，它导致了互动的有效特征筛选规则。这些规则的灵感来自APRIORI算法用于市场篮分析的算法，该算法也属于精细控制内核的权限，并且可以应用于多个学习问题，包括套索和稀疏矩阵估计。生物医学数据集的实验证明了我们方法学在得出有效产生具有最新准确性且可解释的相互作用模型的算法中的功效。
We provide a methodology for learning sparse statistical models that use as features all possible multiplicative interactions among an underlying atomic set of features. While the resulting optimization problems are exponentially sized, our methodology leads to algorithms that can often solve these problems exactly or provide approximate solutions based on combining highly correlated features. We also introduce an algorithmic paradigm, the Fine Control Kernel framework, so named because it is based on Fenchel Duality and is reminiscent of kernel methods. Its theory is tailored to large sparse learning problems, and it leads to efficient feature screening rules for interactions. These rules are inspired by the Apriori algorithm for market basket analysis -- which also falls under the purview of Fine Control Kernels, and can be applied to a plurality of learning problems including the Lasso and sparse matrix estimation. Experiments on biomedical datasets demonstrate the efficacy of our methodology in deriving algorithms that efficiently produce interactions models which achieve state-of-the-art accuracy and are interpretable.
