arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2103.13686cs.LGcs.AIstat.ML
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鲁棒子群发现

Robust subgroup discovery

CWI(荷兰国家数学与计算机科学研究所);LIACS(莱顿大学高级计算机科学研究所)

Hugo Manuel Proença, Peter Grünwald, Thomas Bäck, Matthijs van Leeuwen

摘要:

我们介绍了鲁棒子群发现的问题,即,找到子集的一组可解释的描述,所述子集1)相对于一个或多个目标属性突出,2)在统计上是稳健的,以及3)非冗余的。已经进行了许多尝试,挖掘本地强大的子组或解决模式爆炸,但我们是第一个从全球建模的角度同时解决这两个挑战的。首先,我们用公式表示子组列表的广义模型类,即,子组的有序集合,用于可以由名义或数字变量组成的单变量和多变量目标,包括其定义中的传统的前1个子组发现。这种新的模型类使我们能够使用最小描述长度(MDL)原则,在那里我们诉诸最佳归一化最大似然和贝叶斯编码的名义和数字目标,分别正式的最佳鲁棒子群发现的问题。其次,寻找最优子群列表是NP难的。因此,我们提出了SSD++,一个贪婪的启发式,找到良好的子组列表,并保证最重要的子组根据MDL标准被添加到每次迭代。事实上,贪婪的增益被证明是等价于贝叶斯单样本比例,多项式,或t检验之间的子组和数据集的边缘目标分布加上多个假设检验惩罚。此外,我们在54个数据集上的经验表明,SSD++在质量、对未知数据的概括和子组列表大小方面优于以前的子组发现方法。

英文摘要:

We introduce the problem of robust subgroup discovery, i.e., finding a set of interpretable descriptions of subsets that 1) stand out with respect to one or more target attributes, 2) are statistically robust, and 3) non-redundant. Many attempts have been made to mine either locally robust subgroups or to tackle the pattern explosion, but we are the first to address both challenges at the same time from a global modelling perspective. First, we formulate the broad model class of subgroup lists, i.e., ordered sets of subgroups, for univariate and multivariate targets that can consist of nominal or numeric variables, including traditional top-1 subgroup discovery in its definition. This novel model class allows us to formalise the problem of optimal robust subgroup discovery using the Minimum Description Length (MDL) principle, where we resort to optimal Normalised Maximum Likelihood and Bayesian encodings for nominal and numeric targets, respectively. Second, finding optimal subgroup lists is NP-hard. Therefore, we propose SSD++, a greedy heuristic that finds good subgroup lists and guarantees that the most significant subgroup found according to the MDL criterion is added in each iteration. In fact, the greedy gain is shown to be equivalent to a Bayesian one-sample proportion, multinomial, or t-test between the subgroup and dataset marginal target distributions plus a multiple hypothesis testing penalty. Furthermore, we empirically show on 54 datasets that SSD++ outperforms previous subgroup discovery methods in terms of quality, generalisation on unseen data, and subgroup list size.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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