值得信赖的伙伴：控制布尔矩阵分解中的错误发现率
The Trustworthy Pal: Controlling the False Discovery Rate in Boolean Matrix Factorization
摘要：
布尔矩阵分解（BMF）是一种流行的和强大的技术，用于从数据中推断知识。挖掘结果是两个矩阵的布尔乘积，近似于输入数据集。布尔积是秩为1的二进制矩阵的析取，每个矩阵描述一组样本的特征关系，称为模式。然而，不能保证任何返回的模式实际上不是由噪声引起的，即，是错误的发现。在本文中，我们提出并讨论了在无监督BMF设置的错误发现率的使用。我们证明了两个边界的概率，发现模式是随机Bernoulli分布的噪声。每一个边界利用了一个特定的属性的分解，最大限度地减少近似误差-产生新的见解布尔矩阵分解的最小化。这导致了改进的BMF算法，取代启发式排名选择技术与理论上良好的基础上的方法。我们的实证表明，这两个界限提供了良好的结果，在各种实际设置。
英文摘要：
Boolean matrix factorization (BMF) is a popular and powerful technique for inferring knowledge from data. The mining result is the Boolean product of two matrices, approximating the input dataset. The Boolean product is a disjunction of rank-1 binary matrices, each describing a feature-relation, called pattern, for a group of samples. Yet, there are no guarantees that any of the returned patterns do not actually arise from noise, i.e., are false discoveries. In this paper, we propose and discuss the usage of the false discovery rate in the unsupervised BMF setting. We prove two bounds on the probability that a found pattern is constituted of random Bernoulli-distributed noise. Each bound exploits a specific property of the factorization which minimizes the approximation error---yielding new insights on the minimizers of Boolean matrix factorization. This leads to improved BMF algorithms by replacing heuristic rank selection techniques with a theoretically well-based approach. Our empirical demonstration shows that both bounds deliver excellent results in various practical settings.
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。
