论文标题
潜在模型的选择性推断
Selective Inference for Latent Block Models
论文作者
论文摘要
潜在块模型中的模型选择是统计领域的一项具有挑战性但重要的任务。具体而言，当通过将特定的聚类算法应用于有限尺寸矩阵获得的块结构上构建测试时，会遇到一个重大挑战。在这种情况下，考虑块结构中的选择性偏差至关重要，也就是说，基于群集算法的某些标准，从所有可能的群集成员中选择了块结构。为了解决这个问题，本研究为潜在块模型提供了选择性推理方法。具体而言，我们对潜在块模型的一组行和列群集成员构建统计测试，该模型由平方残基最小化算法给出。提出的测试本质上包括，因此也可以用作行和列群号集的测试。我们还基于模拟退火提出了一个近似版本的测试版本，以避免在搜索最佳块结构时进行组合爆炸。结果表明，与未考虑选择性偏差的天真测试相比，提出的精确测试和近似测试有效地工作。
Model selection in latent block models has been a challenging but important task in the field of statistics. Specifically, a major challenge is encountered when constructing a test on a block structure obtained by applying a specific clustering algorithm to a finite size matrix. In this case, it becomes crucial to consider the selective bias in the block structure, that is, the block structure is selected from all the possible cluster memberships based on some criterion by the clustering algorithm. To cope with this problem, this study provides a selective inference method for latent block models. Specifically, we construct a statistical test on a set of row and column cluster memberships of a latent block model, which is given by a squared residue minimization algorithm. The proposed test, by its nature, includes and thus can also be used as the test on the set of row and column cluster numbers. We also propose an approximated version of the test based on simulated annealing to avoid combinatorial explosion in searching the optimal block structure. The results show that the proposed exact and approximated tests work effectively, compared to the naive test that did not take the selective bias into account.
