We study the problem of inference (estimation and uncertainty quantification problems) on the unknown parameter in the biclustering model by using the penalization method. The underlying biclustering structure is that the high-dimensional parameter consists of a few blocks of equal coordinates. The quality of the inference procedures is measured by the local quantity, the oracle rate, which is the best trade-off between the approximation error by a biclustering structure and the complexity of that approximating biclustering structure. The approach is also robust in that the additive errors are assumed to satisfy only certain mild condition (allowing non-iid errors with unknown joint distribution). By using the penalization method, we construct a confidence set and establish its local (oracle) optimality. Interestingly, as we demonstrate, there is (almost) no deceptiveness issue for the uncertainty quantification problem in the biclustering model. Adaptive minimax results for the biclustering, stochastic block model (with implications for network modeling) and graphon scales follow from our local results.

中文翻译：

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模型建立的惩罚局部推理方法。

我们利用惩罚方法研究了二类聚类模型中未知参数的推断问题（估计和不确定性量化问题）。基本的双簇结构是高维参数由几个相等坐标的块组成。推理过程的质量由本地数量（即甲骨文速率）度量，这是在双聚类结构的近似误差与该近似双聚类结构的复杂度之间的最佳折衷。该方法也很健壮假定附加误差仅满足某些温和条件（允许关节分布未知的非空误差）。通过使用惩罚方法，我们构造了一个置信集并建立了其局部（oracle）最优性。有趣的是，正如我们所展示的，在二类聚类模型中，不确定性量化问题几乎没有欺骗性问题。对于双簇，随机块模型（对网络建模有影响）和graphon标度的自适应minimax结果来自我们的本地结果。