Cellwise Robust Twoblock (CRTB) is introduced, the first cellwise robust method for simultaneous dimension reduction of multivariate predictor and response blocks, in both a dense and a sparse variable-selecting variant. Classical robust methods protect against casewise outliers by downweighting or removing entire observations, a strategy that becomes inefficient -- and eventually breaks down -- when contamination is scattered across individual cells rather than concentrated in whole rows. CRTB combines a column-wise pre-filter for cellwise outlier detection with model-based imputation of flagged cells inside an iteratively reweighted M-estimation loop, retaining the clean cells of partially contaminated rows instead of discarding the observation. An efficient algorithm is provided that uses the classical twoblock SVD as a warm start and converges in a handful of IRLS iterations at a moderate computational cost. The method resists settings where more than $50\%$ of rows contain contaminated cells while retaining comparable efficiency on clean data. A simulation study confirms these properties and shows that CRTB additionally recovers the underlying cellwise outlier pattern with high fidelity and, in the sparse setting, the correct set of informative variables. Two compelling examples illustrate CRTB's practical utility. In each of these, CRTB is shown to be conducive to results that are highly interpretable in the respective domains in the presence of cellwise outliers. As a by-product, the corresponding cells are identified with high fidelity.

翻译：本文提出了一种名为 Cellwise Robust Twoblock（CRTB）的方法，这是首个能够同时处理多变量预测变量组与响应变量组两类数据块维度约简的逐单元格稳健方法，同时包含稠密与稀疏变量选择两种变体。传统稳健方法通过降低或剔除整条观测的权重来防御离群个案，这种策略在污染分散于单个单元格而非集中于整行时效率低下，并最终导致失效。CRTB 将列向预过滤器（用于检测逐单元格离群点）与模型驱动的标记单元格填补技术相结合，嵌入迭代重加权 M 估计框架中，保留部分污染行的清洁单元格而非舍弃整条观测。该方法采用经典的双块奇异值分解作为热启动，通过少量迭代重加权最小二乘迭代即可收敛，计算成本适中。当超过 50% 的行包含污染单元格时，该方法仍能保持稳健性，同时在清洁数据上维持相当效率。模拟研究验证了这些性质，并表明 CRTB 能够高保真地恢复潜在逐单元格离群模式，且在稀疏设置下正确识别出信息变量集合。两个具有说服力的实例展示了 CRTB 的实际应用价值。在存在逐单元格离群点时，CRTB 有助于产生在各自领域高度可解释的结果。作为副产品，相应单元格也能被高保真地识别。