标题： 坐标无关的稀疏充分降维与变量选择 显示英文标题

标题： Coordinate-independent sparse sufficient dimension reduction and variable selection

摘要： 回归中的充分降维（SDR），通过用原始预测变量的最小线性组合来替代它们而不会丢失信息，从而降低维度，在预测变量数量较多时非常有帮助。 标准的SDR方法存在缺陷，因为估计出的线性组合通常包含所有原始预测变量，这使得解释变得困难。 本文提出了一种统一的方法——坐标无关稀疏估计（CISE）——该方法可以同时实现稀疏的充分降维并高效筛选出无关和冗余变量。 从子空间的角度来看，CISE通过引入一个与坐标无关的惩罚项，将其与一系列基于模型和无模型的SDR方法结合在一起。 这导致了一个Grassmann流形优化问题，并提出了一种快速算法。 在适度条件下，基于流形理论和技术，可以证明CISE的表现会像已知真实无关预测变量一样好，这就是所谓的oracle性质。 模拟研究和实际数据示例展示了所提出方法的有效性和效率。 显示英文摘要

摘要： Sufficient dimension reduction (SDR) in regression, which reduces the dimension by replacing original predictors with a minimal set of their linear combinations without loss of information, is very helpful when the number of predictors is large. The standard SDR methods suffer because the estimated linear combinations usually consist of all original predictors, making it difficult to interpret. In this paper, we propose a unified method - coordinate-independent sparse estimation (CISE) - that can simultaneously achieve sparse sufficient dimension reduction and screen out irrelevant and redundant variables efficiently. CISE is subspace oriented in the sense that it incorporates a coordinate-independent penalty term with a broad series of model-based and model-free SDR approaches. This results in a Grassmann manifold optimization problem and a fast algorithm is suggested. Under mild conditions, based on manifold theories and techniques, it can be shown that CISE would perform asymptotically as well as if the true irrelevant predictors were known, which is referred to as the oracle property. Simulation studies and a real-data example demonstrate the effectiveness and efficiency of the proposed approach.