Nowadays, data analysis applied to high dimension has arisen. The edification of high-dimensional data can be achieved by the gathering of different independent data. However, each independent set can introduce its own bias. We can cope with this bias introducing the observation set structure into our model. The goal of this article is to build theoretical background for the dimension reduction method sparse Partial Least Square (sPLS) in the context of data presenting such an observation set structure. The innovation consists in building different sPLS models and linking them through a common-Lasso penalization. This theory could be applied to any field, where observation present this kind of structure and, therefore, improve the sPLS in domains, where it is competitive. Furthermore, it can be extended to the particular case, where variables can be gathered in given a priori groups, where sPLS is defined as a sparse group Partial Least Square.

中文翻译：

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罚偏最小二乘应用于结构化数据

如今，已经出现了应用于高维的数据分析。高维数据的启发可以通过收集不同的独立数据来实现。但是，每个独立的集合都会引入自己的偏差。我们可以应对这种偏见，将观察集结构引入我们的模型。本文的目的是在数据表示这种观察集结构的背景下，为降维方法稀疏偏最小二乘（sPLS）建立理论背景。创新之处在于构建不同的sPLS模型，并通过通用套索惩罚将它们链接起来。该理论可以应用于观察表明这种结构的任何领域，因此可以改善竞争激烈的领域中的sPLS。此外，它可以扩展到特定情况，