论文标题
在概率模型的某些局限
On some limitations of probabilistic models for dimension-reduction: Illustration in the case of probabilistic formulations of partial least squares
论文作者
论文摘要
部分最小二乘（PLS）是指旨在识别两组具有最大协方差的组件的一类还原技术，以建模两组观察到的变量$ x \ in \ in \ mathbb {r}^p $ and p $ and $ y \ in \ mathbb in \ mathbb in \ mathbb in \ mathbb {r} $ ge q $ p $ p $ p $，最近已经针对PLS的几种版本提出了概率配方。 Focusing first on the probabilistic formulation of the PLS-SVD proposed by el Bouhaddani et al., we establish that the constraints on their model parameters are too restrictive and define particular distributions for $(x,y)$, under which components with maximal covariance (solutions of PLS-SVD) are also necessarily of respective maximal variances (solutions of principal components analyses of $x$和$ y $）。我们提出了PLS-SVD的替代概率表述，不再限于这些特定分布。然后，我们提出了El Bouhaddani等人原始模型的限制的数值插图。我们还简要讨论了另一个潜在变量模型中的类似局限性，以减少尺寸。
Partial Least Squares (PLS) refer to a class of dimension-reduction techniques aiming at the identification of two sets of components with maximal covariance, to model the relationship between two sets of observed variables $x\in\mathbb{R}^p$ and $y\in\mathbb{R}^q$, with $p\geq 1, q\geq 1$. Probabilistic formulations have recently been proposed for several versions of the PLS. Focusing first on the probabilistic formulation of the PLS-SVD proposed by el Bouhaddani et al., we establish that the constraints on their model parameters are too restrictive and define particular distributions for $(x,y)$, under which components with maximal covariance (solutions of PLS-SVD) are also necessarily of respective maximal variances (solutions of principal components analyses of $x$ and $y$, respectively). We propose an alternative probabilistic formulation of PLS-SVD, no longer restricted to these particular distributions. We then present numerical illustrations of the limitation of the original model of el Bouhaddani et al. We also briefly discuss similar limitations in another latent variable model for dimension-reduction.
