Latent variable models are crucial in scientific research, where a key variable, such as effort, ability, and belief, is unobserved in the sample but needs to be identified. This paper proposes a novel method for estimating realizations of a latent variable $X^*$ in a random sample that contains its multiple measurements. With the key assumption that the measurements are independent conditional on $X^*$, we provide sufficient conditions under which realizations of $X^*$ in the sample are locally unique in a class of deviations, which allows us to identify realizations of $X^*$. To the best of our knowledge, this paper is the first to provide such identification in observation. We then use the Kullback-Leibler distance between the two probability densities with and without the conditional independence as the loss function to train a Generative Element Extraction Networks (GEEN) that maps from the observed measurements to realizations of $X^*$ in the sample. The simulation results imply that this proposed estimator works quite well and the estimated values are highly correlated with realizations of $X^*$. Our estimator can be applied to a large class of latent variable models and we expect it will change how people deal with latent variables.
翻译:隐性变量模型在科学研究中至关重要,在科学研究中,一个关键变量,如努力、能力和信念,在抽样中没有观察到,但需要确定。本文件提出一个新的方法,用以估计在含有多种测量结果的随机抽样中潜在变量$X+$的实现情况。根据测量是独立的这一关键假设,我们提供了足够条件,使抽样中X+$的实现在一个偏差类别中具有当地独特性,从而使我们能够确定是否实现了$X+$。根据我们的最佳知识,本文是第一个提供这种观察识别资料的文件。然后,我们用Kullback-Leebeller距离两种概率密度之间和不附带条件独立的数值,作为损失函数来训练一个Generalization Eripticon Networks(GEN),从观测到测量结果到在抽样中实现$X+$的映射值图。模拟结果表明,这一拟议的估算值非常有效,估计值与实现$X+$的实现情况高度相关。我们的估测算器将被用于一个巨大的可变变量。