Revealing Unobservables by Deep Learning: Generative Element Extraction Networks (GEEN)
This addresses a fundamental challenge in scientific research for fields relying on latent variable models, offering a potentially transformative approach to handling unobserved variables.
The paper tackles the problem of estimating realizations of a latent variable from multiple measurements by proposing a novel method that identifies these realizations under conditional independence assumptions, with simulation results showing high correlation between estimated and true values.
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.