Revealing Unobservables by Deep Learning: Generative Element Extraction Networks (GEEN)

• URL: http://arxiv.org/abs/2210.01300v1
• Date: Tue, 4 Oct 2022 01:09:05 GMT
• Title: Revealing Unobservables by Deep Learning: Generative Element Extraction Networks (GEEN)
• Authors: Yingyao Hu and Yang Liu and Jiaxiong Yao
• Abstract summary: This paper proposes a novel method for estimating realizations of a latent variable $X*$ in a random sample. To the best of our knowledge, this paper is the first to provide such identification in observation.
• Score: 5.3028918247347585
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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