Yingyao Hu, Yang Liu, Jiaxiong Yao
arXiv 4 Oct 2022 · Statistics — Machine Learning · 2 citations (OpenAlex)
arXiv:2210.01300 · PDF · DOI · OpenAlex · Extracted main text
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.
appendix boundary found by none_found · 100% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Hu, Y.; and Schennach, S. M (2008) Instrumental variable treatment of nonclassical measurement error models self | 0.811 | 4 | 2 | 100% |
| 2 | Kingma, D. P.; and Welling, M (2013) Auto-encoding variational bayes | 0.511 | 2 | 1 | 100% |
| 3 | Yoon, J.; Jordon, J.; and Schaar, M (2018) Gain: Missing data imputation using generative adversarial nets | 0.511 | 2 | 1 | 100% |
| 4 | Aigner, D. J.; Hsiao, C.; Kapteyn, A.; and Wansbeek, T (1984) Latent variable models in econometrics | 0.405 | 1 | 1 | 100% |
| 5 | Belghazi, M. I.; Baratin, A.; Rajeshwar, S.; Ozair, S.; Bengio, Y.;… (2018) Mutual information neural estimation | 0.405 | 1 | 1 | 100% |
| 6 | Bishop, C. M (1998) Latent variable models | 0.405 | 1 | 1 | 100% |
| 7 | Darbellay, G. A.; and Vajda, I (1999) Estimation of the information by an adaptive partitioning of the observation space | 0.405 | 1 | 1 | 100% |
| 8 | Goodfellow, I.; Pouget-Abadie, J.; Mirza, M.; Xu, B.; Warde-Farley,… (2014) Generative adversarial nets | 0.405 | 1 | 1 | 100% |
| 9 | Holston, K.; Laubach, T.; and Williams, J. C (2017) Measuring the natural rate of interest: International trends and determinants | 0.405 | 1 | 1 | 100% |
| 10 | Hu, Y (2017) The econometrics of unobservables: Applications of measurement error models in empirical industrial organization and labor econo… self | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 27 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Identification of Unobservables in Observations | 0.405 | 1 | 1 |