Imputation estimators for unnormalized models with missing data

Masatoshi Uehara, Takeru Matsuda, Jae Kwang Kim
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:831-841, 2020.

Abstract

Several statistical models are given in the form of unnormalized densities and calculation of the normalization constant is intractable. We propose estimation methods for such unnormalized models with missing data. The key concept is to combine imputation techniques with estimators for unnormalized models including noise contrastive estimation and score matching. Further, we derive asymptotic distributions of the proposed estimators and construct confidence intervals. Simulation results with truncated Gaussian graphical models and the application to real data of wind direction demonstrate that the proposed methods enable statistical inference from missing data properly.

Cite this Paper


BibTeX
@InProceedings{pmlr-v108-uehara20b, title = {Imputation estimators for unnormalized models with missing data}, author = {Uehara, Masatoshi and Matsuda, Takeru and Kim, Jae Kwang}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {831--841}, year = {2020}, editor = {Silvia Chiappa and Roberto Calandra}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/uehara20b/uehara20b.pdf}, url = { http://proceedings.mlr.press/v108/uehara20b.html }, abstract = {Several statistical models are given in the form of unnormalized densities and calculation of the normalization constant is intractable. We propose estimation methods for such unnormalized models with missing data. The key concept is to combine imputation techniques with estimators for unnormalized models including noise contrastive estimation and score matching. Further, we derive asymptotic distributions of the proposed estimators and construct confidence intervals. Simulation results with truncated Gaussian graphical models and the application to real data of wind direction demonstrate that the proposed methods enable statistical inference from missing data properly.} }
Endnote
%0 Conference Paper %T Imputation estimators for unnormalized models with missing data %A Masatoshi Uehara %A Takeru Matsuda %A Jae Kwang Kim %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-uehara20b %I PMLR %P 831--841 %U http://proceedings.mlr.press/v108/uehara20b.html %V 108 %X Several statistical models are given in the form of unnormalized densities and calculation of the normalization constant is intractable. We propose estimation methods for such unnormalized models with missing data. The key concept is to combine imputation techniques with estimators for unnormalized models including noise contrastive estimation and score matching. Further, we derive asymptotic distributions of the proposed estimators and construct confidence intervals. Simulation results with truncated Gaussian graphical models and the application to real data of wind direction demonstrate that the proposed methods enable statistical inference from missing data properly.
APA
Uehara, M., Matsuda, T. & Kim, J.K.. (2020). Imputation estimators for unnormalized models with missing data. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:831-841 Available from http://proceedings.mlr.press/v108/uehara20b.html .

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