H-Likelihood Approach to Deep Neural Networks with Temporal-Spatial Random Effects for High-Cardinality Categorical Features

Hangbin Lee, Youngjo Lee
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:18974-18987, 2023.

Abstract

Deep Neural Networks (DNNs) are one of the most powerful tools for prediction, but many of them implicitly assume that the data are statistically independent. However, in the real world, it is common for large-scale data to be clustered with temporal-spatial correlation structures. Variational approaches and integrated likelihood approaches have been proposed to obtain approximate maximum likelihood estimators (MLEs) for correlated data. However, due to the large size of data, they cannot provide exact MLEs. In this study, we propose a new hierarchical likelihood approach to DNNs with correlated random effects for clustered data. By jointly optimizing the the negative h-likelihood loss, we can provide exact MLEs for both mean and dispersion parameters, as well as the best linear unbiased predictors for the random effects. Moreover, the hierarchical likelihood allows a computable procedure for restricted maximum likelihood estimators of dispersion parameters. The proposed two-step algorithm enables online learning for the neural networks, whereas the integrated likelihood cannot decompose like a widely-used loss function in DNNs. The proposed h-likelihood approach offers several advantages, which we demonstrate through numerical studies and real data analyses.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-lee23k, title = {H-Likelihood Approach to Deep Neural Networks with Temporal-Spatial Random Effects for High-Cardinality Categorical Features}, author = {Lee, Hangbin and Lee, Youngjo}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {18974--18987}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/lee23k/lee23k.pdf}, url = {https://proceedings.mlr.press/v202/lee23k.html}, abstract = {Deep Neural Networks (DNNs) are one of the most powerful tools for prediction, but many of them implicitly assume that the data are statistically independent. However, in the real world, it is common for large-scale data to be clustered with temporal-spatial correlation structures. Variational approaches and integrated likelihood approaches have been proposed to obtain approximate maximum likelihood estimators (MLEs) for correlated data. However, due to the large size of data, they cannot provide exact MLEs. In this study, we propose a new hierarchical likelihood approach to DNNs with correlated random effects for clustered data. By jointly optimizing the the negative h-likelihood loss, we can provide exact MLEs for both mean and dispersion parameters, as well as the best linear unbiased predictors for the random effects. Moreover, the hierarchical likelihood allows a computable procedure for restricted maximum likelihood estimators of dispersion parameters. The proposed two-step algorithm enables online learning for the neural networks, whereas the integrated likelihood cannot decompose like a widely-used loss function in DNNs. The proposed h-likelihood approach offers several advantages, which we demonstrate through numerical studies and real data analyses.} }
Endnote
%0 Conference Paper %T H-Likelihood Approach to Deep Neural Networks with Temporal-Spatial Random Effects for High-Cardinality Categorical Features %A Hangbin Lee %A Youngjo Lee %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-lee23k %I PMLR %P 18974--18987 %U https://proceedings.mlr.press/v202/lee23k.html %V 202 %X Deep Neural Networks (DNNs) are one of the most powerful tools for prediction, but many of them implicitly assume that the data are statistically independent. However, in the real world, it is common for large-scale data to be clustered with temporal-spatial correlation structures. Variational approaches and integrated likelihood approaches have been proposed to obtain approximate maximum likelihood estimators (MLEs) for correlated data. However, due to the large size of data, they cannot provide exact MLEs. In this study, we propose a new hierarchical likelihood approach to DNNs with correlated random effects for clustered data. By jointly optimizing the the negative h-likelihood loss, we can provide exact MLEs for both mean and dispersion parameters, as well as the best linear unbiased predictors for the random effects. Moreover, the hierarchical likelihood allows a computable procedure for restricted maximum likelihood estimators of dispersion parameters. The proposed two-step algorithm enables online learning for the neural networks, whereas the integrated likelihood cannot decompose like a widely-used loss function in DNNs. The proposed h-likelihood approach offers several advantages, which we demonstrate through numerical studies and real data analyses.
APA
Lee, H. & Lee, Y.. (2023). H-Likelihood Approach to Deep Neural Networks with Temporal-Spatial Random Effects for High-Cardinality Categorical Features. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:18974-18987 Available from https://proceedings.mlr.press/v202/lee23k.html.

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