H-Likelihood Approach to Deep Neural Networks with Temporal-Spatial Random Effects for High-Cardinality Categorical Features
Jul 24, 2023
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Hangbin Lee
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Youngjo Lee
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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 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 give approximate maximum likelihood estimators (MLEs) for correlated data, but they cannot provide exact MLEs due to the large size of data.We propose a new hierarchical likelihood approach to DNNs with correlated random effects for clustered data.Joint optimization of the negative h-likelihood loss can provide exact MLEs for both mean and dispersion parameters and best linear unbiased predictors for the random effects.Furthermore, the hierarchical likelihood allows a computable procedure for restricted maximum likelihood estimators of dispersion parameters.The proposed two-step algorithm allows online learning for the neural networks, whereas the integrated likelihood cannot decompose like a widely-used loss function in DNNs.Advantages of the proposed h-likelihood approach are illustrated by numerical studies and real data analyses.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 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 give approximate maximum likelihood estimators (MLEs) for correlated data, but they cannot provide exact MLEs due to the large size of data.W…
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