Subject-specific Deep Neural Networks for Count Data with High-cardinality Categorical Features

There is a growing interest in subject-specific predictions using deep neural networks (DNNs) because real-world data often exhibit correlations, which has been typically overlooked in traditional DNN frameworks. In this paper, we propose a novel hierarchical likelihood learning framework for introducing gamma random effects into the Poisson DNN, so as to improve the prediction performance by capturing both nonlinear effects of input variables and subject-specific cluster effects. The proposed method simultaneously yields maximum likelihood estimators for fixed parameters and best unbiased predictors for random effects by optimizing a single objective function. This approach enables a fast end-to-end algorithm for handling clustered count data, which often involve high-cardinality categorical features. Furthermore, state-of-the-art network architectures can be easily implemented into the proposed h-likelihood framework. As an example, we introduce multi-head attention layer and a sparsemax function, which allows feature selection in high-dimensional settings. To enhance practical performance and learning efficiency, we present an adjustment procedure for prediction of random parameters and a method-of-moments estimator for pretraining of variance component. Various experiential studies and real data analyses confirm the advantages of our proposed methods.

Deep Neural Networks for Semiparametric Frailty Models via H-likelihood

For prediction of clustered time-to-event data, we propose a new deep neural network based gamma frailty model (DNN-FM). An advantage of the proposed model is that the joint maximization of the new h-likelihood provides maximum likelihood estimators for fixed parameters and best unbiased predictors for random frailties. Thus, the proposed DNN-FM is trained by using a negative profiled h-likelihood as a loss function, constructed by profiling out the non-parametric baseline hazard. Experimental studies show that the proposed method enhances the prediction performance of the existing methods. A real data analysis shows that the inclusion of subject-specific frailties helps to improve prediction of the DNN based Cox model (DNN-Cox).