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Gaussian processes offer an attractive framework for predictive modeling from longitudinal data, i.e., irregularly sampled, sparse observations from a set of individuals over time. However, such methods have two key shortcomings: (i) They rely on ad hoc heuristics or expensive trial and error to choose the effective kernels, and (ii) They fail to handle multilevel correlation structure in the data. We introduce Longitudinal deep kernel Gaussian process regression (L-DKGPR) to overcome these limitations by fully automating the discovery of complex multilevel correlation structure from longitudinal data. Specifically, L-DKGPR eliminates the need for ad hoc heuristics or trial and error using a novel adaptation of deep kernel learning that combines the expressive power of deep neural networks with the flexibility of non-parametric kernel methods. L-DKGPR effectively learns the multilevel correlation with a novel additive kernel that simultaneously accommodates both time-varying and the time-invariant effects. We derive an efficient algorithm to train L-DKGPR using latent space inducing points and variational inference. Results of extensive experiments on several benchmark data sets demonstrate that L-DKGPR significantly outperforms the state-of-the-art longitudinal data analysis (LDA) methods. 

We consider the problem of learning predictive models from longitudinal data, consisting of irregularly repeated, sparse observations from a set of individuals over time. Such data often exhibit longitudinal correlation (LC) (correlations among observations for each individual over time), cluster correlation (CC) (correlations among individuals that have similar characteristics), or both. These correlations are often accounted for using mixed effects models that include fixed effects and random effects, where the fixed effects capture the regression parameters that are shared by all individuals, whereas random effects capture those parameters that vary across individuals. However, the current state-of-the-art methods are unable to select the most predictive fixed effects and random effects from a large number of variables, while accounting for complex correlation structure in the data and non-linear interactions among the variables. We propose Longitudinal Multi-Level Factorization Machine (LMLFM), to the best of our knowledge, the first model to address these challenges in learning predictive models from longitudinal data. We establish the convergence properties, and analyze the computational complexity, of LMLFM. We present results of experiments with both simulated and real-world longitudinal data which show that LMLFM outperforms the state-of-the-art methods in terms of predictive accuracy, variable selection ability, and scalability to data with large number of variables. The code and supplemental material is available at https://github.com/junjieliang672/LMLFM. 

We consider the problem of learning predictive models from longitudinal data, consisting of irregularly repeated, sparse observations from a set of individuals over time. Such data of- ten exhibit longitudinal correlation (LC) (correlations among observations for each individual over time), cluster correlation (CC) (correlations among individuals that have similar char- acteristics), or both. These correlations are often accounted for using mixed effects models that include fixed effects and random effects, where the fixed effects capture the regression parameters that are shared by all individuals, whereas random effects capture those parameters that vary across individuals. However, the current state-of-the-art methods are unable to se- lect the most predictive fixed effects and random effects from a large number of variables, while accounting for complex cor- relation structure in the data and non-linear interactions among the variables. We propose Longitudinal Multi-Level Factoriza- tion Machine (LMLFM), to the best of our knowledge, the first model to address these challenges in learning predictive mod- els from longitudinal data. We establish the convergence prop- erties, and analyze the computational complexity, of LMLFM. We present results of experiments with both simulated and real-world longitudinal data which show that LMLFM out- performs the state-of-the-art methods in terms of predictive accuracy, variable selection ability, and scalability to data with large number of variables. The code and supplemental material is available at https://github.com/junjieliang672/LMLFM.