  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), which to the best of our knowledge, is the only method 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 addictive 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.
