The Dynamical Gaussian Process Latent Variable Model in the Longitudinal Scenario

A BSTRACT The Dynamical Gaussian Process Latent V ariable Models provide an elegant nonparametric framework for learning the low dimensional representations of the high-dimensional time-series. Real world observational studies, however, are often ill-conditioned: the observations can be noisy, not assuming the luxury of relatively complete and equally spaced like those in time series. Such conditions make it difficult to learn reasonable representations in the high dimensional longitudinal data set by way of Gaussian Process Latent V ariable Model as well as other dimensionality reduction procedures. In this study, we approach the inference of Gaussian Process Dynamical Systems in Longitudinal scenario by augmenting the bound in the variational approximation to include systematic samples of the unseen observations. We demonstrate the usefulness of this approach on synthetic as well as the human motion capture data set. 1 I NTRODUCTION While it isn't trivial to find an unified definition of multivariate longitudinal data; the one definition being alluded to in Pullenayegum & Lim (2016) is the type of data being discussed in this work. Longitudinal designs track a repeated set of variables in experimental subjects over periods of time; however, unlike time series, which are often characterized by regular intervals of n-dimensional observations, longitudinal setups present inconsistent sampling frequencies and only a small subset of variables may be observed at any given time.