Learning from Heterogeneous Data with Deep Gaussian Processes

Deep Gaussian processes (DGPs) are deep models represented by layers of Gaussian processes (GPs). They are flexible Bayesian models capable of capturing highly nonlinear functions while providing well-calibrated uncertainties of the made predictions. Despite these strengths, DGPs encounter difficulties with real-world applications involving heterogeneous datasets and missing values. In this paper, we propose a two-stage framework for DGPs that leverages all available data in such settings. Our inference is performed within a scalable stochastic variational framework, where the variational posterior distributions are reparameterized through sparse GPs. We derive a formulation of the variational lower bound, effectively handling heterogeneous data. Further, through our inference method, we demonstrate the effective use of the GP framework on heterogeneous data. We evaluate our method on a dataset generated by a novel psychosocial screening tool called PROMOTE, which was designed to acquire data for predicting adverse perinatal outcomes and maternal mental health morbidities. Our experimental evaluation of the dataset indicates the effectiveness of our inference framework on various important learning tasks. We demonstrate the model's performance by benchmarking against existing models for high-dimensional heterogeneous data examples.