Gaussian processes (GPs) provide a powerful non-parametric framework for reasoning over functions. Despite appealing theory, its superlinear computational and memory complexities have presented a long-standing challenge. State-of-the-art sparse variational inference methods trade modeling accuracy against complexity. However, the complexities of these methods still scale superlinearly in the number of basis functions, implying that that sparse GP methods are able to learn from large datasets only when a small model is used. Recently, a decoupled approach was proposed that removes the unnecessary coupling between the complexities of modeling the mean and the covariance functions of a GP.

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We study the problem of change-point detection and localisation for functional data sequentially observed on a generald-dimensional space, where we allow thefunctional curvestobeeither sparsely ordensely sampled.

Panel count data describes aggregated counts of recurrent events observed at discrete time points. To understand dynamics of health behaviors and predict future negative events, the field of quantitative behavioral research has evolved toincreasingly rely upon panel count data collected viamultiple self reports, for example, about frequencies ofsmoking using in-the-moment surveysonmobile devices. However, missing reports are common and present a major barrier to downstream statistical learning.

Existing approaches to inference in DGP models assume approximate posteriors that force independence between the layers, and do not work well in practice.

Gaussian processes (GPs) provide a powerful non-parametric framework for reasoning over functions. Despite appealing theory, its superlinear computational and memory complexities have presented a long-standing challenge. State-of-the-art sparse variational inference methods trade modeling accuracy against complexity. However, the complexities of these methods still scale superlinearly in the number of basis functions, implying that that sparse GP methods are able to learn from large datasets only when a small model is used. Recently, a decoupled approach was proposed that removes the unnecessary coupling between the complexities of modeling the mean and the covariance functions of a GP.